1. Unit 61: Engineering Thermodynamics Lesson 8: Second Law of Thermodynamics

2. Objective The purpose of this lesson is to derive a statement for the Second Law of Thermodynamics.

3. Background Water flows down hill does it not! Heat flows from a hot body to a cold one; rubber bands unwind; fluid flows from a high- pressure region to a low-pressure region – and we get old! Our experiences in life suggest that processes have a definite direction.

4. Background The first law of thermodynamics relates several variables involved in a physical process but does not give any information as to the direction of the process. It is the second law of thermodynamics which helps establish the direction of a particular process.

5. First Law of Thermodynamics W Consider once again, a weight W attached to a pulley / paddle wheel

6. Background The first law states that the work done by a falling weight is converted into internal energy of the air contained in the fixed volume, provided the volume is insulated so that Q = 0. It would not be a violation of the first law if we postulated that an internal energy decrease of air is used to turn the paddle and raise the weight! This however would be a violation of the second law of thermodynamics and would thus be an impossibility.

7. Heat Engines, Heat Pumps and Refrigerators We refer to a device operating a cycle as a heat engine, a heat pump or a refrigerator depending on the objective of the particular device… – If the objective of the device is to perform work it is a heat engine. – If the objective is to supply energy to a body it is a heat pump. – If the objective is to extract energy from a body it is a refrigerator

8. A Simple Heat Engine Heat Engine QHQH QLQL W THTH THTH T H = temperature of heat source T L = temperature of heat sink

9. A Simple Heat Engine The net work produced by the engine would be equal to the net heat transfer – a consequence of the first law… W = Q H – Q L Where Q H and Q L are the heat transfer from High to Low temperature reservoirs respectively

10. A Simple Heat Pump or a Refrigerator Heat Pump THTH TLTL QHQH QLQL W T H = temperature of heat source T L = temperature of heat sink

11. A Simple Heat Pump or a Refrigerator Reversing the cycle a net work input would be required. A heat pump would provide energy as heat Q H to the warmer body (e.g. a house) A refrigerator would extract heat energy QL from the cooler body (e.g. a freezer). - W = - Q H – (- Q L ) i.e. W = Q H – Q L

12. A Simple Heat Pump or a Refrigerator Note: the engine of refrigerator operates between two thermal reservoirs, entities which are capable of providing or accepting heat without changing temperatures The atmosphere or a lake act as heat sinks; furnaces, solar collectors, or burners serve as heat sources.

13. Thermal Efficiency / Coefficients of Performance The thermal efficiency of the heat engine and the coefficients of performance of the refrigerator and the heat pump Η = W/Q H ;COP refrig = Q L /W; COP h.p. = Q H /W The second law of thermodynamics places limits on these measure of performance.

14. Thermal Efficiency / Coefficients of Performance The first law would allow a maximum of unity for the thermal efficiency and an infinite COP The second law however establishes limits that cannot be exceeded regardless of the cleverness of proposed designs.

15. Thermal Efficiency / Coefficients of Performance Note: there are devices that we refer to as heat engines which do not strictly meet the definition – they do not operate on a thermodynamic cycle but instead exhaust the working fluid and then intake new fluid e.g. the internal combustion engine.

16. Statements of the 2 nd Law of Thermodynamics We cannot derive a basic law but we merely observe that such a law is never violated. There are a variety of ways to state the 2 nd law. Two such statements are…

17. Clausius Statement It is impossible to construct a device which operates on a cycle and whose sole effect is the transfer of heat from a cooler to a hotter body. This statement relates to a refrigerator (or heat pump). It states that it is impossible to construct a refrigerator that transfers energy from a cooler body to a hotter body without the input of work

18. A Violation as Stated by Clausius Device THTH TLTL QHQH QLQL Q L = Q L

19. Kelvin-Planck Statement It is impossible to construct a device which operates on a cycle and produces no other effect than the production of work and transfer of heat from a single body

20. A Violation of the Kelvin-Planck Statement Device THTH QHQH W Q H = W

21. Kelvin-Planck Statement In other words it is impossible to construct a heat engine that extracts energy from a reservoir, does work and does not transfer heat to a low temperature reservoir. This rules out any heat engine that is 100% efficient.

22. Comparison of the Statements The two statements of the 2 nd law are negative statements Neither has been proved – they are expressions of experimental observation No experimental evidence has ever been obtained that violates either statement. The two statements are equivalent.

23. Reversibility A reversible process is defined as a process which having taken place can be reversed and in so doing leaves no change in either the system or the surroundings. The most efficient engine that can possibly be constructed, an engine that operates with reversible processes only is called a reversible engine. Note: the definition of a reversible processes refers to both the system and the surroundings.

24. Reversibility A reversible process has to be a quasi- equilibrium process. In addition… – No friction is involved in the process – Heat transfer occurs due to infinitesimal temperature difference only – Unrestrained expansion does not occur. The mixing of different substances and combustion lead to irreversibility's.