Thermodynamics-II 3rd Semester Suggested Books: An introduction to Chemical Thermodynamics by Rastogi and Mishra Physical Chemistry, vol 2 by K. L. Kapoor Physical Chemistry by Peter Atkins, Oxford University Press, Oxford Physical Chemistry by Ira N Levine Tata McGraw Hill Education Pvt. Ltd.

SECOND LAW OF THERMODYNAMICS Kelvin: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work R.J.E. Clausius : Heat cannot spontaneously pass from a colder to a warmer body. A. Edington : Entropy is time’s arrow. Enrico Fermi: The state of maximum entropy is the most stable state for an isolated system. G.N.Lewis: In an irreversible process the total entropy of all bodies concerned is increased. Concept of entropy (S) Energy is defined as the capacity of a system to do work. Entropy of a system is considered as an index of exhaustion of its capacity to do work. Thus entropy is a measure of unavailable portion of energy. Entropy has been used to represent randomness. Greater is the randomness larger is the value of entropy. S (gas) > S (liquid) > S (solid) Entropy is an extensive property & state function, ΔS total = ΔSsystem + Δssurroundings In an irreversible process ΔS total > 0, in spontaneous changes there is increase of entropy of universe. dqrev is inexact differential

Entropy (s) As, dqrev is inexact differential, dqrev /T is also exact differential hence dS ≠ dqirr /T. dqrev = dU + P dV when only P-V work is considered ----- (i) Now, let’s consider energy is a function of temperature and volume, U = U(T, V) and its total differential is given by - …. (ii) From (i) & (ii) we have: For Ideal gas: Joule’s law Or, Or, …. change in entropy (dS) depends on changes in T and V : Entropy is a function of T and V and S = S(T, V) Important relation:

2nd Law We know: H = U + PV so, dH = dU + PdV + VdP Relation between enthalpy and entropy We know: H = U + PV so, dH = dU + PdV + VdP Combined form of first and second laws: TdS = dU + PdV So, dH = TdS + VdP Entropy as a function of T and V : Entropy as a function of T and P : Thermodynamic equation of state: , Entropy change for isochoric reversible temperature change of an ideal gas For isochoric process, dV = 0 , so For the change of state from initial state 1 to final state 2,

Entropy change for isothermal reversible volume change of an ideal gas In an isothermal process dT =0, So Entropy change for isobaric reversible temperature change of an ideal gas , for ideal gas Or, , hence So, Entropy change for isothermal reversible pressure change of an ideal gas , so, , hence

Entropy change for an ideal gas under reversible -adiabatic conditions For simultaneous change of T & V the entropy is of an ideal gas We, know, Therefore,

Work performed/heat absorbed Carnot Cycle 1. Reversible isothermal expansion from A to B at Th; the entropy change is qh/Th, where qh is the energy supplied to the system as heat from the hot source. 2. Reversible adiabatic expansion from B to C. No energy leaves the system as heat, so the change in entropy is zero. In the course of this expansion, the temperature falls from Th to Tc, the temperature of the cold sink. 3. Reversible isothermal compression from C to D at Tc. Energy is released as heat to the cold sink; the change in entropy of the system is qc /Tc ; in this expression qc is negative. 4. Reversible adiabatic compression from D to A. No energy enters the system as heat, so the change in entropy is zero. The temperature rises from Tc to Th. 1 4 2 3 The total change in entropy around the cycle is For Ideal gas Efficiency of Carnot cycle is defined as: Work performed/heat absorbed  = .. for rev. process

The Second Law of thermodynamics implies that all reversible engines have the same efficiency regardless of their construction Clausius inequality: In an isolated system the entropy change is greater than zero under irreversible condition but under reversible condition it is equal to zero In general: In an isolated system, there is no exchange of heat, energy and work between the system and surroundings. Therefore and so, Calculation of Entropy Changes of systems and surroundings : Entropy as criteria of spontaneity and equilibrium All natural processes are spontaneous. Experimentally it is found that in a spontaneous process total entropy increases as the change progresses. At equilibrium the entropy becomes maximum. Acknowledgement: An introduction to Chemical Thermodynamics by Rastogi and Mishra Physical Chemistry by Peter Atkins, Oxford University Press, Oxford