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?
2
views
Ch 20: The Second Law of Thermodynamics
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
Not the one you use?Change textbookSelect a different textbook
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 9a
The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of . What is the ideal efficiency of the engine? Use .
Verified step by step guidance1
Understand that the Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. The efficiency of an Otto cycle depends on the compression ratio and the specific heat ratio (γ).
The formula for the efficiency (η) of an ideal Otto cycle is given by: η = 1 - (1 / r^(γ - 1)), where r is the compression ratio and γ is the specific heat ratio.
Identify the given values: the compression ratio (r) is 8.8 and the specific heat ratio (γ) is 1.40.
Substitute the given values into the efficiency formula: η = 1 - (1 / 8.8^(1.40 - 1)).
Simplify the expression to find the ideal efficiency of the engine. Remember, the result will be a decimal that represents the efficiency as a fraction of 1, which can be converted to a percentage by multiplying by 100.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
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 four processes: two isochoric (constant volume) and two adiabatic (no heat transfer). Understanding the Otto cycle is crucial for calculating the efficiency of engines like the one in the Mercedes-Benz SLK230.
Recommended video:
Guided course
10:59
The Otto Cycle
Compression Ratio
The compression ratio 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 engine, as higher compression ratios typically lead to higher thermal efficiency. In this question, the compression ratio is given as 8.8, which is essential for calculating the engine's ideal efficiency.
Recommended video:
Guided course
17:42Finding the Compression Ratio
Adiabatic Process
An adiabatic process is one in which no heat is transferred to or from the system. In the context of the Otto cycle, the adiabatic processes are crucial for determining the work done by the engine and its efficiency. The specific heat ratio (γ), given as 1.40, is used in the efficiency formula for adiabatic processes in the Otto cycle.
Recommended video:
Guided course
06:13Entropy & Ideal Gas Processes
Related Practice
Textbook Question
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?
1
views
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?
2
views
Textbook Question
Calculate the theoretical efficiency for an Otto-cycle engine with and .
1
views
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.)
2
views