Textbook Question
A heat engine does 200 J of work per cycle while exhausting 400 J of waste heat. What is the engine's thermal efficiency?
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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 11
A gas following the pV trajectory of FIGURE EX21.11 does 60 J of work per cycle. What is Vmax?
Verified step by step guidance1
Identify the relationship between pressure (p), volume (V), and work (W) in a thermodynamic cycle. The work done by the gas in one cycle is equal to the area enclosed by the pV curve in the diagram.
Analyze the pV diagram (FIGURE EX21.11) to determine the shape of the enclosed area. For example, if the trajectory forms a rectangle, triangle, or other geometric shape, the area can be calculated using the appropriate formula.
Express the work done in terms of the pressure and volume changes. For a rectangular cycle, the work is given by \( W = (p_{max} - p_{min})(V_{max} - V_{min}) \). Rearrange this equation to solve for \( V_{max} \): \( V_{max} = \frac{W}{p_{max} - p_{min}} + V_{min} \).
Substitute the given work value (60 J) and the pressure values \( p_{max} \) and \( p_{min} \) from the diagram into the equation. Also, include \( V_{min} \), which is the minimum volume from the diagram.
Perform the algebraic manipulation to isolate \( V_{max} \). Ensure all units are consistent (e.g., pressure in Pascals, volume in cubic meters, and work in Joules) before substituting numerical values.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Work in Thermodynamics
In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For gases, this is often calculated using the formula W = PΔV, where W is work, P is pressure, and ΔV is the change in volume. Understanding how work is done by or on a gas during expansion or compression is crucial for analyzing thermodynamic cycles.
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Calculating Works For Multiple Thermodynamic Processes
Pressure-Volume (pV) Diagram
A pressure-volume (pV) diagram is a graphical representation of the relationship between the pressure and volume of a gas during a thermodynamic process. The area under the curve in a pV diagram represents the work done by or on the gas. Analyzing the trajectory on this diagram helps in understanding the different states and processes the gas undergoes in a cycle.
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Max Volume (V_max)
V_max refers to the maximum volume that a gas reaches during its thermodynamic cycle. It is a critical parameter in determining the efficiency and work output of the cycle. To find V_max, one must consider the specific path taken in the pV diagram and the work done, as it directly influences the gas's behavior and the energy transformations occurring within the system.
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Related Practice
Textbook Question
The power output of a car engine running at 2400 rpm is 500 kW. How much (a) work is done and (b) heat is exhausted per cycle if the engine's thermal efficiency is 20%? Give your answers in kJ.
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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
What are (a) Wout and QH and (b) the thermal efficiency for the heat engine shown in FIGURE EX21.14?
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Textbook Question
A Boeing 777 jet engine, the world's largest, has a power output of 82 MW. It burns jet fuel with an energy density of 43 MJ /kg. What is the engine's fuel consumption rate, in kg/s, if its efficiency is 30%?
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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?