The Limits of Efficiency. The Limits of Efficiency. The Limits of Efficiency

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The Limits of Efficiency If a perfectly reversible heat engine is used to operate a perfectly reversible refrigerator, the two devices exactly cancel each other.

Slide 20-1 The Limits of Efficiency A heat engine more efficient than a perfectly reversible engine could be used to violate the second law of thermodynamics.

1 The Limits of Efficiency If a perfectly reversible heat engine is used to operate a perfectly reversible refrigerator, the two devices exactly cancel each other Pearson Education, Inc. Slide 20-1 The Limits of Efficiency A heat engine more efficient than a perfectly reversible engine could be used to violate the second law of thermodynamics Pearson Education, Inc. Slide 20-2 The Limits of Efficiency The maximum possible efficiency of a heat engine e is that of a perfectly reversible engine. The maximum possible coefficient of performance of a refrigerator K max is that of a perfectly reversible refrigerator Pearson Education, Inc. Slide

The Limits of Efficiency A perfectly reversible engine must use only two types of processes: 1. Frictionless mechanical interactions with no heat transfer (Q = 0). 2.

2 The Limits of Efficiency A perfectly reversible engine must use only two types of processes: 1. Frictionless mechanical interactions with no heat transfer (Q = 0). 2. Thermal interactions in which heat is transferred in an isothermal process (ΔE th = 0). Any engine that uses only these two types of processes is called a Carnot engine. A Carnot engine is a perfectly reversible engine; it has the maximum possible thermal efficiency e and, if operated as a refrigerator, the maximum possible coefficient of performance K max Pearson Education, Inc. Slide 20-4 The Carnot cycle A Carnot cycle has two adiabatic segments and two isothermal segments. The Carnot engine The Carnot cycle consists of the following steps: 1. The gas expands isothermally at temperature T H, absorbing heat Q H. 2. It expands adiabatically until its temperature drops to T C. 3. It is compressed isothermally at T C, rejecting heat Q C. 4. It is compressed adiabatically back to its initial state at temperature T H. The efficiency of a Carnot engine is: 2

Engine efficiency To maximize the efficiency of a real engine, the designer must make the intake temperature T H

For this reason, the temperatures inside a jet engine are made as high as possible.

3 Engine efficiency To maximize the efficiency of a real engine, the designer must make the intake temperature T H as high as possible and the exhaust temperature T C as low as possible. For this reason, the temperatures inside a jet engine are made as high as possible. Exotic ceramic materials are used that can withstand temperatures in excess of 1000 C without melting or becoming soft. The Carnot cycle and the second law No engine can be more efficient than a Carnot engine operating between the same two temperatures. QuickCheck The efficiency of this Carnot heat engine is A. Less than 0.5 B. 0.5 C. Between 0.5 and 1.0 D Pearson Education, Inc. Slide

4 QuickCheck The efficiency of this Carnot heat engine is A. Less than 0.5 B. 0.5 C. Between 0.5 and 1.0 D Pearson Education, Inc. Slide Q20.7 A Carnot engine takes heat in from a reservoir at 400 K and discards heat to a reservoir at 300 K. If the engine does 12,000 J of work per cycle, how much heat does it take in per cycle? A. 48,000 J B. 24,000 J C. 16,000 J D J 2016 Pearson Education, Inc. QuickCheck The efficiency of this heat engine is A. Less than 0.5 B. 0.5 C. Between 0.5 and 1.0 D. 1.0 E Pearson Education, Inc. Slide

QuickCheck This heat engine is A. A reversible Carnot engine. B. An irreversible engine. C. An impossible engine. 2017 Pearson Education, Inc. Slide 20-13 Example 1 Suppose 0.

5 QuickCheck This heat engine is A. A reversible Carnot engine. B. An irreversible engine. C. An impossible engine Pearson Education, Inc. Slide Example 1 Suppose mol of an ideal diatomic gas undergoes a Carnot cycle between 227ºC and 27ºC, starting at pa = 10.0 x 10 5 Pa at point a. the volume doubles during the isothermal expansion step a b. Find the pressure and volume at points a, b, c, and d. Find Q, W, and ΔE th for each step and for the entire cycle. Find the efficiency Pearson Education, Inc. Slide In-class Activity #1 A Carnot engine takes 2000 J of heat from a reservoir at 500 K, does some work, and discards some heat to a reservoir at 350 K. How much work does it do, how much heat is discarded, and what is its efficiency? 2017 Pearson Education, Inc. Slide

The Carnot refrigerator Because each step in the Carnot cycle is reversible, the entire cycle may be reversed, converting the engine into a refrigerator.

6 The Carnot refrigerator Because each step in the Carnot cycle is reversible, the entire cycle may be reversed, converting the engine into a refrigerator. The coefficient of performance of the Carnot refrigerator is: Last example? performance Entropy and disorder Entropy provides a quantitative measure of disorder. Many processes proceed naturally in the direction of increasing randomness. Adding heat to a body increases average molecular speeds; therefore, molecular motion becomes more random. The explosion of the firecracker shown increases its disorder and entropy. Entropy in reversible processes We introduce the symbol S for the entropy of the system, and we define the infinitesimal entropy change ds during an infinitesimal reversible process at absolute temperature T as: The total entropy change over any reversible process is: 6

7 Example 2 What is the change of entropy of 1 kg of ice that is melted reversibly at 0ºC and converted to water at 0ºC? The heat of fusion of water is L f = 334 kj/kg Pearson Education, Inc. Slide Example 3 One kilogram of water at 0ºC is heated to 100ºC. Compute its change in entropy. Assume that the specific heat of water is constant over this temperature range Pearson Education, Inc. Slide Q20.3 An ideal gas is taken around the cycle shown in this p-v diagram, from a to c to b and back to a. Process c b is adiabatic. Which of the processes in this cycle could be reversible? A. a c B. c b C. b a D. two or more of A, B, and C E. none of A, B, or C 7

8 Example 4 For the Carnot example earlier (In-class Activity #1), what is the total entropy change during one cycle? 2017 Pearson Education, Inc. Slide 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 decreases, when all systems taking part in the process are included. The entropy of the ink water system increases as the ink mixes with the water. Example In-class Activity 1 #2 Suppose 1.00 kg of water at 100ºC is placed in thermal contact with 1.00 kg of water at 0ºC. What is the total change in entropy? Assume that the specific heat of water is constant over this temperature range. 8

Chapter 16 The Second Law of Thermodynamics

Chapter 16 The Second Law of Thermodynamics To examine the directions of thermodynamic processes. To study heat engines. To understand internal combustion engines and refrigerators. To learn and apply