Textbook Question
A certain brand of freezer is advertised to use kWh of energy per year. What is the theoretical maximum amount of ice this freezer could make in an hour, starting with water at °C?
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Ch 20: The Second Law of Thermodynamics
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 20, Problem 14b
A Carnot engine is operated between two heat reservoirs at temperatures of K and K. How much mechanical work is performed by the engine during each cycle?
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Understand the concept of a Carnot engine: A Carnot engine is an idealized heat engine that operates on the reversible Carnot cycle. It is the most efficient engine possible between two heat reservoirs.
Identify the given temperatures: The high-temperature reservoir (T1) is at 520 K, and the low-temperature reservoir (T2) is at 300 K.
Calculate the efficiency of the Carnot engine using the formula: \( \eta = 1 - \frac{T2}{T1} \). Substitute the given temperatures into this formula to find the efficiency.
Relate the efficiency to work and heat: The efficiency \( \eta \) is also defined as the ratio of the work done by the engine (W) to the heat absorbed from the high-temperature reservoir (Q1), i.e., \( \eta = \frac{W}{Q1} \).
To find the mechanical work performed (W), rearrange the efficiency formula to \( W = \eta \times Q1 \). You will need the value of Q1, the heat absorbed from the high-temperature reservoir, to calculate W.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Carnot Engine
A Carnot engine is a theoretical thermodynamic cycle that operates between two heat reservoirs, achieving maximum efficiency. It is an idealized model that assumes no energy losses due to friction or other inefficiencies, and its efficiency depends solely on the temperatures of the heat reservoirs.
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Entropy of Carnot Engine
Thermodynamic Efficiency
Thermodynamic efficiency of a heat engine is defined as the ratio of work output to heat input. For a Carnot engine, this efficiency is determined by the temperatures of the hot and cold reservoirs, calculated using the formula: Efficiency = 1 - (T_cold/T_hot), where temperatures are in Kelvin.
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Mechanical Work in Thermodynamics
Mechanical work in thermodynamics refers to the energy transferred by the system to its surroundings during a cycle. In the context of a Carnot engine, the work done is the useful energy output, calculated by multiplying the efficiency by the heat absorbed from the hot reservoir during each cycle.
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Related Practice
Textbook Question
A Carnot engine is operated between two heat reservoirs at temperatures of K and K. What is the thermal efficiency of the engine?
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Textbook Question
A Carnot engine is operated between two heat reservoirs at temperatures of K and K. If the engine receives kJ of heat energy from the reservoir at K in each cycle, how many joules per cycle does it discard to the reservoir at K?
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Textbook Question
A certain brand of freezer is advertised to use kWh of energy per year. Assuming the freezer operates for hours each day, how much power does it require while operating?
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Textbook Question
A refrigerator has a coefficient of performance of , runs on an input of W of electrical power, and keeps its inside compartment at °C. If you put a dozen -L plastic bottles of water at °C into this refrigerator, how long will it take for them to be cooled down to °C? (Ignore any heat that leaves the plastic.)
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Textbook Question
The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of . What is the ideal efficiency of the engine? Use .
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