1. The Second Law of Thermodynamics19
Essential University Physics
Richard Wolfson
The Second Law of Thermodynamics
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2. In this lecture you’ll learn
To explain the second law of thermodynamics and the limitations it puts on our ability to extract useful work from thermal energy sources
To understand the thermodynamics of heat engines, refrigerators, and heat pumps
To describe the concepts of energy quality and entropy
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3. Clicker question Which one of the following processes is irreversible?
Stirring sugar into coffee
Building a house
Demolishing a house by removing one piece at a time
Harnessing the energy of falling water to drive machinery
Answer: A
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4. The second law of thermodynamics
The second law of thermodynamics is fundamentally a statement that systems naturally tend toward more disorganized states.
Applied to heat engines, the Kelvin-Planck statement of the second law says that it’s impossible to construct a perfect heat engine—one that operates in a cycle, extracting heat Q and delivering an equal amount of work.
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5. The Carnot engine
A conceptually important heat-engine design is the Carnot engine, whose cycle consists of two adiabatic and two isothermal steps.
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6. Carnot efficiency
The efficiency of the Carnot engine, defined as the ratio of work delivered to heat extracted from the hot reservoir, is
No other engine operating between the same two temperatures can be more efficient than the Carnot engine.
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7. Proof of Carnot’s theorem
The proof involves the Claussius statement of the second law:
It is impossible to build a perfect refrigerator, one whose sole effect is to transfer heat from a cooler object to a hotter one,
And the fact that a reversible engine can also operate as a refrigerator.
Proof of Carnot’s theorem involves showing that a Carnot engine combined with a more efficient engine would constitute a perfect heat engine: =
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8. Clicker question
A clever engineer decides to increase the efficiency of a Carnot engine by cooling the low-temperature reservoir using a refrigerator with the maximum possible COP. Compare the overall efficiency of this modified engine to that of the original engine.
It will be more efficient.
It will have the same efficiency.
It will be less efficient.
Answer: B
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9. Implications for energy technology
The second law limitations on efficiency show that we can’t convert thermal energy to mechanical work with 100% efficiency.
The efficiency depends on the highest and lowest available temperatures:
The former is set by the limitations of materials.
The latter is, at minimum, the temperature of the ambient environment.
Technologies affected include
Electric power plants
Gasoline engines
Jet aircraft engines
A thermal electric power plant The most common heat sources are fossil fuel combustion and nuclear fission.
Typical efficiencies are 30-45%.
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10. Combined cycle: a better power plant
Gas turbines use hot combustion gases to spin a turbine.
Jet aircraft engines are common examples.
Gas turbines have high operating temperatures Th.
But they aren’t very efficient because they have high Tc as well.
Using the exhaust from a gas turbine to drive a conventional steam cycle produces a more efficient combined cycle power plant.
Combined cycle plants have efficiencies approaching 60%.
They therefore emit fewer pollutants and greenhouse gases per unit of electrical energy produced.
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11. Refrigerators and heat pumps
Refrigerators and air conditioners are examples of heat pumps—devices that transfer energy from cooler to hotter objects.
The Clausius statement of the second law says that this transfer can’t occur spontaneously, but requires that external work be supplied.
The coefficient of performance describes the relative amount of work needed:
The larger the temperature difference, the lower the COP and the more work that’s needed.
Heat pumps can be used for both heating and cooling:
They exchange energy with the ambient air or, better,
with the ground, whose temperature stays nearly constant at about 10˚C.
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12. Energy quality Energy is not all created equal!
Since thermal energy can’t be converted to mechanical work or electricity with 100% efficiency, mechanical work and electricity are higher-quality forms of energy.
You can convert them to any other form with 100% efficiency.
High temperature thermal energy is higher quality than lower temperature energy, since it can run a more efficient heat engine and thus produce more mechanical work.
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13. Entropy Entropy is a quantitative measure of energy quality.
Formally, entropy describes the degree of order or disorder in a system.
The lower the entropy, the more ordered the system and the higher the quality of its energy.
The higher the entropy, the more disordered the system and lower the quality of its energy.
Mathematically, the change in entropy ∆S associated with a thermodynamic process between states 1 and 2 is given by
An increase in entropy results in the system’s losing some or all of its ability to do work.
Mixing hot and cold water results in a system with the same energy but higher entropy.
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14. An example: adiabatic free expansion
A gas is confined to one side of a container; the other side is a vacuum.
This is a low-entropy state, since the gas molecules are organized into one side of the container.
The system could do work, by turning a paddle wheel.
But let the gas expand freely into the vacuum.
The new state has the same energy…
…but it has higher entropy
…and it’s lost the ability to do work.
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15. Entropy and the second law
In terms of entropy, the second law reads The entropy of a closed system cannot decrease.
At best, entropy can remain constant.
But irreversible processes and dissipative forces like friction invariably lead to entropy increase.
When the system enlarges to include the entire universe, the second law reads The entropy of the universe cannot decrease.
Any situation that appears to involve an increase in order and thus a decrease in entropy is always accompanied by a corresponding and greater increase in entropy.
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16. Clicker question
Consider a plant using sunlight, carbon dioxide and water to synthesize glucose. How does the entropy of this system change during this process?
The entropy decreases.
The entropy remains the same.
The entropy increases.
Answer: C

17. Summary
The second law of thermodynamics is fundamentally a statement about the tendency of systems to evolve toward more disordered states.
The Kelvin-Planck statement of the second law asserts that it’s impossible to build a perfect heat engine, one that cyclically converts thermal energy into work with 100% efficiency.
The maximum efficiency is the Carnot efficiency: eCarnot = 1 – Tc / Th.
The Clausius statement says that it’s impossible to build a perfect refrigerator, one whose sole effect is to transfer energy from a cooler to a hotter object.
Real refrigerators therefore require mechanical energy input.
In its most general statement, the second law says that the entropy of a closed system cannot decrease.
Entropy is a measure of disorder; the higher the entropy, the more disorder.
High entropy is associated with low-quality energy, and vice versa.
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