Physics Past Paper Questions PDF

```markdown ## JOSHI CLASSES **A TRADITION OF EXCELLENCE | Since 2007** For Admission Enquiries Near Oscar School, Keshavnagar, Mundhwa, Pune - 36 9881056678 / 7385132654 ### 1 ROTATIONAL DYNAMICS **Theory:** **(1)** Derive an expression for kinetic energy, when a rigid body is rolling on a horiz...

```markdown ## JOSHI CLASSES **A TRADITION OF EXCELLENCE | Since 2007** For Admission Enquiries Near Oscar School, Keshavnagar, Mundhwa, Pune - 36 9881056678 / 7385132654 ### 1 ROTATIONAL DYNAMICS **Theory:** **(1)** Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping. Hence find kinetic energy for a solid sphere. (March 2013) (3) **(2)** A particle of mass m, just completes the vertical circular motion. Derive the expression for the difference in tensions at the highest and the lowest points.(March 2013) (3) **(3)** For a particle performing uniform circular motion $\vec{v} = \vec{\omega} \times \vec{r}$, obtain an expression for linear acceleration of the particle performing non-uniform circular motion.(Feb. 2014) (2) **(4)** State and prove the theorem of 'parallel axes'.(Feb. 2014, 2016) (4) **(5)** State the law of conservation of angular momentum and explain with a suitable example.(Oct. 2014; July 2022) (2) **(6)** Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road. Write the necessary equation for maximum safety, speed and state the significance of each term involved in it.(Oct. 2014) (3) **(7)** In circular motion, assuming $\vec{v} = \vec{\omega} \times \vec{r}$, obtain an expression for the resultant acceleration of a particle in terms of tangential and radial component.(Feb. 2015) (2) **(8)** State the theorem of parallel axes and theorem of perpendicular axes about moment of inertia.(Feb. 2015) (2) **(9)** State an expression for the moment of inertia of a solid uniform disc, rotating about an axis passing through its centre, perpendicular to its plane. Hence derive an expression for the moment of inertia and radius of gyration: (i) about a tangent in the plane of the disc, and (ii) about a tangent perpendicular to the plane of the disc.(Oct. 2015) (4) **(10)** Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length.(Oct. 2015) (2) **(11)** In U. C. M. (Uniform Circular Motion), prove the relation $\vec{v} = \vec{\omega} \times \vec{r}$, where symbols have their usual meanings.(Feb. 2016) (2) **(12)** Obtain an expression for total kinetic energy of a rolling body in the form $\frac{1}{2}MV^2(1+ \frac{K^2}{R^2})$(Feb. 2016) (2) **(13)** Obtain an expression for torque acting on a body rotating with uniform angular acceleration.(July 2016, 2017) (3) **(14)** Draw a neat labelled diagram showing the various forces and their components acting on a vehicle moving along curved banked road.(July 2016) (2) **(15)** Explain the concept of centripetal force.(March 2017) (2) **(16)** Explain the physical significance of radius of gyration.(July 2017) (2) **(17)** Define moment of inertia. State its SI unit and dimensions.(October 2008, March 2018) (3) **(18)** Distinguish between centripetal force and centrifugal force.(March 2009, 2010, 2018) (2) **(19)** State and prove the law of conservation of angular momentum.(March 2011, 2018; Oct. 2011, 2015; Feb. 2023) (2) **(20)** Define radius of gyration. Explain its physical significance.(March 2008, 2019, July 2018) (2) **(21)** What is the value of tangential acceleration in U.C.M.?(March 2019) (1) **(22)** Obtain expressions of energy of a particle at different positions in the vertical circular motion.(March 2019) (3) **(23)** Define U.C.M. Name the forces acting on a body executing non-uniform circular motion.(July 2019) (2) **(24)** Explain the principle of conservation of angular momentum with the help of two appropriate examples.(July 2019) (2) **(25)** Define uniform circular motion.(March 2020) (1) **(26)** Obtain the relation between the magnitude of linear acceleration and angular acceleration in circular motion.