1. Chemistry 2402 - Thermodynamics Lecture 7 : Entropy Lecture 8 : Converting Heat to Work Lecture 9: Free Energies

2. Aim The aim of this course is to develop the general principles that govern all equilibrium states. We shall base everything on two results from the statistics of energy distribution: 1.the equilibrium state of an isolated system is that which maximises the entropy. (2nd Law of thermodynamics) 2.dS = q/T where q is the (reversible) heat flow into the system

3. REFLECTIONS ON THE MOTIVE POWER OF FIRE AND ON MACHINES FITTED TO DEVELOP THIS POWER BY S. CARNOT 1824 This image is in the public domain because its copyright has expired. http://commons.wikimedia.org/wiki/Image:Sadi_Carnot.jpeg

4. Thermodynamics and Engines A system that converts heat flow into work and does so in a cyclic way (i.e. so that it can, in principle, go on doing it indefinitely) is called an engine (or, sometimes, a heat engine). If we run such an engine in reverse, i.e. do work to produce a heat flow, we have a refrigerator. Desktop Stirling Engine Source: Richard Wheeler http://commons.wikimedia.org/wiki /Image:Stirling_Engine.jpg Early refrigerator Source: Mike Manning http://en.wikipedia.org/wiki /Image:Monitor_refer.jpg

5. The Newcomen Engine The first application of steam engines was to pump water from mines. James Watt realised that reheating the cooled cylinder wasted heat. He introduced a separate condenser - the increase in efficiency contributed to the Industrial Revolution. This image is in the public domain because its copyright has expired. http://en.wikipedia.org/wiki/Image:Newcomen6325.png

6. A Simple Engine A - an isothermal (i.e. constant temperature) expansion at T h against a fixed pressure P A B - cooling from T h to T c at a fixed volume C - an isothermal compression at T c at the new fixed pressure P C D - heating from T c to T h at a fixed volume A B C D T h T c T c T h

7. Keeping the energy account We can reduce the engine to a path between equilibrium states. T V ThTh TcTc work outA B C D Heat is absorbed in steps D and A, heat is released in steps B and C.

8. Converting Heat to Work All engines can be described as follows. From conservation of energy, w out = q in –q out Why does there have to be any q out at all? engine hot bath T h cold bath T c q in q out w

9. Why must we waste heat? Consider the simpler process of transferring heat from the hot bath to the cold i.e. get rid of the engine.  S = -q in /T h + q in /T c > 0 because T h > T c For this process to be spontaneous (i.e. happen) heat MUST flow into the cold bath. hot bath T h cold bath T c q in = q out

10. What is the minimum amount of lost heat? What is the smallest amount of heat we need to discard to the cold bath so that the overall cycle remains allowed, i.e.  S = 0 (as opposed to spontaneous for which  S > 0)? Answer: If  S = -q in /T h + q out /T c = 0 then q out = q in T c /T h and the maximum work output is w out = q in - q out = q in (1-T c /T h ) Or an efficiency of w out /q in = 1-T c /T h 100% efficiency can only be obtained when the cold bath is at absolute zero.

11. Kelvin’s Temperature Scale In fact, the relation q in /q out = T h /T c is only satisfied by an absolute temperature scale. This is how Kelvin settled on this scale in the first place. "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement." Kelvin 1900 "heavier-than-air flying machines are impossible" Kelvin 1895 This image is in the public domain because its copyright has expired.

12. Flash Quiz! What is the smallest amount of electrical work required to remove 1 J of energy from a freezer at -5 °C, when the surrounding temperature is 25 °C? a) 0 J b) less than 1 J c) exactly 1 J d) more than 1 J hot bath T h (surrounds) cold bath T c (freezer) W in q in q out refridgeration unit

13. Hints What is the smallest amount of electrical work required to remove 1 J of energy from a freezer at -5 °C, when the surrounding temperature is 25 °C? “smallest energy” → most efficient, so  S = +q out /T h - q in /T c = 0 conservation of energy (first law) also means w in + q in = q out refridgeration unit hot bath T h (surrounds) cold bath T c (freezer) W in q in q out

14. Answer What is the smallest amount of electrical work required to remove 1 J of energy from a freezer at -5 °C, when the surrounding temperature is 25 °C? “smallest energy” → most efficient, so  S = +q out /T h - q in /T c = 0 q out = q in × T h / T c conservation of energy (first law) also means w in + q in = q out so w in = q in ( T h /T c - 1) = 1J×(298K/268K - 1) = 0.11 J this is much higher on hotter days or if you set your freezer temperature really cold refridgeration unit hot bath T h (surrounds) cold bath T c (freezer) W in q in q out

15. How do we make an engine that runs at maximum efficiency? Consider the work obtained from an expansion at constant temperature. Let’s hold a piston+cylinder at volume V 1 with a pressure P 1 and then drop the pressure to P 2 let it expand freely to V 2 The work obtained is the shaded area.

16. Slower is better Let’s now do this expansion in a number of pressure steps. The work on the surrounding (i.e. the shaded area) has increased.

17. Reversible and Irreversible Processes In the limit of infinitely many small pressure steps we find the state of the gas in the cylinder always remains very close to the equilibrium volume for the pressure and the maximum work is obtained. This infinitely gradual process is called a quasi-static or reversible process. All real processes – i.e. ones that occur in a finite time – are irreversible.

18. Heat Engine Examples Sources Left: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html Top right: http://www.ent.ohiou.edu/~thermo/me321/quiz.info/ StirlCogen/StirlCogen.html Bottom right: http://www.grc.nasa.gov/WWW/K-12/airplane/otto.html

19. Sample exam questions from previous years Provide a brief explanation of each of the following terms: –heat engine –reversible process

20. Summary You should now Be able to explain the role of heat and work in an engine Understand the significance of the Kelvin temperature scale Be able to represent an engine by a thermodynamic cycle Know the connection between a path on a P-V plot, and the work generated by an engine carrying out that path Be able to calculate the maximum efficiency for an ideal engine or refrigerator Explain the thermodynamic meaning of a reversible process Next Lecture Free energies

21. Air conditioner Cold room T in Outside air T out q in q out w in