Lecture 14 Refrigerators & Entropy
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LECTURE 14 REFRIGERATORS & ENTROPY
Lecture instructor: Kazumi Tolich Lecture 14
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¨ Reading chapter 15-6 to 15-7. ¤ Refrigerators ¤ Air conditions ¤ Heat pumps ¤ Entropy Refrigerators, air conditions, and heat pump
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¨ Heat will flow spontaneously only from a higher temperature to a lower one.
¨ It can be made to flow the other way if work is done on the system.
¨ Refrigerators, air conditioners, and heat pumps all use work to transfer heat from a cold object to a hot object.
¨ Refrigerators, air conditioners, and heat pumps are heat engines running backwards. Refrigerators
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¨ The refrigerator uses work to extract heat from the cold reservoir (the inside of the refrigerator) and exhausts to the kitchen.
¨ More heat is exhausted to the kitchen than is removed from the refrigerator.
¨ An ideal refrigerator would remove the most heat from the interior while requiring the smallest amount of work. This ratio is called the coefficient of performance, COP: Q COP = c W ¨ Typical refrigerators have COP values between 2 and 6. Bigger is better! Heat pump
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¨ A heat pump is the same as an air conditioner, except with the reservoirs reversed.
¨ Heat is removed from the cold reservoir outside, and exhausted into the house, keeping it warm.
¨ Note that the work the pump does actually contributes to the desired result (a warmer house) in this case.
¨ In an ideal heat pump with two operating temperatures (cold and hot), the Carnot relationship holds.
¨ The work needed to add heat Qh to a room is:
¨ The COP for a heat pump: Q COP = h W Clicker question: 1
6 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 of a reversible system
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¨ The change in entropy ΔS for a reversible system: Q ΔS = T
¨ Entropy is associated with the degree of disorder or the unavailability of energy to do work. � = ∆� �
¤ T0 is the lowest temperature utilized. ¨ In a reversible heat engine, it can be shown that the entropy does not change.
¨ Entropy is a state function; it depends only on the state of the system, and not on how the system gets to that state. Change in entropy of an irreversible system
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¨ A real engine will operate at a lower efficiency than a reversible engine; this means that less heat is converted to work.
¨ Any irreversible process results in an increase of entropy. Entropy of the universe
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¨ The total entropy of the universe: ¤ increases whenever an irreversible process occurs. ¤ is unchanged whenever a reversible process occurs.
¨ Since all real processes are irreversible, the entropy of the universe continually increases.
¨ If entropy decreases in a system due to work being done on it, a greater increase in entropy occurs outside the system.
¨ As the total entropy of the universe increases, its ability to do work decreases.
¨ The excess heat exhausted during an irreversible process cannot be recovered; doing that would require a decrease in entropy, which is not possible. 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 ? Organized to less organized
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¨ A molecular view of a hot gas and a cold one:
a) Before they are put into contact.
b) After thermal energy flows from left to right. The fast molecules are no longer separated from the slow molecules.
¨ When heat flows from hot to cold in an irreversible system, microscopic disorganization always increases.
¨ Another way to state the second law: The total entropy (or microscopic disorganization) of all the participants in any physical process cannot decrease during that process. The law of entropy
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¨ The law of entropy means that processes must go in the direction of increasing entropy and are irreversible. ¤ Hot and cold boxes of gas can come to the same temperature spontaneously. But they cannot start from the same temperature and evolve to different temperatures spontaneously. ¤ A book can fall onto a table, converting the gravitational potential energy into kinetic energy, then into thermal energy. But a book sitting on a table cannot jump up by converting its thermal energy into kinetic energy and then into gravitational potential energy. ¤ Conservation of energy would allow this, but not the second law of thermodynamics. Quality of energy
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¨ 100% of kinetic energy can be converted into gravitational potential energy, and vice versa.
¨ However, the creation of thermal energy is irreversible – you can never convert it all back to work.
¨ Friction causes things to slow down and stop. The energy is still there, but the energy quality is lost.
¨ Thermal energy is less useful, or energy of lower quality. Clicker question: 2
15 Second law of thermodynamics and statistics
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¨ Suppose you start with an organized deck of cards (numbers are in orders, and suits are separated). ¨ After you randomly shuffle the cards, the cards are most likely disorganized.
¨ There are many ways to disorganize the cars, but there is only one way to organize it. ¨ It takes more effort to organize.
¨ Everything is evolving into more disorganization. Why is your room messy?
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¨ There are fewer ways to clean your room than making it messy.
¨ Unless you put work into it to organize your room, your room will get messier and messier.
¨ Blame the second law of thermodynamics. Demo: 1
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¨ Entropy of pennies ¤ Demonstration of statistical likeliness toward increased disorganization Heat death of the universe
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¨ The universe began in a highly organized, low-entropy state at the time of the big bang.
¨ The entropy of the universe has been increasing ever since.
¨ The entropy of the universe will continue to increase until the entire universe would have come to the same temperature.
¨ At this point, it would no longer be possible to do any work, nor would any type of life be possible. ¤ All the stars will burn out, and no new stars will be created. ¤ Life will not exist without stars.
¨ This is called the “heat death” of the universe. Entropy and biological systems
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¨ In biological systems entropy often decreases.
¤ A growing leaf makes complex glucose molecules, C6H12O6, from simple CO2 and H2O.
¨ But the second law of thermodynamics says that the total entropy in the universe increases.
¨ If you include the sun’s radiant energy, the total entropy increases as it should. Third law of thermodynamics
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¨ Absolute zero is a temperature that an object can get arbitrarily close to, but never attain.
-8 ¨ Temperatures as low as 2.0 × 10 K have been achieved in the laboratory, but absolute zero will remain ever elusive – there is simply nowhere to “put” that last little bit of energy.
¨ This is the third law of thermodynamics: It is impossible to lower the temperature of an object to absolute zero in a finite number of steps.