Department of Mechanical Engineering ME 322 Mechanical Engineering Thermodynamics. Introduction to 2 nd Law and Entropy.

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1 Department of Mechanical Engineering ME 322 Mechanical Engineering hermodynamics Introduction to 2 nd aw and Entropy ecture 18

Example Consider an adiabatic compressor steadily moving R125, P2 2 430 psia 138F W P1 5 psia 1 100F m 0.15 lbm/s 1 2 0 1 2 W m h h W m h h W 0.15 lbm 160.

2 Example Consider an adiabatic compressor steadily moving R125, P psia 138F W P1 5 psia 1 100F m 0.15 lbm/s W m h h W m h h W 0.15 lbm Btu 3600 s hp-hr 2.15 hp s lbm hr 2545 Btu Really? A compressor that compresses a refrigerant and delivers power? Can I invest my money in this idea? 2

3 he Second aw of hermodynamics Before you invest in the contraption on the pious slide, recall the Second aw of hermodynamics. Energy can only be transformed. he transformation of energy always proceeds from a condition of very useful energy to less useful energy. he Second aw dictates how energy can be transformed. Conclusions with the compressor example he First aw analysis is correct! he First aw is an energy book keeper he Second aw is not being obeyed! he Second aw is the energy transformation police 3

4 What is Entropy? A thermodynamic property otal entropy = S (upper case letter) Specific entropy = s (lower case letter) An indication of molecular disorder igh values = high molecular disorder Gases ow values = low molecular disorder Solids A quantity that can be produced but not destroyed within a system undergoing a process Entropy is not a conserved quantity! 4

5 What is Entropy? Entropy is produced in a process by virtue of irersibilities mechanical friction, fluid friction, heat transfer, mixing, electrical resistance, chemical reactions... Irersibilities are present in all real-world systems and processes Reversible processes Free of entropy production Do not exist they are idealizations he hird aw of hermodynamics he entropy of a perfect crystalline substance at absolute zero is zero! Provides a universal datum state for entropy 5

6 he Second aw Pioneers Sadi Carnot ( ) William homson (ord Kelvin) ( ) William Rankine ( ) Rudolph Clausius ( ) Carnot Cycles Defined Entropy 6

7 he Kelvin-Planck Statement It is impossible to construct a device that operates in a thermodynamic cycle and delivers a net amount of energy as work to its surroundings while receiving energy by heat from a single reservoir. his is impossible! hermal Reservoir C cycle W cycle Implication: No heat engine can ever operate with an energy conversion efficiency of 100% E energy sought energy that costs W cycle in 7

8 Carnot s eat Engine Carnot hypothesized... he energy conversion (thermal) efficiency of an irersible heat engine is always less than the thermal efficiency of a ersible heat engine operating between the same thermal energy reservoirs Reversible engines operating between the same thermal energy reservoirs have the same thermal efficiency he ersible engine is not dependent on the working fluid 8

9 Analysis of the Carnot eat Engine th W 1 cycle in out out in in in Kelvin and Rankine suggested that, out in W cycle in out out th, Carnot 1 in in in emperatures must be on the absolute scale! herefore, the thermal efficiency of a Carnot eat Engine is, th, Carnot 1 his is the maximum efficiency of a heat engine! 9

10 he Clausius Statement It is impossible for any system to operate in such a way that the energy transfer by heat from a cooler body to a hotter body occurs without the input of work. ot System his is impossible! Cold 10

11 Carnot s Refrigerator Carnot hypothesized... he thermal efficiency of an irersible refrigerator is always less than the thermal efficiency of a ersible refrigerator operating between the same thermal energy reservoirs Reversible refrigerators operating between the same thermal energy reservoirs have the same thermal efficiency he ersible refrigerator is not dependent on the working fluid 11

12 Analysis of the Carnot Refrigerator For the Refrigeration cycle in in 1 th COPR W / 1 cycle out in out in COP R, Carnot 1 1 out / in 1 / 1 COP R, Carnot For the eat Pump cycle COP out out 1 th COP W 1 / cycle out in in out 1 1 COP, Carnot, Carnot 1 in / out 1 / 12

13 hinking like Clausius My colleagues, Kelvin and Rankine, have proposed that for a Carnot heat engine, I can rewrite this expression as,,, An alternative way to write this is,,, 0 13

14 hinking like Clausius I have to remember that these expressions have been developed for a Carnot cycle. Since we are considering a cycle that is ersible, it must be true that, d,, 0 I know that if the cyclic integral of a differential quantity is zero, the quantity must be a property. herefore, it must be true that, d is the differential of a property! 14

15 hinking like Clausius I know that d is not a property, but (d / ) for a ersible process is a property! Since I discovered this property, I choose to call it entropy and give it the symbol, S. herefore, In 1865, Clausius wrote, ds We might call S the transformational content of the body, just as we have termed the quantity U the heat and work content of the body. But since I believe it is better to borrow terms for important quantities from the ancient languages so that they may be adopted unchanged in all modern languages, I propose to call the quantity S the entropy of the body, from the Greek trop, meaning a transformation. 15

16 he Inequality of Clausius Clausius demonstrated that for a closed ersible process, ds It can be shown that for a closed irersible process (Sec 7.7) ds herefore, for any closed process, ds his is known as the Inequality of Clausius 16

Classical Approach to 2 nd Law for CM

Classical Approach to 2 nd Law for CM Classical Approach to 2 nd aw for CM Start with observations about the ability to build devices (thermodynamic cycles) Clausius Statement of 2 nd aw concerns cycles that cause heat transfer from low temperature