1. THE SECOND LAW OF THERMODYNAMICS Entropy

2. Entropy and the direction of time Microscopically the eqs. of physics are time reversible ie you can turn the arrow of time around….!!! Macroscopically there is an arrow to time what’s going on… ie processes are irreversible Key is understanding entropy…

3. Irreversibility… The “one way” character of irreversible processes is so pervasive we take it for granted ie if you wrap your hands around a hot cup of Java you would be astonished if your hands became cooler………… The system of (coffee + hands) obeys energy conservation but you don’t expect that the flow of heat energy in the system to be from cold to warmer ie from hands to cup If an irreversible process occurs in a closed system, the entropy of the system always increases, it never decreases

4. New Quantity Entropy Changes in energy do not violate the highly unlikely process of a popped balloon + air turning into a fully expanded balloon There is a quantity that called entropy such that if an irreversible process occurs in a closed system the entropy increases S

5. Arrow of time and Free expansion … One doesn’t expect the gas undergoing free expansion to spontaneously go back to the left hand volume ie the other side…….. Entropy is not a conserved quantity however it is a state variable as are pressure, p, temperature, T, internal energy, E etc….

6. Since Entropy is a state variable can calculate it by knowing only the initial and final states 1) In terms of system’s temp and energy gain or loss as heat 2) Counting the ways in which the atoms of molecules that make up the system can be arranged

7. Well what is it…

8. Example, free expansion of nitrogen gas from initial to final volume…what is entropy?

9. Isothermal process done in a reversible manner has the same initial and final states as an irreversible process undergoing free expansion… since S is a state variable all we need are initial and final states… To find the entropy of an irreversible process in a closed system, replace that process that connects the initial and final states, calculate the entropy for the reversible one and you have the entropy for the irreversible one

10. Consider this irreversible process What is the reversible process that takes the system from initial to final state? If we can calculate the entropy change of the reversible process that takes the system from initial to final state then we have the entropy of the irreversible process…..

11. Prove that S is a state variable That is it can be defined as a function of other state variable and each equilibrium state has a unique value. Prove for the case of an ideal gas going through a series of reversible processes Did not specify a particular reversible process when we integrated, therefore the integration holds for all reversible processes that take a gas for some initial state i to some final state f

12. Change Entropy for an Ideal Gas Consider an ideal gas undergoing a thermodynamic processConsider an ideal gas undergoing a thermodynamic process Apply the First Law of ThermodynamicsApply the First Law of Thermodynamics It is useful to consider infinitesimal changes

13. Change Entropy for an Ideal Gas

15. Change in Entropy is independent of process (none was specified)Change in Entropy is independent of process (none was specified) Assumed a reversible process. Any irreversible process would have larger change in entropy; hence, the inequalityAssumed a reversible process. Any irreversible process would have larger change in entropy; hence, the inequality Equation is an equation of state since it includes only state variables (V, T) and requires knowledge of only the end points of the process.Equation is an equation of state since it includes only state variables (V, T) and requires knowledge of only the end points of the process.

16. Puzzle …the 2 nd Law of Thermo If entropy always increases then what happens if you reversibly transfer heat back to reservoir? Doesn’t entropy decrease ? Yes … but …..

17. If a process occurs in a closed system the entropy of the system increases for irreversible process and remains constant for reversible processes. IT NEVER DECREASES….

18. Second LAW If a process occurs in a closed system the entropy of the system increases for irreversible process and remains constant for reversible processes. IT NEVER DECREASES….

19. The Carnot Engine Cycle Ideals engine, all processes are reversible and now wasteful energy transfers occur ie due to friction and turbulenceIdeals engine, all processes are reversible and now wasteful energy transfers occur ie due to friction and turbulence Two adiabats and two isothermsTwo adiabats and two isotherms Highest possible efficiency (Carnot Theorem)Highest possible efficiency (Carnot Theorem)

20. Can consider a T vs. S plot Entropy change Energy change

21. T vs S Diagrams Isothermal processes are horizontal linesIsothermal processes are horizontal lines Adiabatic processes (isentropic processes) are vertical linesAdiabatic processes (isentropic processes) are vertical lines Area under the curve is heat exchangedArea under the curve is heat exchanged Area enclosed in a cycle is work done (net heat exchanged equals work done because the change in internal energy of the substance is zero)Area enclosed in a cycle is work done (net heat exchanged equals work done because the change in internal energy of the substance is zero)

22. Calculate the Change of Entropy for Melting Ice 10 g of Ice at 0 o C melts to form a puddle of water. What is the increase of entropy of the water? so

23. Microscopic explanation of Entropy 1.Begin with the number of ways the energy of the molecules can be distributed – the multiplicity of the number of states 2.Apply Boltzmann’s entropy equation 3.Include Stirling’s approximation where See section 21-7 for more examples Use only for very large numbers

24. Example of Statistical Approach to Entropy Consider 10 identical molecules to be distributed among 3 cells (1/3 of the container)Consider 10 identical molecules to be distributed among 3 cells (1/3 of the container) Possible distributions are:Possible distributions are: –10,0,0 (3 times); i.e, 10,0,0 / 0,10,0 / 0,0,10 –9,1,0 (6 times); i.e, 9,1,0 / 9,0,1 / 1,9,0 / 0,9,1 / 0,1,9 / 1,0,9 –8,2,0 (6 times) –8,1,1 (3 times) –7,3,0 (6 times) –7,2,1 (6 times) –6,4,0 (6 times) –6,3,1 (6 times) –6,2,2 (3 times) –5,5,0 (3 times) –5,4,1 (6 times) –5,3,2 (6 times) –4,4,2 (3 times) –4,3,3 (3 times) Calculate the entropy associated with the distribution 7,2,1 where

25. Statement of the Second Law and Heat Engines It is impossible to construct a heat engine operating in a cycle that completely converts heat to an equal amount of workIt is impossible to construct a heat engine operating in a cycle that completely converts heat to an equal amount of work (Kelvin - Planck statement) Always some heat that goes out unused…..

26. Heat Engine Efficiency operates through a thermodynamic cycleoperates through a thermodynamic cycle is reversibleis reversible efficiency of a heat engineefficiency of a heat engine

27. Summary of the Laws of Thermodynamics First Law: Conservation of EnergyFirst Law: Conservation of Energy –“You cannot build a perpetual motion machine of the first kind. (You cannot get more energy out than you put in).” –In other words, “YOU CAN’T WIN!” Second Law: Law of increasing entropy or unidirectional flow of thermal energySecond Law: Law of increasing entropy or unidirectional flow of thermal energy –“You cannot build a perpetual motion machine of the second kind. ( You cannot build a machine that is 100% efficient).” –In other words, “YOU LOSE!”