TIFR Previous Year's Questions PDF

1 TIFR Previous Year's Questions 1. A quantity of water is completelyconverted into steam by boiling.[GATE 1991] (a) This is a seoand order phase transition (b) At the boiling point, the chemical potential in the vapour phase is less than that in the liquid pha...

1 TIFR Previous Year's Questions 1. A quantity of water is completelyconverted into steam by boiling.[GATE 1991] (a) This is a seoand order phase transition (b) At the boiling point, the chemical potential in the vapour phase is less than that in the liquid phase (c) The boiling temperature would increase if the boiling were done under increased pressure (d) The entropy of the steam is greater than that of the water 2. The ratio J C p / Cv of H 2 gas is 7/5 at room temperature, and 5/3 at low temperatures (around 50 K). The reason for this change is [GATE 1992] (a) Dissociation of H 2 molecules (b) Suppression of rotational degrees of freedom (c) Formation for random clusters of molecules (d) Liquefaction of the gas 3. If v , v p and vrms denote the average, most probable, and root mean square values respectively of the molecular speeds of a oat room temperature being Maxwellian velocity distribution, then [GATE 1994] (a) vrms  v  v p (b) vrms  v p  v (c) v  vrms  v p (d) v p  v  vrms 4. For an isolated thermodynamical system p, V, T, U, S. and F represent the pressure, volume, temperature, internal energy, entropy; and free energy respectively. Then the following relation is true [GATE 1994] § wF · § wF · § wU · § wU · (a) ¨ wT ¸ S (b) ¨ wT ¸ S (c) ¨ wT ¸ T (d) ¨ wV ¸ P © ¹v © ¹v © ¹P © ¹T 5. If the entropy of a system remains constant in a thermodynamic process the process is [GATE 1995] (a) isobaric (b) isochoric (c) isothermal (d) habatic 6. Which of the following is not an exact different ? [GATE 1997] (a) dQ (Q = heat absorbed) (b) dU (U = internal energy) (c) dS (S = entropy) (d) dV (V = free energy) 7. An ideal gas in a cylinder is compressed adiabatically to one-third..... volume. During this process 20J work is done on the gas by compressing agent. Which of the following statements is true for this case? [GATE 1997] (a) Change in the internal energy in this process is zero (b) The internal energy increases by 20J (c) The internal energy decreases by 20J An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  2 (d) Temperature of the gas deceases. 8. Mean tota energy of a classical three dimensional harmonical at oscillato in equilibrium with a heat reservoir at temperature is : [GATE 1997] 3 (a) k BT (b) k BT (c) 2k BT (d) 3k BT 2 9. The root mean square speed of a particle of mass m in the kinetic theory is given by [GATE 1997] k BT 2k BT 3k BT 8k BT (a) (b) (c) (d) m m m m 10. The sublimation curve of solid ammonia is given by p = 23 – 3750/T and the vaporization curve of the liquid ammonia is given by ln p = 19.5 – 3050/T, where p is in mm of Hg and T is in K. The temperature of the triple point of ammonia is : [GATE 1998] (a) 3750 K (b) 3050 K (c) 700 K (d) 200 K 11. A reversible engine cycle is shown in the following T–S diagram. The efficiency o f the engine is: [GATE 1999] (a) 1/3 (b) 1/2 (c) 1/5 (d) 1/4 12. An engine absorbs heat at a temperature of 1000 K and rejects heat at 600 K. If the engine operates at maximum possible efficiency, the amount o f work performed by th e engine, for 2000 in heat input is: (a) 1600 J (b) 1200 J (c) 800 J (d) 400 J 13. Boyle’s law can be expressed in different form as : [GATE 1999] (a) dV / dP 1 (b) dV / dP V / P (c) dV / dP P / V (4) dV / dP V / P 14. The boiling point of a liquid at pressure P0 is T0. Its molar latent heat of vaporisation is L and molar volume of the liquid phase is negligible as compared to the vapour phase. The vapour phase obeys perfect gas equation. The boiling point T at pressure P is given by [GATE 1999] (a) P / P0 L / RT0 1  T0 / T (b) ln P / P0 L / RT0 1  T0 / T (c) ln P / P0 L / RT0 1  T0 / T (d) P / P0 L / RT0 T0 / T An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  3 15. An amount of heat Q is trasferred from a heat reservoir at temperature TA to another heat reservoir at temperature TB. What is the change in the entropy 'S of the combined system. [GATE 2000] § 1 1 · § 1 1 · Q T § 1 1 · (a) Q ¨ T  T ¸ (b) Q ¨ T  T ¸ (c) ln B (d) Q ¨ T  T ¸ © B A¹ © B A¹ TBTA TA © A B¹ 16. Which of the following is an example of a first order please transition? [GATE 2000] (a) A liquid gas phase tranition of the critical point (b) A paramagnet ferromagnet phase transition (c) A normal metal superconduction phase transition (d) Aliquid gas phase transition from the critical point 17. The mean free path of the particles of a gas at temperature T0 and p0 has a value O0. If the pressure is increased to 1.5 p0 and tine temperature is reduced to 0.75T0 , the mean free path [GATE 2002] (a) revains unchanged (b) is reduced to half (c) is doubled (d) is equal to 1.125O 0 18. A second order phase transition is one inwhich [GATE 2003] (a) the plot of entropy as a function of shows a discontinuity (b) the plot of specific heat as a function of temperature shows a discontinuity (c) the plot of volume as a function of pressure shows a discontinuity (d) the plot of compressibility as a function of temperature is continuous 19. A sample of ideal gas with initial pressure P and volume V is taken through an isothermal expansion proceed during which the change in entropy is found to be 'S. The universal gas constant is R. Then the work done by the gas is given by [GATE 2003] (a) PV 'S / nR (b) nR'S (c) PV (d) P'S / nRV 20. A piston containing an ideal gas is orighially in the state X (see figure). The gas is taken through a thermal cycle X o Y o X as shown: An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  4 The work done by the gas is positive if the direction of the thermal cycle is: (a) clockwise [GATE 2000] (b) counter clockwise (c) neither clockwise nor counter clockwise (d) clockwise from X o Y and counter clockwise from Y o X 21. Hydrogen molecules (mass m) are in thermal equilibrium at a temperatire T. Assuming classical distribution of velocity, the most probable speed at room temperature is: [GATE 2003] 2k BT (a) kBT / m (b) 2k BT / m (c) (d) m / 2 k BT m 22. Which one of the following.......... [GATE 2004] (a) vaporization of a liquid at...... (b)....... (c) normal liquid He to........... (d)........... 23. In the region of co-existence...... phases of a material. [GATE 2004] (a) CP and CV are both infinite.... ª 1 § wV · º (b) CV and E «V ¨ wT ¸ » 0 ¬ © ¹P ¼ ª 1 § wV · º (c) CV and K « ¨ ¸ » 0 ¬ V © wP ¹T ¼ (d) C P , E and K are all infinite 24. For anyprocess, the second law of thermodynamics requires that the change of entropy of the universe be : [GATE 2004] (a) positive only (d) negative or zero (c) zero only (d) negative or zero 1 25. If the equation of state for a gas will internal energy U is pV U ,then the 3 equation for an adiabatic process is : [GATE 2005] 1 1 (a) pV 3 constant (b) pV 2 constant 5 3 (c) pV 3 constant (d) pV 5 constant 3 a 26. The inteznalenergy of n moles ofa gas is given E nRT  where V is the 2 V volume of the gas a t temperature T and a is a positive constant. One mole of An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  5 the gas is state T1,V1 is allowed to expand adiabatically into vacaum to a final state T2 ,V2. The temperature T2 is : [GATE 2005] a§ 1 1· 2 a§ 1 1· (a) T1  R ¨ V  V ¸ (b) T1  3 R ¨ V  V ¸ © 2 1¹ © 2 1¹ 2a§ 1 1· 1a§ 1 1· (c) T1  3 R ¨ V  V ¸ (d) T1  3 R ¨ V  V ¸ © 2 1¹ © 2 1¹ 27. The mean internal of a one-dimensional classical harmonic oscillator in equilibrium with a heat bath of temperature T is: [GATE 2006] 