Textbook Question
A diesel engine performs J of mechanical work and discards J of heat each cycle. How much heat must be supplied to the engine in each cycle?
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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 8a
Calculate the theoretical efficiency for an Otto-cycle engine with and .
Verified step by step guidance1
Understand the Otto cycle: The Otto cycle is a thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It consists of two isochoric processes (constant volume) and two adiabatic processes (no heat exchange).
Identify the formula for the efficiency of an Otto cycle engine: The efficiency \( \eta \) of an Otto cycle engine is given by the formula \( \eta = 1 - \frac{1}{r^{\gamma - 1}} \), where \( r \) is the compression ratio and \( \gamma \) is the specific heat ratio.
Substitute the given values into the formula: You are given \( \gamma = 1.40 \) and \( r = 9.50 \). Substitute these values into the efficiency formula: \( \eta = 1 - \frac{1}{9.50^{1.40 - 1}} \).
Simplify the expression: Calculate \( 1.40 - 1 \) to get \( 0.40 \). Then, compute \( 9.50^{0.40} \) to find the value of the denominator.
Calculate the efficiency: Subtract the result from 1 to find the theoretical efficiency of the Otto-cycle engine.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Otto Cycle
The Otto cycle is a thermodynamic cycle that describes the functioning of a typical spark-ignition piston engine. It consists of two adiabatic and two isochoric processes. Understanding the Otto cycle is crucial for calculating the efficiency of engines that operate on this cycle, such as gasoline engines.
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Specific Heat Ratio (γ)
The specific heat ratio, denoted as γ (gamma), is the ratio of the specific heat at constant pressure (Cp) to the specific heat at constant volume (Cv). It is a critical parameter in thermodynamics, affecting the efficiency of cycles like the Otto cycle. For air, γ is typically around 1.40, which influences the theoretical efficiency calculation.
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Compression Ratio (r)
The compression ratio, denoted as r, is the ratio of the maximum to minimum volume in the cylinder of an internal combustion engine. It is a key factor in determining the efficiency of the Otto cycle, as higher compression ratios generally lead to higher efficiencies. In this question, r is given as 9.50, which is used in the efficiency formula.
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Related Practice
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 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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