Textbook Question
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?
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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 18
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?
Verified step by step guidance1
Step 1: Understand the concept of thermal efficiency. Thermal efficiency is the ratio of useful output energy (or power) to the input energy supplied to the system. It is expressed as a percentage and calculated using the formula: , where is the output power and is the input energy per unit time.
Step 2: Calculate the input energy per hour. The energy density of diesel fuel is given as 140 MJ/gal, and the generator burns 1.2 gal of diesel fuel per hour. Multiply the energy density by the fuel consumption rate to find the input energy per hour: MJ/hour.
Step 3: Convert the output power from kilowatts to megajoules per hour. Since 1 kW is equal to 1 kJ/s, and there are 3600 seconds in an hour, multiply the generator's output power (15 kW) by 3600 to convert it to MJ/hour: kJ/hour.
Step 4: Substitute the values of and into the thermal efficiency formula. Use the formula to calculate the efficiency.
Step 5: Simplify the expression to find the thermal efficiency as a percentage. Ensure the units are consistent throughout the calculation (MJ/hour for both and ).
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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 an energy conversion process converts input energy into useful output energy. It is defined as the ratio of the useful work output to the total energy input, often expressed as a percentage. In this context, it helps determine how effectively the generator converts the energy from diesel fuel into electrical energy.
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Energy Density
Energy density refers to the amount of energy stored in a given volume or mass of a substance, typically expressed in units like MJ/gal or J/kg. For diesel fuel, an energy density of 140 MJ/gal indicates how much energy can be extracted from one gallon of fuel. This concept is crucial for calculating the total energy input to the generator from the fuel consumed.
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Power Output
Power output is the rate at which energy is produced or consumed, measured in watts (W) or kilowatts (kW). In this scenario, the generator has a power output of 15 kW, meaning it generates 15 kilojoules of electrical energy per second. Understanding power output is essential for comparing it to the energy input from the fuel to determine the thermal efficiency.
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Related Practice
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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Textbook Question
A gas following the pV trajectory of FIGURE EX21.11 does 60 J of work per cycle. What is Vmax?
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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
What are (a) Wout and QH and (b) the thermal efficiency for the heat engine shown in FIGURE EX21.14?
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