1 3 (a) k BT (b) k BT (c) k BT (d) 3k BT 2 2 28. A heat pump working on the Carnot cycle maintains the inside temperature of a house at 22ºC by suppling 450 kJs–4. If the outside temperature is 0ºC, the heat taken, in kJs–1, from the outside air is approximately. [GATE 2007] (a) 487 (b) 470 (c) 467 (d) 417 29. The vapour pressure p (in mm of Mg) o fa solid, at temperature T, is expressed by C Anp 23  3863 / T and that of its liquid phase by Anp 19  3063 / T. The triple point (in Kelvin) of the material is : [GATE 2007] (a) 185 (b) 190 (c) 195 (d) 200 30. The pressure versus temperature diagram o f a given system at certain low temperature range is found to be parallel to the temperature axis in the liquid- to-solid transition region. The change in the specific volume remains constant in this region. The conclusion one can get from the above is : [GATE 2008] (a) the entropy of solid is zero in this temperature region (b) the eatrony increases when the system goes from liquid to solid phase in this temperature region (c) the entropy decreases when the system transforms from liquid to solid phase in this region o f temperature (d) the change in entropy is zero in the liquid-to-solid transition region 31. Consider a system of N atoms an ideal gas of type. A at temperature and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas..... same temperature T and volume V. Once the combined system reaches equilibrium. [GATE 2008] (a) the totat entropy of the final system is the same.... the individual system always (b) the entropy of mixing is 2 Nk B An 2 An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  6 (c) the entropy of the final system is less than that of sum of the initial.... of the two gases (d) The entropy of mixing is non zero when the atoms A and B....... type 32. Identify which one is a first order phase transition ? [GATE 2009] (a) A liquid to gas transition at its critical temperature (b) A liquid to gas transition close to its triple point (c) A paramegnetic to ferromagnetic transition in the absence of a magnetic field (d) A metal to-superconductor transition in the absence of a magnetic field 33. A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is : [GATE 2010] 3 1 5 (a) Nk BT (b) Nk BT (c) Nk BT (d) Nk BT 2 2 2 34. In a fiist order phase transition, at the transition temperature, specific heat of the system [GATE 2011] (a) Divines and its entropy remains the same (b)pivages and its entropy has finite discontinuity (c) Remains unchanged and its entropy has finite discontinuity (d) Has finite discontinuity and its entropy diverges 1 35. If the isothermal compressibity of a solid is kT 1010 Pa , the pressure required to increase its density by 1% is approximately. [GATE 2011] (a) 104 Pa (b) 106 Pa (c) 108 Pa (d) 1010 Pa 36. The isothermal compressibility, N of an ideal gas at temperature T0 and volume V0 , is given by [GATE 2011]  wV  wV wV wV (a)  V wP (b) V wP (c) V0 wP (d) V0 wP 0 T 0 0 T 0 T 0 T 0 37. If plack's constant were zero, then the total energy contained in a box filled with radiation of all frequencies at temperature T would be (k is the Boltzmann constant and T is non zero) [GATE 2013] 3 (a) zero (b) infinite (c) kT (d) kT 2 38. N atoms of an ideal gas are enclosed in a container of volume V. The volume of container is changed to 4V, while keeping the total energy constant. The An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  7 change in the entropy of the gas, in units of Nk B ln 2 , is______, where kB is the Boltzmann constant. [GATE 2016] 1.(c, d) 2.(b) 3.(d) 4.(a) 5.(d) 6.(a) 7.(b) 8.(d) 9.(c) 10.(d) 11.(a) 12.(c) 13.(d) 14.(b) 15.(a) 16.(d) 17.(d) 18.(b) 19.(a) 20.(a) 21.(c) 22.(a) 23.(d) 24.(b) 25.(c) 26.(c) 27.(b) 28.(d) 29.(d) 30(d) 31.(b) 32.(b) 33.(c) 34.(b) 35.(c) 36.(a) 37.(d) 38.(2) CSIR-UGC-NET Previous Year's Questions 1. Consider. the tr ansition of liquid water to steam as water boils at a temperature of 100ºC under a pressure of 1 atmosphere. Which one of the following quantities does not change discontinuously at the transition? (a) Gibbs free energy (b) internal energy [NET June 2011] (c) The entropy (d) The specific volume 2. Let 'W be the work done in a quasistatic reversible thermodynamics process. Which of the following state-merits about 'W is correct? (a) 'W is a perfect differential if the process is isothermal [NET Dec.2011] (b) 'W is a perfect differential if the process is adiabatic (c) 'W is always a perfect differential (d) 'W cannot be a perfect differential 3. A large number N of-Brownian particles one-dimension start their diffusive motion from the origin at time t f 0. The diffusion coefficients is D. The number of particles crossing a point at a distance L from the origin, per unit time, depends on L and time t as [NET June 2015] N  L2 / 4/Dt NL 4 Dt / L2 (a) e (b) e 4SDt 4SDt N  L2 / 4/Dt e (c) 3 (d) Ne 4 Dt / L 2 16 D 4. The pressure P of a fluid is related to its number density..... of state P ap  bp 2 where a and b are constants. If the.............. on the system when it is compressed so as to increase. The number density from an initial value of p0 to 2 p0 is [NET Dec. 2014] An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  8 (a) aU0V0 (b) § 3a 7U b · (c) ¨  ¸ U0V0 0 (d) © 2 3 ¹ 5. The specific heat per molecule of a gas of diatomic molecules at high remperature is [NET June 2016] (a) 8k B (b) 3.5k B (c) 4.5k B (d) 6k B 6. When an ideal monatomic gas is expanded diabatic any remain.... V0 to 3V0 its temperature changes from T0 to T. Then the raio T / T0 is [NET June 2016] 2/3 1/3 1 §1· §1· (a) (b) ¨ ¸ (c) ¨ ¸ (d) 3 3 ©3¹ ©3¹ 1.(a) 2.(b) 3.() 4.(d) 5.(b,c) 6.(b) JEST Previous Year's Questions 1. Efficiency of a perfectly reversible (Carrot) beat engine operating between absolute temperature T and zero is equal to [JEST 2012] (a) 0 (b) 0.5 (c) 0.75 (d) 1 2. A thermally insulated ideal gas of volume V1 and temperature T expands to another enclosure of volume V2 through a pious plug. What is the change in the temperature of the gas? [JEST 2012] 1 V (a) 0 (b) T ln V 2 2 V (c) T ln V (d) T ln ª¬ V2  V1 / V2 º¼ 1 3. For which gas the ratio of specific heats CP / CV will be largest? (a) mono-atomic (b) di-atomic [JEST 2014] (c) tri-atomic (d) bexa-atomic 4. Electrons of mass m in a thin, long wire at a temperature T follow a one- dimensional maxwellian velocity distribution. The most probable speed of these electrons is, [JEST 2015] § kT · § 2kT · § 8kT · (a) ¨ ¸ (b) ¨ ¸ (c) 0 (d) ¨ ¸ © 2Sm ¹ © m ¹ © Sm ¹ An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  9 1.(d) 2.(a) 3.(a) 4.(c) Other Examinations Previous Year's Questions 1. The sole effect of a hypothetical thermodynamic process E1 is to convert an amount Q of heat entirely into work. A second hypothetical process E2 converts an amount W of work entirely into heat. It can be said that the second law of thermodynamics is violated by (a) E1 but not E2 (b) E2 but not E1 (c) both E1 and E2 (d) neither process 2. Which of the following expresses the second law of thermodynamics? (Symbols have their usual meanings). (a) 'F d W (b) 'S  Q / T (c) 'U Q W (d) 'S d 0 3. A carnot engine operates between a heat source at 500 K and a heat sink at 300 K. The temperature of the source is increased by 20 K. In order that the efficiecy of the engine remain unchanged, the temperature of the sink should be changed by (a) + 20 K (b) +12 K (c) –12 K (d) –20 K 4. A thermodynamic system is classified as closed if it can (a) Exchange energy with its surroundings, but not matter (b) Exchange both energy and matter with its surroundings (c) Exchange neither energy nor matter with its surroundings (d) Exchange only matter, but not energy, with its surroundings 5. The first law of thermodynamics states that 'U 'Q  'W , where the symbols have their usual meaning. Which one of the following quantity (ies) depend(s) only on the initial........ state, and is (are) independent of the path of the system between these states? (a) 'Q (b) 'W (c) 'U (d) 'U and 'W 6. In an infinitesimal reversible............ depends only on the initial and the find states of the system and is independent of the path between these states? (a) T 'Q (b) 'Q / T (c) T / 'Q (d) T / 'Q 7. Which of the following statement is correct? (a) You can construct an engine operating in cycles, extracting heat Q and pertorming exactly equivalent work W (b)You can construct an engine operating in cycles extracting heat Q and performing more than equivalent amount of work W An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  10 (c) You can have an engine operating cyclically such that the entropy remains constant throughtout the cycle (d)You cannot construct a cyclieally operating engine that will extract heat Q and perform exactly equivalent amount of work W 8. Above a temperature T0 , the specific heat of a certain gas is approximate 3.5R, and is approximately 2.5R below T0. The gas is most likely (a) oxygen (b) ozone (c) carbon dioxide (d) argon 9. During the isothermal reversible expansion of an ideals (a) the entropy and the pressure both increase (b) the entropy and the premre both decrease (c) the entropy increases and the pressure decreases (d) the entropy decreases and the pressure increases 10. An adiabat in the PV-plane is a curve of (a) Constant temperature (b) Constant entropy (c) Costant pressure (d) Constant volume 11. The volume of a thermodynamic system increases irreversibly by an incremental amount GV. If P is the pressure, the work done on the system is: (a) GW PGV (b) GW  PGV (c) GW  PGV (d) GW !  PGV 12. Consider an elastic string of length L under tension W at temperature T. Let U and S be its internal energy and entropy, respectively. Then the conjugate pairs of thermodynamic variables are (a) ( W ,T) and (L,S) (b) (L, W ) and (T,S) (c) (T, L) and (T, u) (d) (L,S) and (T, U) 13. A carrot engine can be used to define an absolute temperature scale. This is made possible by the following property of the carrot engine (a) It involves an adiabatic as well as an isothermal process (b) It is a cyclic process (c) It is most efficient engine operating between two given temperatures (d) It conserves energy 14. Which is the most effective way of increasing the efficiency of a carnot engine operating between temperatures T1 and T2 T1 ! T2 ? (a) Increasing T1 keeping T2 fixed (a) Increasing T2 keeping T1 fixed (c) Decreasing T2 and increasing T1 (a) Increasing T2 keeping T1 fixed 15. Entropy-temperature (S–T) diagram of a carnot cycle is shown below : An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  11 The adiabatic compression is n presented by (a) AB (b) DA (c) CD (d) BC 16. The quantity that remains constant Joule Thomson expansion is : (a) U  pV (b) U  pV  TS (c) U (d) U  TS 17. A steam turbine is operated with an intake temperature 427ºC and exhaust temperature 107ºC. Heat input to the turbine is Q. Then maximum work.......... (a) 0.5Q (b) 0.3Q (c) Q (d) 0.25Q 18. For a system with constant volume and temperature, the thermodynamic equilibrium corresponds to the state with minimum? (a) Helmholtz free energy (b) Gibbs thermodynarnic potential (c) Internal energy (d) Entbalpy 19. A gas of argon atoms is kept in a Container of volume V and pressure P and is in equilibrium with a heat bath at temperature T. The average energy of an argon atom in the gas is : 3 (a) RT (b) 3k BT (c) k BT (d) 3 RT 2 Where kB is Boltzman constant. 5 20. The molar specific heat of a gas as given from the kinetic theory is R. If it is 2 not specified whether it is C p or Cv , one could conclude that the molecules of the gas. (a) Are definitely monatomic (b) Are definitely rigid diatomic (c) Are definitely non-rigid diatomic (d) Can be monatomic or rigid diatomic 1 § wV · 21. Isothermal compressibility NT of a substance is defined as NT  ¨ ¸. V © wP ¹T Its value for n mole of an ideal gas will be An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  12 1 n 1 n (a) (b) (c)  (d)  P P P P 22. Identify the correct statement. (a) The entropy of a system always increases when it undergoes an irreversible process (b) The entropy of a system always decreases when it undergoes an irreversible process (c) The second law of thermodynamics follows directly from principle of conservation of energy (d) The internal energy of ideal gas depends on its tempera ture 23. An ideal gas undergoes an isothermal expansion (at a constant temperature T) to double its volume. The change in the entropy per mole is R (a) 2R (b) –Rla2 (c) Rln2 (d) 2 24. One mole of a monoatomic perfect gas initially at temperature 0ºC expands from volume V0 to 2V0 at constant pressure. The specific heat at constant volume of the gas is 20.8Jmol 1K 1. The amount of heat absorbed is nearly.. (a) 1179J (b) 1279J (c) 1979J (d) 7972J 25. When 100g ice at 0ºC melts the change in entropy in cal/K is about.... heat of fusion (melting) as 80 cal/g. (a) 0 (b) 0.34 (c) 29.3 (d) 39.2 26. The 10g of ice at 0ºC is converted into water at the same temperature. Take latent heat of fision as 20 cal/g. The change in entropy in a.... about. (a) zero (b) 0.14 (c) 2.93 (d) 3.92 27. Consider oxygen gas at 300K having the mass of its molecule as 5.31u1026 kg. The root mean square speed of its molecules, is about. (a) 284 m/s (b) 248 m/s (c) 348 m/s (d) 484 m/s 28. The power per unit area emitted by a surface of a blackbody (in Wm–2)It temperature 230 K is about (a) 112.67 (b)128.67 (c) 158.67 (d) 178.67 1.(a) 2.(a) 3.(b) 4.(a) 5.(c) 6.(b) 7.(d) 8.(a) 9.(c) 10.(b) 11.(a) 12.(b) 13.(c) 14.(c) 15.(b) 16.(a) 17.(a) 18.(a) 19.(c) 20.(d) 21.(a) 22.(d) 23.(c) 24.(d) 25.(c) 26.(c) 27.(d) 28.(c) An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  13 GATE Previous Year's Questions 1. Suppose temperature of the sun goes down by a factor of two, then the total power emitted by the sun will go down by a factor of [GATE 1997] (a) 2 (b) 4 (c) 8 (d) 16 2. Choose the correct alternatives [GATE 1999] (a) internal energy of aVander Waals gas at a given temperature increases as the volume increases (b) internal energy of a perfect gas at a given temperature increases as the volume increases (c) internal energy of a Fermi gas at a given temperature increases as the volume increases (d) internal energy ofa Fermi gas at a given temperature decreases as the volume increases 3. Which among the following sets of Maxwell relations is correct? (U-internal energy, H-enthalpy, A-Helmholtz free energy and G-Gibbs free energy) [GATE 2010] § wU · § wU · § wH · § wH · (a) T ¨ ¸ and P ¨ ¸ (b) V ¨ ¸ and T ¨ ¸ © wV ¹ S © wS ¹V © wP ¹ S © wS ¹ P § wG · § wG · § wA · § wA · (c) P  ¨ wV ¸ and V ¨ ¸ (d) P  ¨ wS ¸ and S ¨ wP ¸ © ¹T © wP ¹ S © ¹T © ¹V 4. A Carnot cytle operates on a working substance between two reservoirs at temperature T1 and T2 , with T1 ! T2. During each cycle, an amount of heat Q1 is extracted from the reervoir at T1 and an amount Q2 is delivered to the reservoir at T. Which of the following statements INCORREC?