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 Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 20, Problem 6a
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
The coefficient of performance is a dimensionless quantity. Its value is independent of the units used for and , as long as the same units, such as watts, are used for both quantities. However, it is common practice to express in Btu/h and in watts. When these mixed units are used, the ratio is called the energy efficiency ratio (). If a room air conditioner has , what is its ?
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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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