Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 43

A proposal is submitted for a novel engine that will operate between \(400 . \mathrm{K}\) and \(300 . \mathrm{K}\) a) What is the theoretical maximum efficiency of the engine? b) What is the total entropy change per cycle if the engine operates at maximum efficiency?

Short Answer

Expert verified
Answer: The theoretical maximum efficiency of the engine is 25%, and the total entropy change per cycle if the engine operates at maximum efficiency is 0.

Step by step solution

01

Calculate the theoretical maximum efficiency of the engine

For an engine operating between two temperatures, the theoretical maximum efficiency is given by the Carnot efficiency formula: Efficiency = \(1 - \frac{T_{cold}}{T_{hot}}\) Where \(T_{cold}\) and \(T_{hot}\) are the cold and hot reservoir temperatures, respectively. In this case, we have: \(T_{cold} = 300 \,\mathrm{K}\) and \(T_{hot} = 400 \,\mathrm{K}\) Now we will insert these values into the Carnot efficiency formula: Efficiency = \(1 - \frac{300}{400}\)
02

Simplify the expression

We will simplify the expression to find the efficiency: Efficiency = \(1 - \frac{300}{400} = 1 - \frac{3}{4} = \frac{1}{4}\) So, the theoretical maximum efficiency of the engine is \(\frac{1}{4}\) or 25%.
03

Calculate the total entropy change per cycle

When the engine operates at its maximum efficiency (Carnot efficiency), we know that the total entropy change per cycle is zero: Total entropy change per cycle = 0
04

Write down the answers

a) The theoretical maximum efficiency of the engine is 25%. b) The total entropy change per cycle if the engine operates at maximum efficiency is 0.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

It is desired to build a heat pump that has an output temperature of \(23^{\circ} \mathrm{C}\). Calculate the maximum coefficient of performance for the pump when the input source is (a) outdoor air on a cold winter day at \(-10.0^{\circ} \mathrm{C}\) and \((\mathrm{b})\) ground water at \(9.0^{\circ} \mathrm{C}\).

An ideal gas undergoes an isothermal expansion. What will happen to its entropy? a) It will increase. c) It's impossible to determine. b) It will decrease. d) It will remain unchanged.

Consider a Carnot engine that works between thermal reservoirs with temperatures of \(1000.0 \mathrm{~K}\) and \(300.0 \mathrm{~K}\). The average power of the engine is \(1.00 \mathrm{~kJ}\) per cycle. a) What is the efficiency of this engine? b) How much energy is extracted from the warmer reservoir per cycle? c) How much energy is delivered to the cooler reservoir?

The entropy of a macroscopic state is given by \(S=k_{B} \ln w\) where \(k_{\mathrm{B}}\) is the Boltzmann constant and \(w\) is the number of possible microscopic states. Calculate the change in entropy when \(n\) moles of an ideal gas undergo free expansion to fill the entire volume of a box after a barrier between the two halves of the box is removed.

20.14 Imagine dividing a box into two equal parts, part \(A\) on the left and part \(B\) on the right. Four identical gas atoms, numbered 1 through 4 , are placed in the box. What are most probable and second most probable distributions (for example, 3 atoms in \(\mathrm{A}, 1\) atom in \(\mathrm{B}\) ) of gas atoms in the box? Calculate the entropy, \(S\), for these two distributions. Note that the configuration with 3 atoms in \(\mathrm{A}\) and 1 atom in \(\mathrm{B}\) and that with 1 atom in A and three atoms in B count as different configurations.
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Mechanics and Materials

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Solid State Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Waves Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free