[GATE 2011] (a) Work done in one cycle Q1  Q2 Q Q (b) T  T 1 2 1 2 (c) Entropy ofthe hotter reservoir decreases (d) Entropy of the universe (costing of the working substance and the two reservoirs) increases 5. A classical gas of molecules each of mass m, is in thermal equilibrium at the absolute temperature T. The velocity components of the molecules along the Cartesian axes are..... The mean value of... [GATE 2013] k BT 3 k BT 1 k BT 2 k BT (a) (b) (c) (d) m 2 m 2 m m An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  14 8. At a certain temperature T, the average speed of nitrogen molecules in an is found to be 400 m/s. The most probable and the mot mean square speeds of the molecules are respectively. [GATE 2012] (a) 355 m/s, 434 m/s (b) 820 m/s, 91 m/s (c) 150 m/s, 301 m/s (d) 422 m/s, 600 m/s 6. Consider a gas of atoms obeying Maxwell-Boltzman statistics. The average G value of ei=p over all the momenta p of each of the particles (where a is a constant vector and a is its magnitude, m is the mass of each atom, T is temperature and k is Boltzmann’s constant) is [GATE 2013] 1 3 (a) One (b) Zero (c)  a 2mkT (d)  a 2mkT e 2 e 2 7. The total power emitted by a spherical black body of radius R at a temperature T is P1. Let P2 be the total power emitted by another spherical black body of radius R/2 kept at temperature 2T. The ratio P1 / P2 is ____ (Give your answer upto two decimal places). [GATE 2016] 1.(d) 2.(a,d) 3.(b) 4.(d) 5.(d) 6.(a) 7.(c) 8.(0.25) CSIR-UGC-NET Previous Year's Questions bS 3 1. The internal energy E of a systern is give; by E , where b is a constant VN and other symbols have their usual meaning. The temperature of this system is equal to [CSIR Dec. 2011] 2 bS 2 3bS 2 bS 3 §S· (a) (b) (c) (d) ¨ ¸ VN VN V 3N ©N¹ 2. Consider a Maxwellian distribution of the velodcy of the molecules of anideal gas. Let Vmp and Vrms denote the most probable velocity and the root mean square velocity, respectively. The magnitude of the ratio Vmp / Vrms is : (a) 1 (b) 2/3 [CSIR Dec. 2011] (c) 2/3 (d) 3/2 3. A particle is confined to the region x t 0 by a potential which increases linearly as u x u0 x. The mean position of the particle at temperatureT is: k BT (a) u (b) k BT / u0 [CSIR June 2011] 0 An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  15 k BT (c) u0 (d) u0k BT 4. A given quantity of gas is taken from the state A o C reversibly by two paths, A o C directly and A o B o C as shown in the........ [NET Dec. 2012] during the A o C the work done by the pass is 100J and the heat absorbed is 150J. If during the process A o B o C the work doen by the pass 10J, the heat absorbed is : (a) 20J (b) 80J (c) 220J (d) 80J 5. For temperature T1 ! T2 the......... probability distribution F(v) of the speed v of a molecule in three dimension is correctly represented by the following figure : [CSICR June 2013] (a) (b) (d) (d) 6. The speed v of the molecules of mass m of an ideal gas obeys Maxwell’s velocity disnibution law-at an equilibrium temperature T. Let vx , v y , vz denote the components of the velocity and kB the Boltzmann constant. The 2 average value of Dv x  Ev y where D and E are constant, is 2 2 2 2 (a) D  E kBT / m (b) D  E kBT / m [CSIR Dec. 2013] An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  16 (c) D  E 2 kBT / m (d) D  E 2 kBT / m \ 7. A Carnot cycle operates as a heat engine between two bodies of equal heat capacity until their temperatures become equal. If the initial temperatures of the bodies are T1 and T2 , respectively, and T1 ! T2 then their common final temperature is [CSIR Dec. 2013] 1 (a) T12 / T2 (b) T22 / T1 (c) T1T2 (d) T1  T2 2 8. The free eneruF of a system depends on a thermodynamics variable \ as F a\ 2  b\ 6 [NETJune 2014] with a, b > 0. The value of \ , when the system is in thermodynamic equilibrium, is 1/4 1/4 1/4 (a) zero (b) r a / 6b (c) r a / 3b (d) r a / b 9. When a gas expands adiabatically from volume V1 to V2 by a quasi-static reversible process, it cools from temperature T1 to T2. If cow the same process is carried out adiabatically and irreversibly, and T2' is the temperature of the gas when it has equilibrated, then [NET Dec. 2014] (a) T2' T2 (b) T1' T2 ' 2 § V  V1 · ' T2V1 (c) T2 T2 ¨ V ¸ (d) T2 V2 © 2 ¹ 10. The condition for the liquid and vapour phases of a liquid to be in equilibrium dP QA is given by the approximate equation dT Tvvap (Clausrus claperon equation), where vvap is the volume per particle in the vapour phase, and Q1 is the latent heat, when may be taken to be a constant. If the vapour obeys ideal gas law, which of the following plots is correct? [NET June 2015] (a) (b) An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  17 (c) (d) 11. A vessel has two compartments of volume V1 and V2 , containing an ideal gas at pressures p1 and p2 , and tempdratures T1 and T2 respectively. If the wall separating the compartments is removed, the resulting equllibriuin temperature will be [NET June 2013] p1T1  p2T2 V1T1  V2T2 (a) p1  p2 (b) V1  V2 p1V1  p2V2 1/2 (c) p V / T  p V / T (d) T1T2 1 1 1 2 2 2 12. The heat capacity of (the interior of) are frigerator is 4.2 kJ/K. The minimum work that must be done to lower the internal temperature from 18ºC to 17ºC when the outside temperature is 27ºC will be [NET Dec. 2015] (a) 2.20 kJ (b) 0.80 kJ (c) 0.30 kJ (d) 0.14 kJ 1.(b) 2.(c) 3.(a) 4.(b) 5.(a) 6.(b) 7.(c) 8.(c) 9.(b) 10.(c) 11.(c) 12.(d) JEST Previous Year's Questions 1. A monoatomic ideal gas at 17ºC is adiabatically compressed to 1/8 of its original volume. The temperature after compression is [JEST 2012] (a) 2.1ºC (b) 17ºC (c) 200.5ºC (d) 887º C 2. Consider an ideal gas of mass mat temperature T1 which is mixed isobarically ( i.e., at constant pressure) with an equal, mass of same gas at temperature T2 in a thermally insulated container. What is the change of entropy of the universe? [JEST 2012] § T1  T2 · § T1  T2 · (a) 2cC ln ¨ ¸ (b) 2 cC ln ¨ ¸ p ¨ 2 TT ¸ p ¨ 2 TT ¸ © 1 2 ¹ © 1 2 ¹ §T T · § T T · 1 2 1 2 (c) 2cC p ln ¨ 2T T ¸ (d) 2cC p ln ¨¨ 2 T T ¸¸ © 1 2 ¹ © 1 2 ¹ An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  18 3. For a diatomic ideal gas near room temperature, what fraction of the heat supplied is available for external work if the gas is expanded at constant pressure? [JEST 2013] (a) 1/7 (b) 5/7 (c) 3/4 (d) 2/7 4. An ideal gas is compressed adiabitically from an initial volume to a final volume aV and a work W is done on the system in doing so. The final temperature the § T · gas will be ¨ T ¸ Cv ¹ [JEST 2015] © W 1 J (a) (b)... V r a  Dr W 1 J (c).... (d) V a a  Dr 5. The entropy temperature diagramof two..... A and B are shown in the figure 5. The efficiencies of the followin equlances is correct? [JEST 2015] Figure-5 (a) K A K B / 2 (b) K A KB (c) K A 3KB (d) K A 2K B 6. An ideal gas with adiabatic exponent J undergoes a process in which its pressure P is related to its volume V by the relation P P0  DV , where P0 and D are positive coostants. The volume staris from being very close to zero and increases monotonically to P0 / D. At what value of the volume during the process does the gas have maximum entropy? [JEST 2016] P0 JP0 JP0 P0 (a) D 1  J (b) D 1  J (c) D 1  J (d) D 1  J 7. A gas of N molecules of mass m is confined in a cube of volume V L3 at temperature T. The box is in a uniform gravitational field  gzˆ. Assume that the potential energy of a molecule is U = mgz, where z  0, L is the vertical coordinate inside the box. The pressure P(z) at height z is : [JEST 2016] An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  19 § mg z  L / 2 · exp ¨  ¸ N mgL © k BT ¹ P z (a) V 2 § mgL · sinh ¨ ¸ © 2k BT ¹ § mg z  L / 2 · exp ¨  ¸ N mgL © k BT ¹ P z (b) V 2 § mgL · cosh ¨ ¸ © 2 k BT ¹ k BTN (c) P z V N (d) P z mgL V 8. An ideal gas has a specific heat ratio C p / Cv 2. Starling at a temperature T1 the gas under goes an isothermal compression to increase its density by a factor of two. After this an adiabatic compression increases its pressure by a factor of two. The temperature of the gas at the end of the second process would be: [JEST 2016] T1 T1 (a) (b) 2T1 (c) 2T1 (d) 2 2 1.