Chapter 10 Thermodynamics and Thermochemistry PDF

Thermodynamics and Thermochemistry 403 60 ` Chapter E3 10 Thermodynamics and Thermochemistry (iii) Open system : This type of system can exchange matter as well as energy with its surroundings. The boundary is neither sealed nor insulated. Sodium reacting with water in an open beaker is an example o...

Thermodynamics and Thermochemistry 403 60 ` Chapter E3 10 Thermodynamics and Thermochemistry (iii) Open system : This type of system can exchange matter as well as energy with its surroundings. The boundary is neither sealed nor insulated. Sodium reacting with water in an open beaker is an example of open system. (iv) Homogeneous system : A system is said to be homogeneous when it is completely uniform throughout. A homogeneous system is made of one phase only. Examples: a pure single solid, liquid or gas, mixture of gases and a true solution. (v) Heterogeneous system : A system is said to be heterogeneous when it is not uniform throughout, i.e., it consist of two or more phases. Examples : ice in contact with water, two or more immiscible liquids, insoluble solid in contact with a liquid, a liquid in contact with vapour, etc. (vi) Macroscopic system : A macroscopic system is one in which there are a large number of particles (may be molecules, atoms, ions etc. ) (3) Macroscopic properties of the system Thermodynamics deals with matter in terms of bulk (large number of chemical species) behaviour. The properties of the system which arise from the bulk behaviour of matter are called macroscopic properties. The common examples of macroscopic properties are pressure, volume, temperature, surface tension, viscosity, density, refractive index, etc. The macroscopic properties can be subdivided into two types, (i) Intensive properties : The properties which do not depend upon the quantity of matter present in the system or size of the system are called intensive properties. Its examples are pressure, temperature, density, specific heat, surface tension, refractive index, ID Thermodynamics Basic concepts D YG U Thermodynamics (Greek word thermo means heat and dynamics means motion) is the branch of science which deals with the study of different forms of energy and the quantitative relationships between them. The complete study of thermodynamics is based upon three generalizations called first, second and third law of thermodynamics. These laws have been arrived purely on the basis of human experience and there is no theoretical proof for any of these laws. ST U (1) System, surroundings and Boundary : A specified part of the universe which is under observation is called the system and the remaining portion of the universe which is not a part of the system is called the surroundings. The system and the surroundings are separated by real or imaginary boundaries. The boundary also defines the limits of the system. The system and the surroundings can interact across the boundary. (2) Types of systems (i) Isolated system : This type of system has no interaction with its surroundings. The boundary is sealed and insulated. Neither matter nor energy can be exchanged with surrounding. A substance contained in an ideal thermos flask is an example of an isolated system. (ii) Closed system : This type of system can exchange energy in the form of heat, work or radiations but not matter with its surroundings. The boundary between system and surroundings is sealed but not insulated. For example, liquid in contact with vapour in a sealed tube and pressure cooker. 404 Thermodynamics and Thermochemistry Macroscopic properties which determine the state of a system are referred to as state variables or state functions or thermodynamic parameters. The change in the state properties depends only upon the initial and final states of the system, but it is independent of the manner in which the change has been brought about. In other words, the state properties do not depend upon a path followed. (vii) Irreversible process : When the process occurs from initial to final state in single step in finite time and cannot be reversed, it is termed an irreversible process. Amount of entropy increases in irreversible process. Irreversible processes are spontaneous in nature. All natural processes are irreversible in nature Internal energy, heat and Work (1) Internal energy (E) : “Every system having some quantity of matter is associated with a definite amount of energy. This energy is known as internal energy.” E  E translatio nal  Erotational  E vibrationa l  E bonding  Eelectronic ...... ID (5) Thermodynamic equilibrium : “A system is said to have attained a state of thermodynamic equilibrium when it shows no further tendency to change its property with time”. (vi) Reversible process : A process which occurs infinitesimally slowly, i.e. opposing force is infinitesimally smaller than driving force and when infinitesimal increase in the opposing force can reverse the process, it is said to be reversible process. 