LECTURE 11 SECOND LAW OF THERMODYNAMICS

Lecture instructor: Kazumi Tolich Lecture 11

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¨ Reading chapter 18.5 to 18.10 ¤ The second law of thermodynamics ¤ Heat engines ¤ Refrigerators ¤ Air conditions ¤ Heat pumps ¤ Entropy Second law of thermodynamics

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¨ The second law of thermodynamics states:

Thermal energy flows spontaneously from higher to lower temperature.

Heat engines are always less than 100% efficient at using thermal energy to do work.

The total entropy of all the participants in any physical process cannot decrease during that process. Heat engines

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¨ Heat engines depend on the spontaneous heat flow from hot to cold to do work.

¨ In each cycle, the hot reservoir supplies heat � to the engine which does work �and exhausts heat � to the cold reservoir.

� = � − �

¨ The energy efficiency of a heat engine is given by

� � = � Carnot’s theorem and maximum efficiency

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¨ The maximum-efficiency heat engine is described in Carnot’s theorem:

If an engine operating between two constant-temperature reservoirs is to have maximum efficiency, it must be an engine in which all processes are reversible. In addition, all reversible engines operating between the same two temperatures, � and �, have the same efficiency.

¨ This is an idealization; no real engine can be perfectly reversible.

¨ The maximum efficiency of a heat engine (Carnot engine) can be written as:

� � = 1 − � Quiz: 1

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¨ Consider the heat engine at right. � denotes the heat extracted from the hot reservoir, and � denotes the heat exhausted to the cold reservoir in one cycle. What is the work done by this engine in one cycle in Joules? Quiz: 11-1 answer

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¨ 4000 J

¨ � = � − � = 8000 J − 4000 J = 4000 J Quiz: 2

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¨ What kind of engine is this? A. a reversible (Carnot) heat engine B. an irreversible heat engine C. a hoax Quiz: 11-2 answer

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¨ An irreversible engine

¨ The efficiency of this engine: � = = = 0.5

¨ The maximum efficiency this engine could have based on the temperatures of the hot and cold reservoirs:

� = 1 − = = 0.55

¨ Since � > �, this is an irreversible engine.

¨ If � = �, this would have been a reversible engine.

¨ If � < �, this would have been a hoax. Refrigerators, air conditions, and heat pump

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¨ Refrigerators, air conditioners, and heat pumps all use work to transfer heat from a cold object to a hot object: � = � + � ¨ The coefficient of performance, COP: of refrigerators is

� COP = �

¨ The COP for a heat pump is

� COP = � Quiz: 3

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¨ In an ideal heat pump with two operating temperatures, cold � and hot �, what is the work needed add heat � to a room? A. � 1 − B. � C. � 1 − D. � E. � F. Quiz: 11-3 answer

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¨ � 1 − ¨ In an ideal heat pump, the Carnot relationship holds: = ¨ � = � + � ¨ � = � − � = � 1 − = � 1 − Quiz: 4

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¨ If you run a refrigerator in a thermally insulated room with the door to the refrigerator open, the temperature of the room A. increases. B. remains the same. C. decreases. D. Any of these can happen depending on how efficient the refrigerator is. E. Any of these can happen depending on the relative sizes of the room and the refrigerator. Quiz: 11-4 answer

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¨ increases.

¨ The origin of the work done on the engine is the Kitchen electric energy that you buy from the electric company.

¨ This work is converted into heat and added to the kitchen.

¨ More heat is dumped in the kitchen than extracted.

¨ � = � + � Kitchen Example: 1

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¨ A refrigerator with a coefficient of performance of 1.75 absorbs 4 Qc = 3.45 × 10 J of heat from the low temperature reservoir during each cycle. a) How much mechanical work is required to operate the refrigerator for a cycle? b) How much heat does the refrigerator discard to the high temperature reservoir during each cycle? Change in entropy

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¨ Entropy is a state function that is associated with the degree of disorder or the quality of energy.

¨ The change in entropy ∆� for a reversible system is given by

� ∆� = �

¨ The entropy of the universe remains the same during a reversible process.

¨ All real processes must go in the direction of increasing entropy and are irreversible. ¤ In the process on the right, the end state is less ordered than the initial state—the separation between low and high temperature areas has been lost. Quiz: 5

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¨ We have established that this engine is an irreversible heat engine. We have learned that the change in entropy for a reversible system is given by ∆� = . Can we calculate the change in entropy of this engine during one cycle? A. Yes B. No Quiz: 11-5 answer

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¨ Yes

¨ Since entropy is a state function, we can replace this irreversible process with two equivalent reversible processes and calculate the difference in entropy.

¨ In an irreversible heat engine, the entropy increases by ∆� = − + > 0 Example: 2

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¨ On a winter day, a certain house loses Q = 5.00 ×108 J of heat to the outside (about 500,000 Btu). What is the total change in entropy due to this heat transfer alone, assuming an average indoor temperature of 21.0 ºC and an average outdoor temperature of 5.00 ºC ? Quiz: 6

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¨ During which of the following processes does the entropy of the universe increase? A. Ice dropped in hot coffee makes chilly coffee. B. A book falls onto a table. C. A damped pendulum eventually comes to rest. D. A Carnot engines does work on a piston in a cycle. Quiz: 11-6 answer

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¨ Ice dropped in hot coffee makes chilly coffee.

¨ A book falls onto a table.

¨ A damped pendulum eventually comes to rest.

¨ A Carnot engines does work on a piston in a cycle.

¨ Entropy of the universe increases during irreversible process.

¨ Conservation of energy would allow the reversing of all of these processes, but not the second law of thermodynamics. ¤ Chilly coffee does not spontaneously separate into hot coffee and ice. ¤ A book on the table does not spontaneously gather thermal energy and convert into kinetic energy and then to gravitational potential energy to jump up. ¤ A pendulum at equilibrium position does not spontaneously gather thermal energy to start swinging. n Creation of thermal energy is irreversible – you can never convert it all back to work. Quiz: 7

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¨ A growing leaf makes complex glucose molecules, C6H12O6, from simple CO2 and H2O. Or the theory of evolution tells us that the life started as simple single-cell creatures and evolved into complex organisms. Does it mean that the 2nd law of thermodynamics is violated?

A. Yes

B. No Quiz: 11-7 answer

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¨ No

¨ In biological systems entropy often decreases.

¨ But the second law of thermodynamics says that the total entropy in the universe increases.

¨ If you include the heat flow of sun’s radiant energy which is responsible for all the lives on earth, the total entropy increases as it should. Second law of thermodynamics and statistics

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¨ Why is entropy of the universe always increasing? ¤ Increasing disorganization is more statistically probable, and it takes effort to organize. n Suppose you start with an organized deck of cards (numbers are in orders, and suits are separated). n After you randomly shuffle the cards, the cards are most likely disorganized. n There are many ways to disorganize the cars, but there is only one way to organize it. ¤ Blame the second law of thermodynamics for your messy room. Third law of thermodynamics

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¨ The third law of thermodynamics:

It is impossible to lower the temperature of an object to absolute zero in a finite number of steps.

¤ Temperatures as low as 4.5 × 10-10 K have been achieved in the laboratory, but absolute zero will remain ever elusive.