(d) 2.(a) 3.(d) 4.(d) 5.(b) 6.(c) 7.(a) 8.(b) TIFR Previous Year's Questions 1. A car tyre is slowly pumped up to a-pressure of 2 atmospheres in an environment at 15ºC. At this point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N 2 ) that was inside the tyre to be adiabatic, its temperature after the burst is [TIFR 2010] (a) –55°C (b) –37°C (c) –26°C (d) –4.9°C 2. The pV diagram given below represents a [TIFR 2010] An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  20 (a) Carnot refrigerator (b) Carnot engine (c) gas turbine refrigerator (d) gas turbine engine 3. A closed, tharnally-insulated box contains one mok of an ideal monatomic gas G in thermodynamic equilibrium with blackbody radiation B. The total internal 4 energ of the system is U U G  U B where UG and U B DT are the energies of the ideal gas and radiation respectively. If U B U B at a certain temperature T0 K , then the energy required to raise the temperature from T0 K to T0  1 K in terms of the gas constant R, is [TIFR 2011] (a) 7.5R (b) 6.3R (c) 1.5R (d) 0.33R 4. The phase diagram of a pure substance is given in the figure in low where 'T' denotes the critical point : The phase transitions occurring along the line magnetic : [TIFR 2011] (a) D melting; E condensation J sublimation (b) D sublimation; E vaporisation; J melting (c) D melting, E vaporisation; J condensation (d) D sublimation; E melting; J vaporisation 5. Consider a sealed but themally conducting container of total V p. Which is in equilibrium with a thermal bath at temperature T. The is divided into two equal chantbers by a thinbut impermeable partition. One o f these chambers contains an ideal gas, while the other half is a vacuum (see figure) [TIFR 2012] An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  21 If the partition is rernovecl and the ideal gas isallowid to expand and fill the entire container, then the entropy per molecule of the system will increase byan amount : (a) 2k B (b) k B An 1/ 2 (c) k B An 2 (d) kB An 2 / 2 6. A system at temperature T has three energy states 0, rH. The entropy of the system in the low temperature T o 0 and high temperature T o f limits are, respectively, [TIFR 2013] (a) ST o0 0 and ST of kB exp 3 (b) ST o0 ST of k B ln 3 (c) ST o0 0 and ST of k B ln 3 (d) ST o0 0 and ST of 3kB / 2 7. A binary star is observed to consist of a blue star B (peak wavelength 400 nm) and a red star R (peak. wavelength 800 nm) orbiting each other. As observed from the Earth, B and R appear equally bright. Assuming that the stars radiate as perfect blackbodies, it follows that the ratio.of volumes VB / VR of the two stars is [TIFR 2013] 1 1 (a) (b) 64 (c) 16 (d) 64 16 8. A classical ideal gas, consisting of N particles N o f is confined in a box of volume Vat temperature T and pressure p. The probability that, at any instant of time, a small sub-volume v0 becomes totally void (i.e. no particles inside), due to a......... [TIFR 2013] § v · 0 §  Nv0 · § v0V · pv0 (a) exp ¨ ¸ (b) exp ¨ ¸ (c) exp ¨ ¸ (d) © V ¹ © V ¹ © N ¹ NT 9. The PV-diagram for a CArnot cycle execuded irrideal gas with.... is the shown below. Note that 1, 2, 3 and 4 label the change over points in the cycle..... X T2 § p2 · ¨ ¸ , then X = [TIFR 2013] T3 © p3 ¹ 1 1 (a) 1 J (b) 0 (c) 1 (d)  J 10. The entropy S of a black hole is known to be of the form [TTFR 2013] S Dk B A An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  22 where A is theesurface area of the black hole and D is a constant, which can be w ri tten i n term s of e (velocity of light in vacuum), = (reduced Planck’ss constant) and GN (Newton’s constant of gravitation). Taking the radius of the 2GN M black hole as R it follows that the entropy S is [ O is a numerical c2 constants ] GN2 M 2 k B =ck B GN2 M 2 k B GN M 2 k B (a) 4 (b) OG M (c) (d) O =c N O=c 4 O=c 11. A monotomic gas is described by the equation of state p V  bn nRT where b and R are constants and other quantities have their usual meanings. The maximum density (in moles per unit volume) to which this gas can be compressed is [TIFR 2013] 1 1 (a) (b) b (c) (d) Infinity bn b 12. A certain amount of fluid with beat capacity CF Joules/ºC is initially at a temperature 0° C. It is then brought into contact with a heat bath at a temperature of 100°C, and the system is allowed to come into equilibrium. In this process, the entropy (in Joules /°C) of the Universe changes by [TIFR 2013] (a) 100CF (b) 0 (c) 0.055CF (d) 0.044CF 13. One mole of an ideal gas undergoes the cycle ACBA shown in the PV diagram below. One of the curved line,s in the cycle represents an isothermal at than... temperature T, while the other represents an adiabatic change. The net heat..... is [TIFR 2014] V V (a)  p2 V1  V2  RT ln V (b)  p2 V3  V2  RT ln V 2 2 1 1 1 2 (c)  p2 V3  V2  JRT V2  V3 (d) p2V1  V2  JRT ln 14. Consider the CO molecule as a system of two point particle which has both translational and rotational degrees of freedom : Using classical statical An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  23 mechanics, the molar specific heat CV of CO as is given in terms of the Boltzmann constant kB by [TIFR 2014] 5 3 1 (a) kB (b) 2k B (c) kB (d) kB 2 2 2 15. An ideal gas at a temperature T is enelosed-irr.arigid container whose walls are initially at temperature T1 where T1  T. The walls arc covered on the outsidewith perfect thermal insulation and the system is allowed to come to equilibrium. The pressure exerted by the gas on the walls of the container (a) remains constant throughout [TIFR 2014] (b) is lower at the initial state than at the anal state (c) is higher at the initial stage than at the final state (d) is the same at the initial and final stages 16. A thermally-insolated container of volume V0 is divided into two equal halves by a non -permeable partition. A real gas with equation of state [TIFR 2014] § a2 · b3 ¨ p  3 ¸ nRT ¨ V ¹¸ © where ‘a’ and ‘b’ are constants, is confined to one of these halves at a temperature T0. The partition is now removed suddenly and the gas is allowed to expand to fill the entire container. The final temperature of the gas, in terms of its specific heat CV , will be 3a 2 2a 2 3a 2 2a 2 (a) T0  (b) T0  (c) T0  (d) T0  2CV V02 3CV V02 2CV V02 3CV V02 17. A manufacturer is able to offer two models of heat-conserving windows, as described below Window A is a simple pane....... consists of two extremely thin panes of glass, seperated by an air..... as shown in the... below above. If the thermal conductivity of glass is known to be..........., then the ratio of heat flow QA through window A to the hollow QB...... given by [TIFR 2014] An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  24 QA QB 1 1 (a) (b) (c) 4 (d) 16 16 4 18. In a cold country, in winter a lake was freezing.... it took 2 hours to form a layer of ice 2 cm thick on-the water.......... throughout the layer, the thickness of ice would get doubled after [TIFR 2015] (a) 2 more hours (b) 4 more hours (c) 6 more hours (d) 8 more hours 19. The equation ofstate of a gas is given by [TIFR 2015] RT b V  P T where R is the gas constant and b is another constant parameter. The specific heat at constant pressure CP and the specific heat at constant volume CV for this gas is related by CP  CV 2 § RT 2 · § dP · 2 § dP · 2 (a) R (b) R ¨¨1  ¸ (c) R ¨1  ¸ (d) R ¨1  2 ¸ © dP ¹¸ © RT 2 ¹ © RT ¹ 20. An ideal diatomic gas is initially at a temperature 0ºC. Then it expands reversibly and adiabatically to 5 tines it volume. Its final temperature will be approximately [TIFR 2015] (a) -180°C (b) -150°C (c) -130°C (d) 0°C 21. In the temperature range 100–1000 C, the molar specific heat of a metal varies with temperature T(measured in degrees Celsius) according to the formula Cp 1  T / 5 J  deg C1mol 1. If 0.2 kg of the metal at 600 C is brought in thermal contact with 0.1 kg of the same metal at 300 C, the final equilibrium temperature, in deg C, will be [TIFR 2016] (a) 466 (b) 567 (c) 383 (d) 519 ª § DN · º 2 22. The equation of state for a gas is given by « p  ¨© V ¹¸ » V  EN Nk BT where «¬ »¼ P, V, T, Ar and kB represent pressure, volume, temperature, number of atoms and the Boltmann constant, respectively, while D and E are constants specific to the gas. If the critical point C corresponds to a point of inflexion of the p-Vcurve, then the critical volume VC and critical pressure pe for this gas are given by An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  25 (a) VC 3E N , pe D 2 / 3E 2 (b) VC 3E N , pe D / 27E 2 [TIFR 2016] (c) VC 3E N , pe 8D 2 / 27E (d) VC 3E N , pe D 2 / 27E2 1.