60 (4) State of a system and State Variables initial state, it is termed cyclic process. For a cyclic process dE = 0 and dH = 0. E3 viscosity, melting point, boiling point, volume per mole, concentration etc. (ii) Extensive properties : The properties whose magnitude depends upon the quantity of matter present in the system are called extensive properties. Its examples are total mass, volume, internal energy, enthalpy, entropy etc. These properties are additive in nature. Any extensive property if expressed as per mole or per gram becomes an intensive property. (i) Characteristics of internal energy (a) Internal energy of a system is an extensive property. (i) Chemical Equilibrium : A system in which the composition of the system remains fixed and definite. (c) The change in the internal energy does not depend on the path by which the final state is reached. (ii) is done between achieved D YG U The criterion for thermodynamic equilibrium requires that the following three types of equilibrium exist simultaneously in a system, Mechanical Equilibrium : No chemical work between different parts of the system or the system and surrounding. It can be by keeping pressure constant. (iii) Thermal Equilibrium : Temperature remains constant i.e. no flow of heat between system and surrounding. U (6) Thermodynamic process : When the thermodynamic system changes from one state to another, the operation is called a process. The various types of the processes are ST (i) Isothermal process : In this process operation is done at constant temperature. dT = 0 thus E  0. (ii) Adiabatic process : In this a process there is no exchange of heat takes place between the system and surroundings. The system is thermally isolated, i.e., dQ = 0 and its boundaries are insulated. (iii) Isobaric process : In this process the pressure remains constant throughout the change i.e., dP = 0. (iv) Isochoric process : In this process volume remains constant throughout the change, i.e., dV = 0. (v) Cyclic process : When a system undergoes a number of different processes and finally return to its (b) Internal energy is a state property. (d) There is no change in internal energy in a cyclic process. (e) The internal energy of an ideal gas is a function of temperature only. (f) Internal energy of a system depends upon the quantity of substance, its chemical nature, temperature, pressure and volume. (g) The unit of E is ergs in CGS or joules in SI 1 Joule = 10 7 ergs. (ii) Change in internal energy ( E ) : It is neither possible nor necessary to calculate the absolute value of internal energy of a system then, E  E f  Ein ; E is positive if E f  Ein and negative if E f  Ein. (2) Heat (q) and work (w) : The energy of a system may increase or decrease in several ways but two common ways are heat and work. Heat is a form of energy. It flows from one system to another because of the difference in temperature between them. Heat flows from higher temperature to lower temperature. Therefore, it is regarded as energy on the move. Thermodynamics and Thermochemistry Work is said to be performed if the point of application of force is displaced in the direction of the force. It is equal to the force multiplied by the displacement (distance through which the force acts). There are three main types of work which we generally come across. These are, Gravitational work, electrical work and mechanical work. 405 If a system does work (w) on the surroundings, its internal energy decreases. In this case, E  q  (w)  q  w i.e.