1. VIII. Entropy for a reversible process at constant T dQ is path dependent dS is path independent S is function of state S is additive function for any process (including irreversible) For closed, isolated system (dQ = 0): 2.The second law of thermodynamics any reversible cycle: ΔS=0 any irreversible process in closed isolated system: ΔS>0 1. Macroscopic definition of entropy

2. Example 1: This P-V diagram represents a system consisting of a fixed amount of ideal gas that undergoes three different processes in going from state A to state B. Rank the change in entropy of the system for each process. V State A I P State B 2 3 ΔS 1 = ΔS 2 = ΔS 3 = S B - S A The same as: ΔT 1 = ΔT 2 = ΔT 3 = T B - T A ΔU 1 = ΔU 2 = ΔU 3 = U B - U A Example 2: Which of the following statements is false? A. The change of entropy in a cyclic process is zero B. The change of entropy for any adiabatic process is zero C. The change of entropy for any isothermal process is zero D. Entropy for a closed, isolated system is constant E. Entropy of a system can decrease

3. Example 3: 50.0 kg of water is converted to ice at 0.0ºC. What is the change in entropy of water? m = 85.0 kg T = 0.0ºC L = 334*10 3 J/kg ΔS - ? Example 4: The isolated system is 50.0 kg of ice at 0 ˚C plus the temperature reservoir at slightly above 0 ˚C that is used to melt the ice. What is the change in entropy of the system when the ice is melted ? Solution: The system is isolated: Q ice = -Q reservoir The ice and the reservoir are at almost the same temperature: T ic = T reservoir =T The system consists of both the ice and the temperature reservoir: ΔS = 0. Therefore the process is reversible!

4. 3. Entropy of ideal gas

5. 3a. Free expansion of ideal gas A given amount of an ideal gas undergo free expansion from volumeV 1 to V 2 Gas forms a closed and thermally isolated system. Because of that: W=0, Q=0ΔU=0 ΔT=0 T 1 = T 2 General equation for the entropy change of any ideal gas: Closed and thermally isolated system with ΔS>0: the process is irreversible! Example: Two moles of an ideal gas undergo an adiabatic free expansion from V 1 = 1.00 L to V 2 = e1.00 L = 2.72 L. (The gas is an isolated system). The change in the entropy of the gas is __ J/K. The process is irreversible!

6. 3b. Reversible isothermal expansion of ideal gas

7. 3c. Reversible Adiabatic Expansion of Ideal Gas

8. 4. Microscopic interpretation of entropy number of possible microscopic states Example 6: A thermally insulated box is divided by a partition into to compartments, each having volume V. Initially one compartment contains n moles of an ideal gas at temperature T, and other compartment is evacuated. We then break the partition, and gas expands to fill both compartments. What is the entropy change in this free- expansion process?