(c) 2.(a) 3.(a) 4.(d) 5.( ) 6.(c) 7.(a) 8.(b) 9.(a) 10.(d) 11.(c) 12.(d) 13.(b) 14.(a) 15.(c) 16.(a) 17.(d) 18.(c) 19.(c) 20.(c) 21.(d) 22.(d) Other Examinations Previous Year's Questions 1. In the Carrot cycle shown in the figure, the curves (a) ab and cd are adiabatic, bc and da are isothermal (b) db and ca are isothermal, bc and ad are adiabatic (c) ad and ed are isothermal, be and da are isobaric (d) ab and cd are isobaric, bc and da are isothermal 2. An ideal gas engine produces 1 kJ of useful work. If it operators between 400K and 300K, the amount of energy lost as waste heat is (a) 4 kJ (b) 2 kJ (c) 1 kJ (d) 3 kJ 3. The internal energy U is related to the Helmholtz free energy F by the relation: ­° w 2 § F · ½° ­° w 2 § F · ½° (a) U T ® 2 ¨ ¸ ¾ (b) U T ® 2 ¨ ¸¾ °¯ wT © T ¹ °¿V °¯ wT © T ¹ °¿V ­ w § F ·½ ­ w § F ·½ (c) U T 2 ® ¨ ¸ ¾ (d) U V ® wT ¨ T ¸ ¾ ¯ wT © T ¹ ¿V ¯ © ¹ ¿V 4. Two insulated containers connected with a... cock are initially..... Arrideal gas is filled in one of them and then allowed to expand into the other container by opening the cock. In this process the work done (W), the heat evolved (Q) and the.... thermal energy 'U are...... (a) W 0, Q 0 and 'U 0 (b) W ve, Q 0 and 'U ve An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  26 (c) W ve, Q 0 and 'U ve (d) W ve, Q 0 and 'U ve 3 5. A simple calculation for the entropy S of an ideal gas gives S Nk B ln V  S0 2 where N is the number of molecules in the gas, V is its volume and S0 an arbitrary cosntant. The expression is erroneous because (a) It does not contain temperature T (b) It does not contain pressure P (c) It is not extensive (d) It does not take into account the interaction between the molecules of the gas 6. Imagine dividing a fluid with internal energy V, entropy S, volume V, particle number N,Tenaprature T, pressure P and chemical potential P into two equal parts. The variables that remain unaffected by this division are (a) U, S S and N (b) U, V, T and P (c) T, P and P (d) T, P and S 7. N1 molecules of oxygen are confined in volume V1 at temperature T and have entropy S1; N1 molecules of oxygen are confined in volume V2 at temperature T and have entropy S2. The gases are mixed in a volume V V1  V2. The entropy S of the mixture is: (a) S  S1  S2 (b) S S1  S 2 § V 1 2 V · (c) S ! S1  S2 (d) RT ¨ ln V  V  ln V  V ¸ © 1 2 1 2¹ 8. Which ofthe following expressions arecorrect? (a) dH TdS  VdP , Where H is enthalpy (b) dF SdT  PdV , Where F is Helmholtz free energy (c) dG SdT  VdP , Where G is Gibbs function (d) SdT dE  PdV , where E is internal energy 9. Consider a perfect gas in a vessel rushing into an evacuated vessel and let the whole system be isolated. Let V1 and V2 denote the initial and final volumes of the gas. The increase in entropy of the system is: V V V2 1 2 V2 1 2 (a) Zero (b) R ln V (c) T ³ du  R ln V (d) T ³ du 1 V 1 V 1 1 10. In order to attain thermal equlibriam at a fixed volume, the system minimises An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  27 (a) S (b) H E  pV (c) G U  TS  pV (d) F U  TS Where the symbols have their usual meaning. 11. The particle density fluctuations in a pure substance are maximum at (a) Its freezing point (b) Its boiling point (c) At critical point (d) At triple point 12. A thermally insulated cubical box has two chambers ofequal volume. Initially, one mole of a mono atomic ideal gas is placed in one of the chambers while the other chamber is kept empty. The gas slowly leaks through a small hole and eventually occupies the whole box. The change in entropy of the gas is given uy (a) R/ In 2 (b) R ln 2 (c) zero (d) 2R 13. One mole of ideal monotomo gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas arc respectively chagncd to V' to such a way the entropy of the gas is unchange, then which of the following is true? (a) V ' 2V , T ' T / 2 (b) V ' 8V , T ' T / 4 (c) V ' 4V , T ' 8T (d) V ' V / 2 , T ' 2T 14. Coasider a thermodynamic system of N particles with internal energy U volume V and entropy is chemical potential is given by § wU · § wN · § wU · § wU · (a) ¨© wS ¹¸ (b) ¨© wU ¹¸ (c) ¨© wN ¹¸ (d) ¨© wN ¹¸ V ,N S ,V S ,N S ,V 15. The heat capacity at costant pressure of a certain gas in 1.4 times its heat capacity at constant volume. A best model for the molecules of this gas is : (a) rigid triangles (b) point particles (c) rigid dumbbells (d) non-rigid dumbbells that can vibrate 16. A carnot engine operates between a source at temperature 300K and a sink at temperature 200 K. Let K be the efficiency of the Carnot engine when the temperatures of both the source and the sink are decreased by the same amount. Then. (a) K  13 (b) K ! 13 (c) K 1 3 (d) K 1 2 § wS · § wP · 12. Consider the Maxwell relation ¨© wV ¹¸ ¨ ¸ © wT ¹V , N where the symbols have T ,N the usual meaning this relafion can be derived from (a) Helmholtz free energy F U  TS An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  28 (b) Gibbs free energy G U  TS  PV (c) Grand thermodynamic potential Z  U  TS  PN (d) Enthalpy H U  PV 18. We have S = (U, V, N), S = entropy, V= volume, U= internal energy, N= number of particles, P = Pressure, T = Temperature, P = chemical Potential. Which of the following statements is correct? § wS · 1 § wS · P (a) ¨© wV ¹¸  (b) ¨© wV ¹¸  U ,N T U ,N T § wS · P § wS · P (c) ¨© wV ¹¸ T (d) ¨© wN ¹¸ T U ,N V ,U 19. Consider a sample of argon gas contained in a box of volume V. The root- mean square speed of the argon atoms is vm. If the gas is allowed to expand at constant pressure to a volume of 2V, the root mean square speed of the gas molecules would be Xm (a) Xm / 2 (b) 2Xm (c) (d) 2Xm 2 20. A classical ideal gas in an enclosure is in equilibrium with a heat bath at a constant temperature. The ratio of the root mean square speed Vrms , mean speed Xmean and the most probable speed Xmp namely Vrms : Vmean : Vmp is 8 3 2 (a) 3 : : 2 (b) : :1 S 2 S S S 1 (c) S: 3: 2 (d) : : 3 8 2 21. The average speed of molecules in a as at 20ºC is v. At what temperature will be 2v? (a) 899ºC (b) 563ºC (c) 80ºC (d) 90ºC 22. At 100ºC, water vapour and......... a closed container. If P and S represent the chemical potential and......... (a) Pvapour Pliquid (b) Svapour Sliquid (c) Svapour ! Sliquid (d) Pvapour ! Pliquid 23. Finite changes in a second order plase transition occur in : (a) S (v) V (c) CP (d) T Where the symbols have their standard meaning. An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  29 24. The presiure versus tenaperature diagram for a pure subtance is shown below: The region.represented byA, B & C respectively are (a) Solid, liquid and vapour (b) Vapour, solid and squid (c) Solid, vapour and liquid (d) Vapour liquid and solid 