(March 2020) (2) **(27)** State and prove the principle of parallel axes in rotational motion.(March 2020) (3) **(28)** State the formula for moment of inertia of solid sphere about an axis passing through its center.(Oct. 2021) (1) **(29)** Using the energy conservation, derive the expression for minimum speeds at different locations along a al circular motion controlled by gravity.(Oct. 2021) (4) **(30)** Define moment of inertia of a rotating rigid body, State its SI Unit and dimensions.(March 2022) (2) **(31)** Derive an expression for the kinetic energy of a body rotating with a uniform angular speed.(March 2022) (2) **(32)** Derive an expression for kinetic energy of a rotating body.(July 2022) (3) **(33)** If friction is made zero for a road, can a vehicle move safely on this road?(Feb. 2023) (1) **(34)** Derive an expression for linear velocity at lowest position, midway position and the top-most position for a particle revolving in a vertical circle, if it has to just complete circular motion without string slackening at top.(Feb. 2023) (4) ***(316)*** --- ## JOSHI CLASSES **Summary of Board Questions** **A TRADITION OF EXCELLENCE | Since 2007** ### Problems: **(1)** A car of mass 1500kg rounds a curve of radius 250 m at 90 km/hour. Calculate the centripetal force acting on it. [Ans. 3750 N] (March 2013) (2) **(2)** A wheel of moment of inertia 1 kgm² is rotating at a speed of 40 rad/s. Due to friction on the axis, the wheel comes to rest in 10 minutes. Calculate the angular momentum of the wheel, two minutes before it comes to rest. [Ans. 8 kg-m²/s](March 2013) (2) **(3)** A ballet dancer spins about a vertical axis at 2.5n rad/sec. with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new rotation in r.p.m.[Ans. 100 r.p.m](Oct 2013) (3) **(4)** A racing car completes 5 rounds on a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of n² m/s². [Ans. 144 m](Oct 2013) (2) **(5)** In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a vertical axis, calculate tension in the string (g = 9.8 m/s²)[Ans. 1.491 N](Oct 2013) (3) **(6)** A stone of mass 1 kg is whirled in horizontal circle attached at the end of a 1 m long string. If the string makes an angle of 30º with vertical, calculate the centripetal force acting on the stone.(g = 9.8 m/s²).[Ans. 5.658 N](Feb. 2014) (2) **(7)** A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 12 cm,calculate its moment of inertia about an axis passing through its centre and perpendicular to its length.[Ans. 650 g-cm²](Feb. 2014) (2) **(8)** A body starts rotating from rest. Due to a couple of 20 Nm it completes 60 revolutions in one minute. Find the moment of inertia of the body.[Ans. 95.51 kg.m²] (Oct. 2014) (3) **(9)** A stone of mass 5 kg, tied to one end of a rope of length 0.8 m, is whirled in a vertical circle. Find the minimum velocity at the highest point and at the midway point. [g = 9.8 m/s²][Ans. 4.484 m/s](Oct 2014) (2) **(10)** The spin dryer of a washing machine rotating at 15 r.p.s. slows down to 5 r.p.s. after making 50 revolutions. Find its angular acceleration.[Ans. - 12.56 rad/s²](Feb. 2015) (2) **(11)** A horizontal disc is freely rotating about a transverse axis passing through its centre at the rate of 100 revolutions per minute. A 20 gram blob of wax falls on the disc and sticks to the disc at a distance of 5 cm from its axis. Moment of inertia of the disc about its axis passing through its centre of mass is 2 × 10-4 kg m². Calculate the new frequency of rotation of the disc.[Ans. 80 r.p.m](Feb. 2015) (3) **(12)** A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at lowest point as 7 m/s. Find the velocity at the highest point. [Acceleration due to gravity = 9.8 m/s²]. [Ans. 5.422 m/s](Oct. 2015) (3) **(13)** A coin kept at a distance of 5 cm from the centre of a turntable of radius 1.5 m just begins to slip when the turntable rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the turntable. [g = 9.8 m/s²][Ans. 0.4533](Feb. 2016) (2) **(14)** A stone of mass 2 kg is whirled in a horizontal circle attached at the end of 1.5 m long string.