(Change in internal energy)=(Heat added to the system) – (work done by the system) Electrical work = potential difference  charge = Enthalpy and Enthalpy change Gravitational work = mgh Heat content of a system at constant pressure is called enthalpy denoted by ‘H’. (i) Units of heat and work : The heat changes are measured in calories (cal), Kilo calories (kcal), joules (J) or kilo joules (kJ). These are related as, 1 cal = 4.184 J; 1kcal = 4.184kJ The S.I. unit of heat is joule (J) or kilojoule. The Joule (J) is equal to Newton – metre (1 J= 1 Nm). 1 Joule = 10 7 ergs = 0.2390 cal. 1 cal > 1 joule > 1 erg Heat absorbed by the system = q positive Heat evolved by the system = q negative = w positive Work done by the system = w negative. D YG Work done on the system Zeroth law of thermodynamics This law forms the basis of concept of temperature. This law can be stated as follows, U “If a system A is in thermal equilibrium with a system C and if B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other whatever the composition of the system.” A ⇌ C ST A ⇌ Heat change at constant pressure can be given as q  E  PV ……….(ii) At constant pressure heat can be replaced at enthalpy. H  E  PV ………(iii) H  Heat change or heat of reaction (in chemical process) at constant pressure U (ii) Sign conventions for heat and work ……….(i) ID Work is measured in terms of ergs or joules. The S.I. unit of work is Joule. From first law of thermodynamics, q  E  PV E3 V.q 60 Mechanical work = Force  displacement = F.d The relationship between internal energy, work and heat is a mathematical statement of first law of thermodynamics. B ⇌ C B First law of thermodynamics Helmholtz and Robert Mayer proposed first law of thermodynamics. This law is also known as law of conservation of energy. It states that, “Energy can neither be created nor destroyed although it can be converted from one form into another.” E2  E1  E  q  w i.e. (Change in internal energy) = (Heat added to the system) +(Work done on the system) E  Heat change or heat of reaction at constant volume. In case of solids and liquids participating in a reaction, H  E (PV  0) Difference between H and E is significant when gases are involved in chemical reaction. H  E  PV H  E  nRT PV  nRT Here, n  nP – nR Specific and Molar heat capacity (1) Specific heat (or specific heat capacity) of a substance is the quantity of heat (in calories, joules, kcal, or kilo joules) required to raise the temperature of 1g of that substance through 1 o C. It can be measured at constant pressure (c p ) and at constant volume (cv ). (2) Molar heat capacity of a substance is the quantity of heat required to raise the temperature of 1 mole of the substance by 1 o C.  Molar heat capacity = Specific heat capacity  Molecular weight, i.e., Cv  cv  M and C p  c p  M. 406 Thermodynamics and Thermochemistry (3) Since gases on heating show considerable tendency towards expansion if heated under constant pressure conditions, an additional energy has to be supplied for raising its temperature by 1o C relative to that required under constant volume conditions, i.e., C p  Cv or C p  Cv  Work done in expansion, PV ( R) where, C p  molar heat capacity at constant If the external pressure is decreased by an infinitesimal amount dP, the gas will expand by an infinitesimal volume, dV. As a result of expansion, the pressure of the gas within the cylinder falls to Pgas  dP , i.e., it becomes again equal to the external pressure and, thus, the piston comes to rest. Such a process is Pext –step dP the repeated for a numberPext of times, i.e., in each gas expands by a volume dV. pressure molar heat capacity at constant dV volume. (4) Some useful relations of Cp and Cv Pgas (i) C p  Cv  R  2 calories  8.314 J gas. Cp Cv   (Ratio of molar capacities) (iv) For monoatomic gas, Cv  3 calories whereas, C p  Cv  R  5 calories 5 R  2  1. 66 (v) For monoatomic gas, ( )  3 Cv R 2 U Cp D YG 7 R Cp  2  1. 40 (vi) For diatomic gas ( )  5 Cv R 2 (vii) For triatomic gas ( )  Cp Cv  Since the system is in thermal equilibrium with the surroundings, the infinitesimally small cooling produced due to expansion is balanced by the absorption of heat from the surroundings and the temperature remains constant throughout the expansion. The work done by the gas in each step of expansion can be given as, dw  (Pext  dP)dV  Pext.dV  dP. dV ID (iii) Fig. 10.1 3 3 R (for monoatomic gas) and Cv   x 2 2 (for di and polyatomic gas), where x varies from gas to 8R  1. 