25. The transition from ordinary liquid helium (He I) to superfluid helium (He II) is an example ofa second order lambda point transition. The quantities that remain constant in such a transition at the transitionpoint are : (a) entopx volume, specific heat at conitant pressure and Gibbs free energy (b) pressure, volume and isothermal compressibility (c) specific heat at constant pressure, isothermal compressibility and pressure (d) pressure, volurne, entropy and Gibbs free energy 26. When two phases 1 and 2 of a system are in thermodynamic equilibrium, their temperature T, pressure p and chemical potential p satisfy (a) T1 T2 , p1 p2 and P1 P2 (b) T1 T2 , p1 p2 and P1 z P 2 (c) T1 T2 , P1 P 2 and p1 z p2 (d) T1 T2 but, p1 z p2 , P1 z P 2 27. What a cry gal melts into a liquid at constant pressure, which of the following quantities Change s cont in uousty at the phase transikn? (a) Gibbs free energy (b) Volume (c) Internal energy (d) Entropy 28. A solid melts into a liquid via first order phase tarnsition. The relationship between the pressure P and the temperature T of the phase transition is P P 2T  P0 , where P0 is a constant. The entropy ch.a nge associated with the phase transition is 1.0 J mole–4 K–1. The Clausius-Clapeyron equation for § · dP the latent heat is L T ¨ ¸ 'V. Here 'v vliquid  vsolid is the change in © dT ¹ molar volume at the phase transition. The correct statement relating the values of the volumes is: (a) vliquid vsolid (b) vliquid vsolid  1 1 (c) vliquid vsolid  (d) vliquid vsolid  2 2 29. Experimental measurements of the capacity per mole of at minimum at low temperature shown that the data can he fitted to the formula Ge aT 2 | bT 3 , An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  30 where............ b 2.48 u105 JK 4 mole 1 and T is the temperature in Kelyin. The entropy of a mole of...... temperature is given by the formula. b 3 (a) aT  T  c where c ! 0 is a constant 3 aT b 3 (b)  T  c , where c ! 0 is a constant 2 3 b3 aT b 3 (c) aT  T (d)  T 3 2 3 30. A box containing 2 moles of diatomic ideal gas at temperature T0 is connected to another identical box containing 2 moles of a monoatomic ideal gas at temperature 5T0. There are no thermal losses and the heat capacity of the boxes is negligible. Find the final temperature of the mixture of the goes (ignore the vibrational degrees of freedom for the diatomic molecules. (a) T0 (b) 1.5T0 (c) 2.5T0 (d) 3T0 31. Ages of molecule each having mass ‘m’ is in thermal equilibrium at a temperature T. Let v1, v2 , v3 to be the Cartesian components of velocity vG of a 2 molecule. The mean value of vx  Dv y  Evz is : 2 2 k BT 2 2 k BT (a) 1  D  E (b) 1  D  E m m 2 2 k BT 2 2 k BT (c) E  D (d) D  E m m 32. A solid metallic cube of heat capacity S is at temperature 300K. It is brought in contact with a reservoir at 600K. If the heat transfer takes place only between the reservoir and the cube, the entropy change of the universe after reaching the thermal equilibrium is (a) 0.69 S (b) 0.54 S (c) 0.27 S (d) 0.19 S 33. A real as has specific volume v at temperature T. Its coefficient of volume expansion and isothermal compressibility are D and kP respectively. Its molar specific heat at constant pressure CP and molar specific heat at constant volume CV are related as TvD (a) CP CV  R (b) CP CV  kT TvD 2 (c) CP CV  (d) CP CV kT An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  31 34. A rigid triangular molecule consists of three non-collinear atoms joined by rigid rods. The constant pressure molar specific heat CP of an ideal gas consisting of such molecules is (a) 6R (b) 5R (c) 4R (d) 3R 35. An ideal gas expands in a process in which its pressure depends on the volume as p p0e  aV , where p0 and D are two positive constants. If n is the number of moles in the gas, the maximum temperature that it will attain in this process is (R is the universal gas constant) (a) p0 / eDnR (b) p0 / Dn3 R (c) ep0 / DnR (d) p02 / DnR 36. An ideal gas undergoes an isothermal change of volume. The initial and final volumes are given to be 1.0 litre and 2.7 litres respectively. If in this process the entropy per mole changes from S1 to S2. The value of differences S2  S1 is nearest to (R is the universal gas constant) (a) +2.7 R (b) +1.7R (c) +1.0 R (d) –1.0 R 37. An U, T, S and P denote, respectively the internal energy, temperature a pure entropy and pressure of a thermolymanamic system. Then a change..... the free energy F U  TS measures. (a) the heat exchanged at constant pressure (b) the work done by the system at constant entropy (c) the work done on the system constant temperature (d) the heat exchanged at constant temperature 38. An ideal gas undergoes an isothermal expansion (at a constant temperature T) from an initial volume V1 to a final volume V2. The change to the entropy per mole is : (a) R V1 / V2 (b) R / ln V1 / V2 (c) R ln V1 / V2 (d) R ln V2 / V1 39. A gas at a pressure PA and volume VA is compressed adiabatically to a volume VB at pressure PB. If the pressure volume relation for the gas during abiabatic compression pV 5/3 K (where K is a constant), the work done during the compression : § 2 · 5§ 2 · (a) K ¨¨ 2/3 ¸ 4/3 ¸ (b) 2 ¨¨ 2/3 ¸ 4/3 ¸ © VB  VA ¹ © VB  VA ¹ 1 5 (c) pBVB  p AVA (d) pBVB  p AV A 2 3 An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  32 40. A gas, the molecules of which have mass m, is at equilibrium at absolute temperature T. The root-mean-square of the relative velocity between any two molecules of the gas is : (a) 4k BT / Sm (b) 3k BT / 2m (c) 3k BT / m (d) 6k BT / m 41. Let Vx ,V y and Vz denote the components of the velocity a long x– y– and z– directions respectively, of an ideal gas particle. At the absolute temperature T, the average value of the product Vx2V y2Vz2 is proportional to : (a) T (b) T 3/2 (c) T 3 (d) T 4 42. The equation of state of an ideal gas is p nk BT ,where 'p' is the thermody- namic pressure and n = A/V is the thermodynamic variable for the number of particle per unit voltune. The 'n' dependence of the free energy 'f' per unit volume of the ideal gas is obtained by the following expression, where CT is tunperature-defoident constant. (a) p nk BT ln n  CT (b) 2nk BT n ln n  CT 3 (c) nk BT (d) 3nk BT 2 43. Suppose you measured vx (the x-component of the velocity) of every a tom in a one-l i tre can of hel i um gas ( 4He), kept in equilibrium at 300 K and at atmo- spheric pressure, at a particular instant of time. The standard deviation 2 vx2  vx in the measurement is approximately equal to (a) 450 m/s (b) 1120 m/s (c) 1400 m/s (d) 800 m/s (e) 14000 m/s 44. A thermally 'insulated box of volume 2V has a partition which divides it into two chambers of equal volume. Each chamber contains He gas at temperature T and pressure P. On removing the partition, the molecules in the two cham- bers mix with each other. The change in entropy of the system is PV PV 2 PV (a)  An 2 (b) 0 (c) An 2 (d) An 2 T T T 45. A vessel containing equal number of molecules of two monatomic gases A and B is at temperature T. Their masses are m and 4 m respectively the rrot mean squared velocity of the atoms in the mixture is 3 8kT 8kT 3 16kT 16kT (a) (b) (c) (d) 4 Sm Sm 4 5Sm 5Sm 46. A mixture contains the same number of moles of two ideal gases A and B, with An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  33 adiabatic constants J A and J B respectively. The adiabatic constant of the mixture satisfies : 1 1§ 1 1 · 1 1§ 1 1 · (a) J  1 ¨  ¸ (b) J  1 2 ¨ J  1  J  1 ¸ 2 © J A 1 J B 1 ¹ © A B ¹ 1 1§ 1 1 · 1 1§ 1 1 · (c) J  1 2 ¨ J  1  J  1 ¸ (d) J  1 2 ¨ J  1  J  1 ¸ © A B ¹ © A B ¹ 47. Two solid blocks, one at the temperature T1 ant the