**If the string makes an angle of 30º with vertical, compute its period. (g=9.8 m/s²)[Ans. 2.291 s] (July 2016) (2) **(15)** A uniform solid sphere has a radius 0.1 m and density 6 × 103 kg/m³. Find its moment of inertia about a tangent to its surface. [Ans. 0.3485 kg.m²](July 2016) (2) **(16)** A solid sphere of mass 1 kg rolls on a table with linear speed 2 m/s, find its total kinetic energy. [Ans. 2.8J](March 2017) (2) **(17)** A vehicle is moving on a circular track whose surface is inclined towards the horizontal at an angle of 10°.The maximum velocity with which it can move safely is 36 km/hr. Calculate the length of the circular track.[π = 3.142] [Ans. 363.7 m] (March 2017) (3) **(18)** A small body of a mass 0.3 kg oscillates in vertical plane with the help of a string 0.5 m long with a constant speed of 2 m/s. It makes an angle of 60º with the vertical. Calculate tension in the string.(g = 9.8 m/s²)[Ans. 3.87 N](July 2017) (2) **(19)** A uniform solid sphere has radius 0.2 m and density 8 × 103 kg m³. Find the moment of inertia about the tangent to its surface. (π = 3.142) [Ans. 15.02 kg.m²](July 2017) (3) **(20)** Curve on a curve on highway has a radius of curvature 400 m. A car goes around a curve at a speed of 32 m/s. What is the minimum value of coefficient of friction that will prevent the card from sliding? (g = 9.8 m/s²) [Ans. 0.21612](March 2018) (2) **(21)** The frequency of revolution of a particle performing circular motion changes from 60 r.p.m to 180 r.p.m. in 20 seconds. Calculate the angular acceleration of the particle. (π = 3.142)[Ans. 0.628 rad/s²](July 2018) (2) **(22)** A meter gauge train is moving at 72 km/hr along a curved railway of radius of curvature 500 m at a certain place. Find the elevation of outer rail above the inner rail so that there is no side pressure on the rail.(g = 9.8 m/s²) [Ans. 0.08163 m](July 2018) (3) --- ## JOSHI CLASSES **Summary of Board Questions** **A TRADITION OF EXCELLENCE | Since 2007** **(23)** A solid sphere of diameter 50 cm and mass 25 kg rotates about an axis through its centre.Calculate its moment of inertia. If its angular velocity changes from 2 rad/s to 1 rad/s in 5 seconds, calculate the torque applied.[Ans. I = 0.625 kg·m²; t = 1.25 N-m](July 2018) (3) **(24)** A wheel of moment of inertia 1 kg m² is rotating at a speed of 30 rad/s. Due to friction on the axis, it comes to rest in 10 minutes. Calculate the average torque of the friction. [Ans. – 0.05 Nm](March 2019) (2) **(25)** The radius of gyration of a body about an axis, at a distance of 0.4 m from its centre of mass is 0.5 m.*Find its radius of gyration about a parallel axis passing through its centre of mass.[Ans. 0.3 m](March 2019) (2) **(26)** A car rounds a curve of radius 625 m with a speed of 45 m/s. What is the minimum value of coefficient of friction which prevents the car from sliding?[Ans. 0.3306](July 2019) (2) **(27)** Find the frequency of revolution of a round disco stage revolving with an angular speed of 300 degree/second.[Ans. 0.8333 Hz](July 2019) (2) **(28)** Energy of 1000 J is spent to increase the angular speed of a wheel from 20 rad/s to 30 rad/s. Calculate the moment of inertia of the wheel.[Ans. 4 kg-m²](March 2020) (2) **(29)** In a circus, a motor-cyclist having mass of 50 kg moves in a spherical cage of radius 3m. Calculate the least velocity with which he must pass the highest point without losing contact. Also calculate his angular speed at the highest point.[Ans. 5.422 m/s; 1.807 rad/s](March 2020) (3) **(30)** A motor cyclist (to be treated as a point mass) is to undertake horizontal circles inside the cylindrical wall of a well of inner radius 4 m. The co-efficient of static friction between tyres and the wall is 0.2. Calculate the minimum speed and period necessary to perform this stunt.