33 6R dP.dV , the product of two infinitesimal quantities, is negligible. The total amount of work done by the isothermal reversible expansion of the ideal gas from volume V1 to volume U (1) Isothermal Expansion : For an isothermal expansion, T  0 ; E  0. According to first law of thermodynamics, q  w ST This shows that in isothermal expansion, the work is done by the system at the expense of heat absorbed. Since for isothermal process, E and T are zero respectively, hence, H  0 (i) Work done in reversible isothermal expansion : Consider an ideal gas enclosed in a cylinder fitted with a weightless and frictionless piston. The cylinder is not insulated. The external pressure, Pext is equal to pressure of the gas, Pgas. Pext  Pgas  P is, V2 w  2.303 nRT log 10 Expansion of an ideal gas E  q  w Pgas E3 (ii) Cv  60 Cv  given as, w  nRT log e V2 V1 or V2 V1 At constant temperature, according to Boyle’s law, V P P P1 V1  P2 V2 or 2  1 So, w  2.303 nRT log 10 1 V1 P2 P2 Isothermal compression work of an ideal gas may be derived similarly and it has exactly the same value with positive sign. V P w compressio n  2.303 nRT log 1  2.303 nRT log 2 V2 P1 (ii) Work done in irreversible isothermal expansion : Two types of irreversible isothermal expansions are observed, i.e., (a) Free expansion and (b) Intermediate expansion. In free expansion, the external pressure is zero, i.e., work done is zero when gas expands in vacuum. In intermediate expansion, the external pressure is less than gas pressure. So, the work done when volume changes from V1 to V2 is given by  V2 w   Pext  dV   Pext (V2  V1 ) V1 Thermodynamics and Thermochemistry Pgas. (2) Adiabatic Expansion : In adiabatic expansion, no heat is allowed to enter or leave the system, hence, q 0. According to first law of thermodynamics, E  q  w  E  w work is done by the gas during expansion at the expense of internal energy. In expansion, E decreases while in compression E increases. The molar specific heat capacity at constant volume of an ideal gas is given by  dE  Cv    or dE  Cv.dT  dT v and for finite change E  Cv T So, w  E  Cv T Spontaneous and Non-spontaneous processes A process which can take place by itself under the given set of conditions once it has been initiated if necessary, is said to be a spontaneous process. In other words, a spontaneous process is a process that can occur without work being done on it. The spontaneous processes are also called feasible or probable processes. On the other hand, the processes which are forbidden and are made to take place only by supplying energy continuously from outside the system are called non-spontaneous processes. In other words, non spontaneous processes can be brought about by doing work. Examples of Spontaneous and Non-spontaneous processes (1) The diffusion of the solute from a concentrated solution to a dilute solution occurs when these are brought into contact is spontaneous process. ID The value of T depends upon the process whether it is reversible or irreversible.     60 work done during intermediate expansion is numerically less than the work done during reversible isothermal expansion in which Pext is almost equal to  T P  T1 P2 or w  Cv (T2  T1 )   RPext  2 1 P1 P2  E3 Since Pext is less than the pressure of the gas, the 407 PV   constant D YG where, P = External pressure, V = Volume   where, Cp  Cp Cv molar specific heat capacity at constant pressure, Cv  molar specific heat capacity at constant volume.  T1  T  2   P   1  P   2      1 P   2  P1 1      U knowing  , P1 , P2 and initial temperature T1 , the final temperature T2 can be evaluated. ST (ii) Irreversible adiabatic expansion : In free expansion, the external pressure is zero, i.e, work done is zero. Accordingly, E which is equal to w is also zero. If E is zero, T should be zero. Thus, in free expansion (adiabatically), T  0 , E  0 , w  0 and H  0. In intermediate expansion, the volume changes from V1 to V2 against external pressure, Pext.  