# The Second Law of Thermodynamics

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The Second Law of Thermodynamics
Chapter 20 The Second Law of Thermodynamics

Goals for Chapter 20 To learn what makes a process reversible or irreversible To understand heat engines and their efficiency To see how internal combustion engines operate To learn the operation of refrigerators and heat engines To see how the second law of thermodynamics limits the operations of heat engines and refrigerators To do calculations with Carnot engines and refrigerators To understand entropy and to use it to analyze thermodynamic processes

Introduction Why does heat flow from the hot lava into the cooler water? Could it flow the other way? It is easy to convert mechanical energy completely into heat, but not the reverse. Why not? We need to use the second law of thermodynamics and the concept of entropy to answer the above questions.

Directions of thermodynamic processes
The direction of a reversible process can be reversed by an infinitesimal change in its conditions. The system is always in or very close to thermal equilibrium. All other thermodynamic processes are irreversible. Figure 20.1 illustrates an irreversible and a reversible process.

Heat engines A heat engine is any device that partly transforms heat into work or mechanical energy. Simple heat engines operate on a cyclic process during which they absorb heat QH from a hot reservoir and discard some heat QC to a cold reservoir. Figure 20.3 at the right shows a schematic energy-flow diagram for a heat engine.

The efficiency of a heat engine
The thermal efficiency e of a heat engine is the fraction of QH that is converted to work. e = W/QH Read Problem-Solving Strategy 20.1. Follow Example 20.1 to analyze a heat engine using Figure 20.4 at the right.

Internal-combustion engines
Figure 20.5 below illustrates a four-stroke internal-combustion engine. The compression ratio r is the ratio of the maximum volume to the minimum volume during the cycle.

The Otto cycle and the Diesel cycle
Figures 20.6 and 20.7 below show pV-diagrams for idealized Otto cycle and Diesel cycle engines. In both cases, the efficiency depends on the compression ratio r.

Refrigerators A refrigerator takes heat from a cold place (inside the refrigerator) and gives it off to a warmer place (the room). An input of mechanical work is required to do this. A refrigerator is essentially a heat engine operating in reverse. Figure 20.8 at the right shows an energy-flow diagram of a refrigerator. The coefficient of performance K of a refrigerator is K = |QC|/|W|.

Practical refrigerators
Figure 20.9 below shows the principle of the mechanical refrigeration cycle and how the key elements are arranged in a practical refrigerator.

Air conditioner An air conditioner works on the same principle as a refrigerator. (See Figure below.) A heat pump operates in a similar way.

The second law of thermodynamics
The second law of thermodynamics can be stated in several ways: No cyclic process can convert heat completely into work. No cyclic process can transfer heat from a colder place to a hotter place without the input of mechanical work. Figure at the right illustrates both statements.

The Carnot cycle A Carnot cycle has two adiabatic segments and two isothermal segments. The pV-diagram in Figure below shows the complete cycle.

Analyzing a Carnot cycle
Follow the derivation of the efficiency of a Carnot engine. eCarnot = 1 – TC/TH Follow Example 20.2 using Figure at the right. Follow Example 20.3.

The Carnot refrigerator
A Carnot engine run in reverse is a Carnot refrigerator. The coefficient of performance of a Carnot refrigerator is Kcarnot = TC/(TH – TC). Follow Example 20.4.

The Carnot cycle and the second law
No engine can be more efficient than a Carnot engine operating between the same two temperatures. Follow the proof of this in the text, using Figure below.

Entropy and disorder Entropy provides a quantitative measure of disorder. The explosion of the firecracker in Figure increases its disorder and entropy. Follow the discussion in the text of the entropy for reversible processes. Follow Example 20.5 for melting ice. Follow Example 20.6 for heating water.

Entropy change in some adiabatic processes

Entropy in cyclic processes
The entropy change during any reversible cycle is zero. Figure below helps to explain why. For an irreversible process the entropy of an isolated system always increases. Entropy is not a conserved quantity. Follow Example

Entropy and the second law
The second law of thermodynamics can be stated in terms of entropy: No process is possible in which the total entropy of an isolated system decreases. In Figure below, the entropy (disorder) of the ink-water system increases as the ink mixes with the water. Spontaneous unmixing of the ink and water is never observed.

Microscopic interpretation of entropy
Follow the discussion of the microscopic interpretation of entropy, using Figure at the right. The entropy of a macrostate having w microstates is S = k ln w.

A microscopic calculation of entropy change
Follow Example for a free expansion using Figure below.