[Ans. 14 m/s; 1.796 s](Oct. 2021) (2) **(31)** Calculate the moment of inertia of a uniform disc of mass 10 kg and radius 60 cm about an axis perpendicular to its length and passing through its centre.[Ans. 1.8 kg-m²](March 2022) (1) **(32)** The surface density of a uniform disc of radius 10 cm is 2 kg/m². Find its M.I. about an axis passing through its centre and perpendicular to its plane.[Ans. 3,142 × 10-4 kg-m²](July 2022) (2) ### Theory: #### 2 MECHANICAL PROPERTIES OF FLUIDS **(1)** Derive the relation between surface tension and surface energy per unit area. (March 2013) (2) **(2)** Show that the surface tension of a liquid is numerically equal to the surface energy per unit area.(Oct 2013) (2) **(3)** Explain the rise of liquid in the capillary on the basis of pressure difference.(Feb. 2014) (2) **(4)** Define angle of contact. State its any two characteristic.(Oct. 2011, 2014; July 2022) (2) **(5)** Derive an expression for excess pressure inside a drop of liquid.(Feb. 2015) (2) **(6)** Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube.(Oct. 2015) (2) **(7)** Derive Laplace's law for spherical membrane of bubble due to surface tension.(Feb. 2016, March 2018) (3) **(8)** Draw a neat diagram for the rise of liquid in a capillary tube showing the components of a surface tension.(March 2010, July 2016) (2) **(9)** Draw a neat labelled diagram for a liquid surface in contact with a solid, when the angle of contact is acute.(March 2017) (2) **(10)** Define surface tension and surface energy.(July 2017) (3) **(11)** What is capillarity? State any two uses of capillarity.(October 2010, March 2011, July 2018, 2022) (2) **(12)** Obtain an expression for the rise of a liquid in a capillary tube.(March 2019) (3) **(13)** On the basis of molecular theory explain the phenomenon of surface tension.(July 2019) (3) **(14)** Define angle of contract.(Oct. 2021) (1) **(15)** Explain surface tension on the basis of molecular theory.(Oct. 2021) (3) **(16)** State the formula for critical velocity in terms of Reynold's number for a flow of a fluid.(March 2022) (1) **(17)** Derive an expression for terminal velocity of a spherical object falling under gravity through a viscous medium.(March 2022) (3) **(18)** Define coefficient of viscosity. State its formula and S.I. units.(Feb. 2023) (2) **(19)** Obtain the relation between surface energy and surface tension.(Feb. 2023) (2) **Problems**: **(1)** The surface tension of water at 0°C is 75.5 dyne/cm. Find surface tension of water at 25°C. [a for water = 0.0021/°C][Ans. 71.52 dyne/cm](March 2013, 2015) (2) **(2)** A soap bubble of radius 12 cm is blown. Surface tension of soap solution is 30 dyne/cm. Calculate the work done in blowing the soap bubble.[Ans. 1.086 × 105 erg](Oct 2013) (2) **(3)** Calculate the density of paraffin oil, if glass capillary of diameter 0.25 mm dipped in paraffin oil of surface tension 0.0245 N/m rises to a height of 4 cm.[Angle of contact of paraffin with glass = 28° and acceleration due to gravity = 9.8 m/s².)(Feb. 2014) (3) **(4)** Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section.[Ans. 4.525 cm](Oct. 2014) (2) --- ## JOSHI CLASSES **A TRADITION OF EXCELLENCE | Since 2007** **Summary of Board Questions:** **(5)** A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0.072 N/m, atmospheric pressure = 1.013 × 105 N/m²][Ans. 1.01372 × 105 N/m²] (Oct. 2015) (2) **(6)** The energy of the free surface of a liquid drop is 5 times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system. [Ans. 2.236 cm](Feb. 2016) (2) **(7)** The total free surface energy of a liquid drop is $\pi \sqrt{2}$ times the surface tension of the liquid. Calculate the diameter of the drop in S.I. unit. [Ans. 1.1896 m](July 2016) (2) **(8)** The total energy of free surface of a liquid drop is $2\pi$ times the surface tension of the liquid. What is the diameter of the drop? [Assume all terms in SI unit]. [Ans. 1.414 m](March 2017) (3) **(9)** Two soap bubbles have radii in the ratio 4:3. What is the ratio of work done to blow these bubbles? [Ans. 16:9](July 2017) (2) **(10)** Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of soap solution is $30 \frac{dyne}{cm}$. ($\pi$ = 3.142) [Ans. 2262 erg](March 2018) (2) **(11)** A horizontal circular loop of a wire of radius 0.02 m is lowered into crude oil and a film is formed. The force due to the surface tension of the liquid is 0.0113 N. Calculate the surface tension of the crude oil.