Textbook Question
What are (a) the heat extracted from the cold reservoir and (b) the coefficient of performance for the refrigerator shown in FIGURE EX21.21?
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Ch 21: Heat Engines and Refrigerators
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 21, Problem 21
The heat engine shown in FIGURE P21.62 uses 2.0 mol of a monatomic gas as the working substance.c. What is the engine's thermal efficiency?
Verified step by step guidance1
Identify the type of cycle the heat engine is operating on (e.g., Carnot, Otto, etc.) and the properties of the working substance, which in this case is a monatomic gas.
Calculate the total heat absorbed (Q_in) by the engine during the heating part of the cycle. This can be done using the formula Q = nC_\(\Delta\) T, where n is the number of moles, C is the molar heat capacity at constant volume for a monatomic gas (3/2 R), and \(\Delta\) T is the change in temperature.
Calculate the total heat expelled (Q_out) by the engine during the cooling part of the cycle, using a similar approach as for Q_in.
Use the formula for thermal efficiency, \(\eta\) = 1 - \(\frac{Q_{out}\)}{Q_{in}}, to find the efficiency of the engine. Substitute the values of Q_out and Q_in obtained from the previous steps.
Interpret the result in terms of efficiency, considering that for real engines, the efficiency is always less than 1 (or 100%).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Thermal Efficiency
Thermal efficiency is a measure of how well a heat engine converts heat energy into work. It is defined as the ratio of the work output of the engine to the heat input from the hot reservoir. The efficiency can be expressed as a percentage, and higher efficiency indicates a more effective engine. For ideal engines, the maximum efficiency can be calculated using the Carnot efficiency formula, which depends on the temperatures of the hot and cold reservoirs.
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Thermal Efficiency & The Second Law of Thermodynamics
First Law of Thermodynamics
The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of a heat engine, this principle implies that the heat absorbed from the hot reservoir minus the work done by the engine equals the heat expelled to the cold reservoir. This law is fundamental in analyzing energy transfers and understanding how engines operate within the constraints of energy conservation.
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Monatomic Gas Behavior
Monatomic gases consist of single atoms and exhibit specific thermodynamic properties, such as a distinct relationship between pressure, volume, and temperature described by the ideal gas law. For monatomic gases, the specific heat capacities at constant volume and pressure are well-defined, which influences the calculations of work done and heat transfer in thermodynamic processes. Understanding these properties is crucial for determining the performance of the heat engine using such gases.
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Related Practice
Textbook Question
Which, if any, of the heat engines in FIGURE EX21.22 violate (a) the first law of thermodynamics or (b) the second law of thermodynamics? Explain.
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Textbook Question
At what cold-reservoir temperature (in ℃) would a Carnot engine with a hot-reservoir temperature of 427℃ have an efficiency of 60%?
Textbook Question
An air conditioner removes 5.0 x 10⁵ J/min of heat from a house and exhausts 8.0 x 10⁵ J/min to the hot outdoors. What is the air conditioner's coefficient of performance?
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Textbook Question
What are (a) the thermal efficiency and (b) the heat extracted from the hot reservoir for the heat engine shown in FIGURE EX21.16?
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Textbook Question
A 15 kW electric generator burns 1.2 gal of diesel fuel per hour. The energy density of diesel fuel is 140 MJ/gal. What is the generator's thermal efficiency?