1. ERT 108 Physical Chemistry The Second Law of Thermodynamics by Miss Anis Atikah binti Ahmad anisatikah@unimap.edu.my

2. Outline The Second Law of Thermodynamics Heat Engines Entropy Calculation of entropy changes Entropy, Reversibility and Irreversibility The thermodynamics temperature scale What is entropy?

3. The Second Law of Thermodynamics Kelvin-Plack formulation of the second law of thermodynamics: It is impossible for a system to undergo cyclic process whose sole effects are the flow of heat into the system from a heat reservoir and the performance of an equivalent amount of work by the system on the surroundings.

4. The Second Law of Thermodynamics It is impossible to build a cyclic machine that converts 100% heat into work. Does this system violate the first law?

5. The Second Law of Thermodynamics Any heat engine must eject heat into the cold reservoir

6. Heat Engines Heat engine: a device that operates in a thermodynamic cycle and does a certain amount of net positive work as a result of heat transfer from a high-temperature body to a low- temperature body. (eg: the internal-combustion engine and the gas turbine)

7. Heat Engines The efficiency of heat engine: The efficiency value is less than 1, q C has a negative value and q H has a positive value. Work output per cycle Energy input per cycle Cold reservoir Hot reservoir

8. Heat Engines The cycle for a reversible heat engine (Carnot cycle):

9. Heat, Work and ΔU for Reversible Carnot Cycle

10. Work flow in Carnot cycle

11. Carnot cycle For a complete cycle (assuming perfect gas); Dividing by T and integrating over Carnot cycle; First Law

12. Carnot cycle Thus; 0 0 Differential of state function; independent of the path taken to reach final state.

13. Carnot cycle Since b  c and d  a are adiabatic; dq= 0 ; Thus; 0 0

14. Carnot cycle For Carnot cycle the efficiency can be also written as; Where is the maximum possible efficiency for the conversion of heat to work. Work output per cycle Energy input per cycle Because

15. Exercise 1 Calculate the maximum work that can be done by reversible heat engine operating between 500 and 200 K if 1000 J is absorbed at 500 K

16. Solution Calculate the maximum work that can be done by reversible heat engine operating between 500 and 200 K if 1000 J is absorbed at 500 K

17. Entropy, S Closed sys, rev. process

18. Calculation of Entropy Changes 1.Cyclic process; 2.Reversible adiabatic process; 3.Reversible phase change at constant T & P at constant P,, thus 0 Rev. phase change at const. T & P Rev. adiab. proc.

19. Calculation of Entropy Changes 4.Reversible isothermal process 5.Constant-pressure heating with no phase change If is constant over the temperature range, then Rev, isothermal proc. Const. P, no phase change

20. Calculation of Entropy Changes 6. Reversible change of state of a perfect gas; Perfect gas

21. Calculation of Entropy Changes 7. Irreversible change of state of a perfect gas; 8. Mixing of different inert perfect gases at constant T & P Perfect gas

22. Exercise 2 One mole of a perfect gas at 300 K is reversibly and isothermally compressed from a volume of 25.0 L to a volume of 10.0 L. Because the water bath in the surroundings is very large, T remains essentially constant at 300 K during the process. Calculate ΔS of the system.

23. Exercise 2-Solution One mole of a perfect gas at 300 K is reversibly and isothermally compressed from a volume of 25.0 L to a volume of 10.0 L. Because the water bath in the surroundings is very large, T remains essentially constant at 300 K during the process. Calculate ΔS. This is an isothermal process, ΔT=0, thus ΔU=0 (for perfect gas, U depends only on T. ( )

24. Exercise 3 Calculate ΔS for the melting of 5.0 g of ice (heat of fusion= 79.7 cal/g) at 0 °C and 1 atm. Estimate ΔS for the reverse process

25. Exercise 3- Solution Calculate ΔS for the melting of 5.0 g of ice (heat of fusion= 79.7 cal/g) at 0 °C and 1 atm. Estimate ΔS for the reverse process. Identify type of process: ▫ Phase change at constant T & P ▫ At constant P, q= ΔH ▫ Thus, Calculate ΔS;

