Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

Q31PE

Expert-verified
College Physics (Urone)
Found in: Page 551
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

Steam locomotives have an efficiency of \(17\% \) and operate with a hot steam temperature of \(425{\;^o}C\). (a) What would the cold reservoir temperature be if this were a Carnot engine? (b) What would the maximum efficiency of this steam engine be if its cold reservoir temperature were \(150{\;^o}C\)?

For a Carnot’s engine, the temperature of the cold reservoir is \(306.34\;^\circ {\rm{C}}\). Maximum efficiency can be achieved, when the temperature of the cold reservoir is \(150\;^\circ {\rm{C}}\), is \(39.4\% \).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Introduction

We calculate the temperature of the hot reservoir by using the formula for efficiency of the Carnot engine when the efficiency and temperature of the cold reservoir are given. We further find the efficiency when the temperature of the cold reservoir is 150oC.

Step 2:  Given parameters and formula for efficiency of heat engine

Efficiency of engine\(\eta = 17\% \)

The temperature of the hot reservoir \({T_h} = 425\;^\circ {\rm{C}} = 698\;{\rm{K}}\)

The efficiency of the Carnot engine \(h = 1 - \frac{{{T_c}}}{{{T_h}}}\)

Here,

\(\eta \) - efficiency of the engine.

\({T_c}\)- the temperature of the cold reservoir.

\({T_h}\)- temperature of hot reservoir.

Step 3:  Calculate the temperature of cold reservoir

The temperature of cold reservoir is calculated as

\(\begin{aligned}{}h &= 1 - \frac{{{T_c}}}{{{T_h}}}\\0.17 &= 1 - \frac{{{T_c}}}{{698\;{\rm{K}}}}\\\frac{{{T_c}}}{{698\;{\rm{K}}}} = 1 - 0.17\end{aligned}\)

\(\begin{aligned}{}{T_c} &= 698\;{\rm{K}} \times 0.83\\ &= 579.34\;{\rm{K}}\\ &= 306.34{\;^o}{\rm{C}}\end{aligned}\)

Step 4:  Calculate efficiency when temperature of cold reservoir is 150oC

Temperature of cold reservoir \({T_c} = 150\;^\circ {\rm{C}}\)

Efficiency of engine is

\(\begin{aligned}{}h &= 1 - \frac{{{T_c}}}{{{T_h}}}\\ &= 1 - \frac{{423\;{\rm{K}}}}{{698\;{\rm{K}}}}\\ &= 0.394\\ &= 39.4\% \end{aligned}\)

Therefore, the temperature of cold reservoir is \(306.34{\;^o}{\rm{C}}\) for Carnot engine. Maximum efficiency is \(39.4\% \)when temperature of cold reservoir is \(150\;^\circ {\rm{C}}\).

Most popular questions for Physics Textbooks

Is a temperature difference necessary to operate a heat engine? State why or why not.

In some Northern European nations, homes are being built without heating systems of any type. They are very well insulated and are kept warm by the body heat of the residents. However, when the residents are not at home, it is still warm in these houses. What is a possible explanation?

Grocery store managers contend that there is less total energy consumption in the summer if the store is kept at a low temperature. Make arguments to support or refute this claim, taking into account that there are numerous refrigerators and freezers in the store.

What is the decrease in entropy of 25.0 g of water that condenses on a bathroom mirror at a temperature of 35.0 º C, assuming no change in temperature and given the latent heat of vaporization to be 2450 kJ/kg?

Does a gas become more orderly when it liquefies? Does its entropy change? If so, does the entropy increase or decrease? Explain your answer.
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

Work Energy and Power

Read explanation

Radiation

Read explanation

Astrophysics

Read explanation

Physics of Motion

Read explanation

Scientific Method Physics

Read explanation

Fluids

Read explanation

Torque and Rotational Motion

Read explanation

Nuclear Physics

Read explanation

Fields in Physics

Read explanation

Measurements

Read explanation

Space Physics

Read explanation

Electricity

Read explanation

Physical Quantities and Units

Read explanation

Medical Physics

Read explanation

Electrostatics

Read explanation

Further Mechanics and Thermal Physics

Read explanation

Mechanics and Materials

Read explanation

Engineering Physics

Read explanation

Energy Physics

Read explanation

Force

Read explanation

Particle Model of Matter

Read explanation

Waves Physics

Read explanation

Magnetism

Read explanation

Modern Physics

Read explanation

Atoms and Radioactivity

Read explanation

Dynamics

Read explanation

Electricity and Magnetism

Read explanation

Conservation of Energy and Momentum

Read explanation

Fundamentals of Physics

Read explanation

Kinematics Physics

Read explanation

Circular Motion and Gravitation

Read explanation

Linear Momentum

Read explanation

Rotational Dynamics

Read explanation

Oscillations

Read explanation

Translational Dynamics

Read explanation

Geometrical and Physical Optics

Read explanation

Thermodynamics

Read explanation

Magnetism and Electromagnetic Induction

Read explanation

Electromagnetism

Read explanation

Electric Charge Field and Potential

Read explanation

Turning Points in Physics

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.