RT RT  w  Pext (V2  V1 )   Pext  2  1  P P1   2  T P  T1 P2   Pext  2 1 P1 P2    R   (3) Heat flows from a hot reservoir to a cold reservoir is spontaneous process. U (i) Reversible adiabatic expansion : The following relationships are followed by an ideal gas under reversible adiabatic expansion. (2) Mixing of different gases is spontaneous process. (4) Electricity flows from high potential to low potential is spontaneous process. (5) Expansion of an ideal gas into vacuum through a pinhole is spontaneous process. All the above spontaneous processes becomes non-spontaneous when we reverse them by doing work. Spontaneous process and Enthalpy change : A spontaneous process is accompanied by decrease in internal energy or enthalpy, i.e., work can be obtained by the spontaneous process. It indicates that only exothermic reactions are spontaneous. But the melting of ice and evaporation of water are endothermic processes which also proceeds spontaneously. It means, there is some other factor in addition to enthalpy change (H ) which explains the spontaneous nature of the system. This factor is entropy. Second law of thermodynamics All the limitations of the first law of thermodynamics can be remove by the second law of thermodynamics. This law is generalisation of certain experiences about heat engines and refrigerators. It has been stated in a number of ways, but all the statements are logically equivalent to one another. (1) Statements of the law (i) Kelvin statement : “It is impossible to derive a continuous supply of work by cooling a body to a 408 Thermodynamics and Thermochemistry (iii) Ostwald statement : “It is impossible to construct a machine functioning in cycle which can convert heat completely into equivalent amount of work without producing changes elsewhere, i.e., perpetual motions are not allowed.” (iv) Carnot statement : “It is impossible to take heat from a hot reservoir and convert it completely into work by a cyclic process without transferring a part of it to a cold reservoir.” The entropy change of a system may be defined as the integral of all the terms involving heat exchanged (q) divided by the absolute temperature (T) during each infinitesimally small change of the process carried out reversibly at constant temperature. S  S final  S initial  q rev T If heat is absorbed, then S  ve and if heat is evolved, then S  ve. (2) Units of entropy : Since entropy change is expressed by a heat term divided by temperature, it is expressed in terms of calorie per degree, i.e.,cal deg-1. In SI units, the entropy is expressed in terms of joule ID (2) Proof of the law : No rigorous proof is available for the second law. The formulation of the second law is based upon the observations and has yet to be disproved. No deviations of this law have so far been reported. However, the law is applicable to cyclic processes only. Entropy is represented by the symbol “S”. It is difficult to define the actual entropy of a system. It is more convenient to define the change of entropy during a change of state. 60 (ii) Clausius statement : “It is impossible for a self acting machine, unaided by any external agency, to transfer heat from one body to another at a higher temperature or Heat cannot itself pass from a colder body to a hotter body, but tends invariably towards a lower thermal level.” (1) Definition : Entropy is a thermodynamic state quantity which is a measure of randomness or disorder of the molecules of the system. E3 temperature lower than that of the coldest of its surroundings.” The Carnot cycle (3) Characteristics of entropy : The important characteristics of entropy are summed up below (i) Entropy is an extensive property. Its value depends upon the amount of the substance present in the system. D YG U Carnot, a French engineer, in 1824 employed merely theoretical and an imaginary reversible cycle known as carnot cycle to demonstrate the maximum convertibility of heat into work. per degree Kelvin, i.e., JK 1. The system consists of one mole of an ideal gas enclosed in a cylinder fitted with a piston, which is subjected to a series of four successive operations. For cyclic process, the essential condition is that net work done is equal to heat absorbed. This condition is satisfied in a carnot cycle. T  T1 w  2  Thermodynamic efficiency q2 T2 U Thus, the larger the temperature difference between high and low temperature reservoirs, the more the heat converted into work by the heat engine. T2  T1  1 , it follows that w  q 2. This means T2 ST Since that only a part of heat absorbed by the system at the higher temperature is transformed into work. The rest of the heat is given out to surroundings. The efficiency of the heat engine is always less then 1. This has led to the following enunciation of the second law of thermodynamics. It is impossible to convert heat into work without