26. Exercise 3- Solution Calculate ΔS for the melting of 5.0 g of ice (heat of fusion= 79.7 cal/g) at 0 °C and 1 atm. Estimate ΔS for the reverse process. ΔS for reverse process (freezing of 5g liquid water );

27. Exercise 4 The specific heat capacity c P of water is nearly constant at 100 cal/g K in the temperature range of 25°C to 50°C at 1 atm. (a)Calculate ΔS when 100 g of water is reversibly heated from 25°C to 50°C at 1 atm. (b)Without doing a calculation, state whether ΔS for heating 100g of water from 50°C to 75°C at 1 atm will be greater, equal to or less than ΔS for the 25°C to 50°C heating.

28. Exercise 4- Solution The specific heat capacity c P of water is nearly constant at 100 cal/g K in the temperature range of 25°C to 50°C at 1 atm. (a)Calculate ΔS when 100 g of water is reversibly heated from 25°C to 50°C at 1 atm.

29. Exercise 4 - Solution The specific heat capacity c P of water is nearly constant at 100 cal/g K in the temperature range of 25°C to 50°C at 1 atm. (b)Without doing a calculation, state whether ΔS for heating 100g of water from 50°C to 75°C at 1 atm will be greater, equal to or less than ΔS for the 25°C to 50°C heating. Thus, ↑T, ↓ΔS ΔS for heating 100g of water from 50°C to 75°C at 1 atm will be smaller than ΔS for the 25°C to 50°C heating.

30. Entropy, Reversibility and Irreversibility Reversible Process, ΔS univ = 0 In reversible process, any heat flow btween system & surroundings must occur with no finite temperature difference

31. Entropy, Reversibility and Irreversibility Irreversible Process, ΔS univ > 0 When energy leaves the system as work, More work is done when a change is reversible than when it is irreversible; Recall first law; rearranging

32. Irreversible Process, ΔS univ > 0 Substituting into Entropy, Reversibility and Irreversibility Clausius inequality Dividing by T;

33. Irreversible Process, ΔS univ > 0 Suppose that the system is isolated from its surroundings, thus dq= 0 Entropy, Reversibility and Irreversibility

34. Entropy & Equilibrium Thermodynamic equilibrium in an isolated system is reached when the system’s entropy is maximized. Entropy, Reversibility and Irreversibility S Time Equilibrium reach S=S max

35. This expression enabled Kelvin to define thermodynamic temperature scale The thermodynamics temperature scale Kelvin scale is defined by using water at its triple point as the notional of hot source and defining that temperature as 273.16 K If it is found that the efficiency of heat engine equal to 0.2, then the temperature of cold sink is (0.8) x 273.16 K =220 K, regardless of the working substance of the engine. rearranging -a scale that is independent of the choice of a particular thermometric substance.

36. What is entropy? Entropy is a measure of the probability, p of the thermodynamic state a a a a a a a a b b b b b b b b a a a a a a a a b b b b b b b b a a a a a a a a b b b b b b b b Partition removedSystem proceed to equilibrium Irreversible mixing of perfect gas at constant T & P The probability that all a molecules will be in the left half & all b molecules in right half is extremely small. The most probable distribution has a and b molecules equally distributed.

37. What is entropy? Entropy is a measure of molecular disorder of a state. Eg: In mixing two gases, the disordered (mixed state) is far more probable than the ordered (unmixed) state.

38. What is entropy? Entropy is related to the distribution or spread of energy among the available molecular energy levels. The greater the number of energy levels, the larger the entropy is. Increasing the system’s energy (eg:by heating) will increase its entropy because it allows higher energy levels to be significantly occupied Increasing the volume of a system at constant energy also allows more energy level to be occupied.

39. What is entropy? Boltzmann made link btween distribution of molecules over energy levels and the entropy; Where k= 1.381 x 10 -23 JK -1 W= probability/ways in which the molecules of a system can be arranged while keeping the energy constant

40. Exercise True or false? ▫ ΔS uni for a reversible process in a closed system must be zero ▫ ΔS for a reversible process in a closed system must be zero ▫ For a closed system, equilibrium has been reached when S has been maximized. What is ΔS uni for each steps of a Carnot cycle?