($\pi$ = 3.142) [Ans. 0.045 N/m](July 2018) (3) **(12)** A rod of length 4 cm is movable on a rectangular frame of wire. A film is formed in the frame. A force of 3.2 × 10-3 N is applied to the rod for its equilibrium. Find the surface tension of the liquid.[Ans. 0.04 N/m](July 2019) (1) **(13)** Calculate the work done in blowing a soap bubble of radius 0.1 m. (Surface tension of soap solution = $\frac{30 dyne}{cm}$) [Ans. 7.541 × 10-3 J](March 2020) (2) **(14)** Compare the amount of work done in blowing two soap bubbles of radii in the ratio 4 : 5. [Ans. 16:25](Oct. 2021) (2) **(15)** Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Fine the decrease in the surface area. [Ans. 2.011 × 10-6 m²](March 2022) (2) **(16)** Find the difference of pressure between inside and outside of a spherical water drop of radius 2 mm, if surface tension of water is $73 \times 10^{-3} N/m$. [Ans. 73 N/m²](July 2022) (2) **(17)** Calculate the work done in blowing a soap bubble to a radius of 1 cm. The surface tension of a soap solution is 2.5 x 10-2 N/m.[Ans. 62.84 × 10-6 J](Feb. 2023) (2) ### Theory: #### 3 KINETIC THEORY OF GASES AND RADIATION **(1)** Draw a neat labelled diagram for Ferry's perfectly black body.(March 2013, July 2018) (2) **(2)** Explain black body radiation spectrum in terms of wavelength.(Oct 2013) (2) **(3)** Show that R.M.S. velocity of gas molecules is directly proportional to square root of its absolute temperature.(Feb. 2014, March 2017) (2) **(4)** Show graphically spectrum of energy distribution of black body in terms of wavelengths.(Oct. 2008, 2009, Feb. 2014) (2) **(5)** Explain Maxwell distribution of molecular speed with necessary graph.(Oct 2014) (3) **(6)** With a neat and labelled diagram, explain Ferry's perfectly black body. (Oct 2014) (2) **(7)** State: (a) Wein's displacement law and (b) First law of thermodynamics.(Feb. 2015) (2) **(8)** Define 'emissive power' and 'coefficient of emission of a body'.(Feb. 2016) (2) **(9)** State Kirchhoff's law of radiation and prove it theoretically.(March 2012, July 2017, 2019) (3) **(10)** What is perfectly black body? Explain Ferry's black body.(March 2019) (3) **(11)** State Boyle's law. On the basis of kinetic theory of gases, obtain an expression for kinetic energy per unit volume of gas.(March 2020) (3) **(12)** Explain energy distribution spectrum of a black body radiation in terms of wavelength.(March 2020) (3) **(13)** Draw a neat, labelled diagram of Ferry's black body.(Oct. 2021) (2) **(14)** State: (a) Stefan - Baltzmann law radiation. (b) Wien's displacement law.(Oct. 2021) (2) **(15)** Derive an expression for a pressure exerted by a gas on the basis of kinetic theory of gases.(March 2022; Feb. 2023) (4) **(16)** Define: (i) Emissive power (ii) Co-efficient of emission(July 2022) (2) ### Problems: **(1)** Calculate the kinetic energy of 10 gram of Argon molecules at 127°C.(Universal gas constant R = 8320 J/k mole K, Atomic weight of Argon = 40) [Ans. 1248 J](March 2013) (3) --- ## JOSHI CLASSES **A TRADITION OF EXCELLENCE | Since 2007** **(2)** The kinetic energy of nitrogen per unit mass at 300 K is 2.5 × 106 J/kg. Find the kinetic energy of 4 kg oxygen at 600 K. (Molecular weight of nitrogen = 28, Molecular weight of oxygen = 32) [Ans. 1.75 × 107 J](Oct 2013) (3) **(3)** Calculate the average molecular kinetic energy:(a) per kilomole (b) per kilogram of oxygen at 27°C. [R = 8320 J/kmole K, Avogadros number = 6.03 × 1026 molecules/K mole] [Ans. (a) 3.744 × 106 J (b) 1.17 × 105 