other T2 F1 ! T2 with the same temperature independent heat capacity C are put in contact with each other. The change in entropy of the universe after they have equilibrated is : ª§ T  T 2 ·º « 1 2 ¸» §T · (a) C An «¨¨ 4T T 1 ¸» (b) C An ¨ T ¸ ¬© 1 2 ¹¼ © 2¹ § T T · 1 2 (c) C An ¨ T  T ¸ (d) C © 1 2 ¹ 48. The specific heat at constant volume of the electrons in a metal Cv DT. Where T is the temperature and D is a constant. The specific entropys is given by D 2T 2 (a) N B (b) N B DT (c) DT (d) NB 49. N1 moles of an ideal monoatomie gas are mixed with N 2 moles of an ideal diatomic gas. If the mixture is allowed to expand adiabatically, the relation between its pressure and volume is PV J constant, where J is equal to 3 7 N1  N 2 N1  N 2 5 N1  7 N 2 (a) 5/3 (b) 5 5 (c) 3 N  5 N (d) 3 N1  5 N 2 N1  N 2 1 2 5 7 50. A certain gas has equation of state p DN 2T / V 2 , where p is the pressure, N, the number of moles ‘V’ the volume and T, the temperature D is a constant_ One mole of the gas undergoes expansion from volume ‘V’ to as `2V’ at con- stant temperature T. Given that 1 the change in energy in the isotheriormal expansion is DT DT DT (a) 0 (b) (c) (d) An 2 V V V An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  34 1.(b) 2.(d) 3.(c) 4.(a) 5.(c) 6.(c) 7.(c) 8.(a) 9.(b) 10.(d) 11.(c) 12.(b) 13.(b) 14.(d) 15.(c) 16.(b) 17.(a) 18.(c) 19.(b) 20.(a) 21.(a) 22.(a) 23.(c) 24.(b) 25.(d) 26.(a) 27.(a) 28.(c) 29.(a) 30.(c) 31.(a) 32.(d) 33.(c) 34.(c) 35.(a) 36.(c) 37.(a) 38.(d) 39.(c) 40.(d) 41.(c) 42.(a) 43.(d) 44.(c) 45.(a) 46.(a) 47.(a) 48.(c) 49.(c) 50.(a) STATICALS-I GATE Previous Year's Questions 1. A cavity of volume V contains blackbody radiation at an absolute temperature T. Which of the following option is incorrect? [GATE 1991] (a) The internal energy of the radiation is proportional to T 2 (b) The specific heat of radiation is proportional to T 3 (c) The pressure of the rad ia6on is proportional to T 4 (d) Although the radiation is in thermal evailiniurn, the camber olphotons in the cavity is not coastant in time. 2. The distribution function f H for a photon gas is given by [GATE 1995] 1 (a) exp H / kT (b) exp H / kT  1 1 1 (c) exp H / kT  1 (d) exp H / kT  1 3. A m iaocanonical ensemble represents [GATE 1997] (a) a system in contact with a heat reservoir (b) an isolated system in equariwn (c) a system that can exchange particles with its surroundings (d) a system under constant extemat pressure 4. A system has N distinguishable particles. Each particle can occupy one of the two non-degenerate states with an energy difference of 0.1 eV. If the system is in thermal equilibrium at room temperature, the approximate fraction of particles in the higher energy state is : [GATE 1998] (a) an assembly of Bose gas condences to the band state An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  35 (b) there is an appreciable of occuration of the..... in an electron system (c) there is a significantly large occupancy of the ground state in a system of bosons (d) the bosons essentially beharve like fermous 6. Choose the correct alternatives [GATE 1999] At the same temperature (a) a fermion gas will exert the greatest pressure (b) a boson gas will exert the greatest pressure (c)a fennion gas will exert least pressure (d) a boson gas will exert the least pressure 7. Two particles are said to be distinguish when [GATE 2000] (a) the average distance between them is largeg compared to their do Broglie wavelength (b) the average distance between them is small compared to their do Broglie wavelength (c) they have overlapping wavepackers (d) their total wave function is symmetric under particle exchange 8. In a canonical ensemble [GATE 2000] (a) the energy and the temperature are constants (b) the entropy and, the energy are constans (c) the temperature and the density are constants (d) the density and the entropy are constants 9. The Fermi energy of a free electron gas depends on the electron density p as [GATE 2000] (a) p1/2 (b) p 2/3 (c) p 1/3 (d) p 2/3 10. For an energystate E of a photon gas, the density of states is proportional to [GATE 2001] (a) 3 (b) E (c) E 1 2 (d) E 2 11. The rotational partition function of a diatomic molecule of moment of inertia 1 at a temperature T is given by [GATE 2001] 1k BT 2k BT 3k BT 1k BT (a) (b) (c) (d) =2 =2 =2 2= 2 12. In a classical micro-canonical ensemble for a system of N non-intercting particles, the fundamental volume in phase space which is regarded as "equivalent to one micro-state" is [GATE 2002] An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  36 (a) h314 (b) h 214 (c) h14 (d) h where h is the Planck’s constant. 13. Which of the following statements is true? [GATE 2002] (a) In a micro-canonical ensemble the total number of particles N and the energy E are constants while in a canonical ensemble N and teinperatureT are constants (b) In a micro-canonical ensemble the total number of particles N is a constant but the energy E is variable while in a canonical ensemble N and T are constants (c) In a macro-canonical ensemble N and E are constants while in a canonical ensemble N and T both vary (d) In a micro-canonical ensemble N and E are constants while in acanonicat ensemble N is a constant but T varies 14. Which of the following relations between the particle number density n and temp enure T must hold good fora gas consisting of non-interacting particles to be describe by quantum statistics? [GATE 2002] (a) n / T 1/2  1 (b) n / T 3/2  1 (c) n / T 3/2 !! 1 (d) n / T 3/2 and n / T 1/2 can have any value 15. Which of the following conditions should be satisfied by the temperature T of a system of N non-interacting particles occupying a volume V, for Bose-Einstein condensation to take place? [GATE 2002] 2 ­ ½ 3 h 2 °° N °° T ® ¾ (a) 2Smk B ° § 3 · ° (b) V]¨ ¸ ¯° © 2 ¹ ¿° 1 ­ ½ 2 h 2 ° ° N °° T ® ¾ (c) 2Smk B ° § 3 · ° (d) V] °¯ ¨© 2 ¹¸ °¿ where m is the mass of each particle of the system, kB is the Boltzman constant, h is the the planck's constant well ] is the well known Zeta function. 16. Consider the Fermi-Dirac distribution function (E) isom temperature (300K) where E refers to energy. If EF is the Fermi energy, which of the following is true ? [GATE 2003] (a) f E a step function An Institute for NET/JRF Physical Science, IIT-JAM, JEST TIFR & M.Sc. Entrances  37 (b) f EF has a value of 1/2 (c) States with E  EF are filled completely (d) f E is large and tends to infinity as E decreases much below EF 17. Consider black body radiation in a cavity maintained at 2000K. If the volume of the cavity is reversibly and adiabatically increased from 10cm3 to 610cm3 , the temperature of the cavity changes to [GATE 2004] (a) 800K (b) 700 K (c) 600K (d) 500K 18. The number of states for a system of N identical free particles in a three dimensional space having total energy between E and E  GE GE  E is proportional to [GATE 2005] § 3N 1 · ¨ 2 ¸ GE N 1 (a) ¨ E ¸ (b) (c) (d) N N GE © ¹ E 2 GE NE 2 GE 19. The total number of accessible states of N non intracting particles of spin 1/2 is (a) 2 N (b) N 2 (c) 2 N N /2 (d) N 20. The dimension of phase space of ten rigid diatomic molecules is [GATE 2005] (a) 5 (b) 10 (c) 50 (d) 100 21. Aone dimensional random walker takes steps to left or right with equal probability. The probability that the random walker starting from origin is back to origin after N even number of steps is [GATE 2005] 14 N! §1· N! ¨ ¸ (a) § N · !§ N ·! © 2 ¹ (b) §¨ N ·¸ !§¨ N ·¸ ! ¨ ¸¨ ¸ ©2¹©2¹ ©2¹©2¹ 2N N §1· §1· (c) 2 N !¨ ¸ (d) N !¨ ¸ ©2¹ ©2¹ 22. If the partition function of a harmonic oscillator with frequency Z at a kT temperature T is , then the free energy of N such independent osci