compensation. Entropy and Entropy change (ii) Entropy of a system is a state function. It depends upon the state variables (T , p, V , n). (iii) The change in entropy in going from one state to another is independent of the path. (iv) The change in entropy for a cyclic process is always zero. (v) The total entropy change of an isolated system is equal to the entropy change of system and entropy change of the surroundings. The sum is called entropy change of universe. S universe  S sys  S Surr (a) In a reversible process, S universe  0 and, therefore S sys  S Surr (b) In an irreversible process, S universe  0. This means that there is increase in entropy of universe is spontaneous changes. (vi) Entropy is a measure of unavailable energy for useful work. Unavailable energy = Entropy × Temperature (vii) Entropy, S is related to thermodynamic probability (W) by the relation, S  k log e W and S  2.303 k log10W Thermodynamics and Thermochemistry In general, there will be an overall increase of the total entropy (or disorder) whenever the disorder of the surroundings is greater than the decrease in disorder of the system. The process will be spontaneous only when the total entropy increases. T2 p  nR ln 2. T1 p1 Assuming C p , is constant (a) Thus, for an isothermal process (T constant), V p S  nR ln 2 or  nR ln 2 V1 p1 (b) For T2 S  n C p ln T1 isobaric (c) isochoric For T2 S  n Cv ln T1 process (p constant), 60 (4) Entropy changes in system & surroundings and total entropy change for Exothermic and Endothermic reactions : Heat increases the thermal motion of the atoms or molecules and increases their disorder and hence their entropy. In case of an exothermic process, the heat escapes into the surroundings and therefore, entropy of the surroundings increases on the other hand in case of endothermic process, the heat enters the system from the surroundings and therefore. The entropy of the surroundings decreases. S  nC P ln process (V constant), (d) Entropy change during adiabatic expansion : In such process q=0 at all stages. Hence S  0. Thus, reversible adiabatic processes are called isoentropic process. E3 where, k is Boltzmann's constant 409 (5) Entropy change during phase transition : The change of matter from one state (solid, liquid or gas) to another is called phase transition. Such changes occur at definite temperature such as melting point (solid to liquid). boiling point (liquid to vapours) etc, and are accompanied by absorption or evolution of heat. Free energy and Free energy change When a solid changes into a liquid at its fusion temperature, there is absorption of heat (latent heat). Let H f be the molar heat of fusion. The entropy (i) The free energy of a system is the enthalpy of the system minus the product of absolute temperature and entropy i.e., G  H  TS change will be (ii) Like other state functions E, H and S, it is also expressed as G. Also G  H  TS system where S is ID Gibb's free energy (G) is a state function and is a measure of maximum work done or useful work done from a reversible reaction at constant temperature and pressure. U D YG S f  H f Tf Similarly, if the latent heat of vaporisation and H vap and sublimation are denoted by H sub , respectively, the entropy of vaporisation and sublimation are given by H vap Tb and S sub  U S vap  H sub Ts Since H f , H vap and H Sub are all positive, these ST processes are accompanied by increase of entropy and the reverse processes are accompanied by decrease in entropy. (6) Entropy change for an ideal gas : In going from initial to final state, the entropy change, S for an ideal gas is given by the following relations, (i) When T and V are two variables, S  nC v ln T2 V  nR ln 2. T1 V1 Assuming constant (ii) (1) Characteristics of free energy When T and p are two variables, Cv is entropy change for Helmholtz equation. system (iii) At equilibrium only. This is Gibb's G  0 (iv) For a spontaneous process decrease in free energy is noticed i.e., G  ve. (v) At absolute zero, TS is zero. Therefore if G is – ve, H should be – ve or only exothermic reactions proceed spontaneously at absolute zero. (vi) Gsystem  TS universe , where H  0 (vii) The standard free energy change, G o  2. 303 RT log 10 K , where K is equilibrium constant. (a) Thus if K  1, then G o  ve thus reactions with equilibrium constant K>1 are thermodynamically spontaneous. (b) If K