J] (Feb. 2015) (3) **(4)** A pinhole is made in a hollow sphere of radius 5 cm whose inner wall is at temperature 727°C. Find the power radiated per unit area. [Stefan's constant $\sigma = 5.7 \times 10^{-8} J/m^2sK^4$, emissivity (e) = 0.2] [Ans. 1.14 × 104 watt/m²] (Oct. 2015) (2) **(5)** Compute the temperature at which the r.m.s. speed of nitrogen molecules is 832 m/s. [Universal gas constant, R = 8320 J/k mole K, molecular weight of nitrogen = 28.] [Ans. 776.53 K](Oct. 2015) (2) **(6)** A metal sphere cools at the rate of 4°C / min. when its temperature is 50°C. Find its rate of cooling at 45° C if the temperature of surrounding is 25°C.[Ans. 3.2°C/min.](Feb. 2016) (3) **(7)** A body cools from 62°C to 54°C in 10 minutes and 48°C in next 10 minutes. Find the temperature of the surroundings. [Ans. 30°C](July. 2016) (3) **(8)** A body cools at the rate of 0.5° C/min. when it is 25°C above the surroundings. Calculate the rate of cooling when it is 15°C above the same surroundings.[Ans. 0.3°C/min](March 2017) (2) **(9)** At what temperature will average kinetic energy of gas be exactly half of its value at N.T.P.?[July 2017) (2) **(10)** A body cools from 80°C to 70°C in 5 minutes and to 62°C in the next 5 minutes. Calculate the temperature of the surroundings.[Ans. 30°C](Feb. 2018) (3) **(11)** Compare-the rates of loss of heat by a black body at 627°C and 327°C, if the temperature of surrounding is 27°C[Ans. 5.33:1](July 2018) (3) **(12)** The difference between two molar specific heats of a gas is 6000 J/kg. K. If the ratio of specific heats is 1.4 calculate the molar specific heat at constant volume. [Ans. 15000 J/kg K](Oct. 2021) (2) **(13**) The difference between the two molar specific heats of a gas is 9000 J/kg K. If the ratio of the two specific is 1.5, calculate the two molar specific heats. [Ans. Cp = 27000 J/kg K; Cν = 18000 J/kg K](March 2022) (2) **(14)** Calculate the energy radiated in half a minute by a black body of surface area 200 cm² at 127°C. [Ans. 875.5 J] (July 2022) (3) **(15)** Compare the rate of loss of heat from a metal sphere at 827°C with rate of loss of heat from the same at 427°C, if the temperature of surrounding is 27°C[Ans. 6.267] (Feb. 2023) (2) ### Theory: #### 4 THERMODYNAMICS **(1)** State first law of thermodynamics.(Feb. 2015) (4) **(2)** What is isothermal process?(March 2020, Oct. 2021) (1) **(3)** Write a note on free expansion in thermodynamic process.(Oct 2021) (2) **(4)** What is a thermodynamic process ? Give any two types of it.(March 2022) (2) **(5)** What are mechanical equilibrium and thermal equilibrium ?(March 2022) (2) **(6)** In which thermodynamic process the total internal energy of system remains constant?(July 2022) (1) **(7)** State zeroth law of thermodynamics. What are the limitations of first law of thermodynamics?(July 2022) (3) **(8)** Derive an expression for the work done during an isothermal process.(Feb. 2023) (2) **Problems:** **(1)** 0.5 mole of gas at temperature 450 K expands isothermally from an initial volume of 3L to final volume of 9L. **(a)** What is the work done by the gas? (R = 8.319 J mol-1 K-1) **(b)** How much heat is supplied to the gas?[Ans. (a) 2.057 kJ (b) 2.057 kJ](Oct 2021) (3) **(2)** The initial pressure and volume of a gas enclosed in a cylinder are 2 × 105 N/m² and 6 × 10-3 m³ respectively. If work done in compressing the gas at constant pressure is 150 J, find the final volume of the gas.[Ans. 5.25 x 10-3 m³](March 2022) (2) **(3)** An automobile engine develops 62.84 kW while rotating at a speed of 1200 rpm. What torque does it deliver? [Ans. 500 N·m](July 2022) (1) **(4)** A system releases 125 kJ of heat while 104 kJ of work is done on the system. Calculate the change in internal energy of the gas.[Ans. 21 kJ](July 2022) (2) **(5)** 104 J of work is done on certain volume of a gas. If the gas releases 125 kJ of heat, calculate the change in internal energy of the gas.[Ans. 124.9 kJ](Feb. 2023) (2) **(6)** An