Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Problem 1186

A carnot's engine whose sink is at a temperature of \(300 \mathrm{~K}\) has an efficiency of \(40 \%\) By what amount should the temperature of the source change to increase the efficiency to \(60 \%\) (A) \(275 \mathrm{~K}\) (B) \(325 \mathrm{~K}\) (C) \(300 \mathrm{~K}\) (D) \(250 \mathrm{~K}\)

Short Answer

Expert verified
The change in temperature of the source required to increase the efficiency to \(60\%\) is \(250K\), which corresponds to answer choice (D).

Step by step solution

01

Calculate the Initial Temperature of the Source

The initial efficiency (η) is given as \(40\%\), and the sink temperature (Tsink) is given as 300K. We will use the formula for the efficiency of a Carnot engine: \(η = 1 - (T_{sink} / T_{source})\) We will now solve for the initial temperature of the source (Tsource_initial): \(0.4 = 1 - (300 / T_{source\_initial})\) To find the initial temperature of the source, isolate Tsource_initial: \(0.6T_{source\_initial} = 300\), \(T_{source\_initial} = 300 / 0.6 = 500 K\)
02

Find the New Temperature for 60% Efficiency

Now we want to find the new source temperature (Tsource_new) required for a 60% efficiency. Using the efficiency formula, we have: \(η_{new} = 1 - (T_{sink} / T_{source\_new})\) Plug in the new efficiency (0.6) and the sink temperature (300K): \(0.6 = 1 - (300 / T_{source\_new})\) Solve for Tsource_new: \(0.4T_{source\_new} = 300\), \(T_{source\_new} = 300 / 0.4 = 750K\)
03

Calculate the Change in Temperature of the Source

Now we can find the difference between the new source temperature and the initial source temperature: ΔT = Tsource_new - Tsource_initial ΔT = 750K - 500K ΔT = 250K The change in temperature of the source is 250K, which corresponds to answer choice (D).

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

The Volume of an ideal gas is 1 liter column and its Pressure is equal to $72 \mathrm{~cm}\( of \)\mathrm{Hg}$. The Volume of gas is made 900 \(\mathrm{cm}^{3}\) by compressing it isothermally. The stress of the gas will be \(\ldots \ldots \ldots \ldots .\) Hg column. (A) \(4 \mathrm{~cm}\) (B) \(6 \mathrm{~cm}\) (C) \(7 \mathrm{~cm}\) (D) \(8 \mathrm{~cm}\)

A Carnot engine having a efficiency of \(\mathrm{n}=(1 / 10)\) as heat engine is used as a refrigerators. if the work done on the system is \(10 \mathrm{~J}\). What is the amount of energy absorbed from the reservoir at lowest temperature ! (A) \(1 \mathrm{~J}\) (B) \(90 \mathrm{~J}\) (C) \(99 \mathrm{~J}\) (D) \(100 \mathrm{~J}\)

The temperature of a substance increases by \(27^{\circ} \mathrm{C}\) What is the value of this increase of Kelvin scale? (A) \(300 \mathrm{~K}\) (B) \(2-46 \mathrm{~K}\) (C) \(7 \mathrm{~K}\) (D) \(27 \mathrm{~K}\)

Two cylinders \(\mathrm{A}\) and \(\mathrm{B}\) fitted with piston contain equal amounts of an ideal diatomic gas at \(300 \mathrm{k}\). The piston of \(\mathrm{A}\) is free to move, While that of \(B\) is held fixed. The same amount of heat is given to the gas in each cylinders. If the rise in temperature of the gas in \(\mathrm{A}\) is \(30 \mathrm{~K}\), then the rise in temperature of the gas in \(\mathrm{B}\) is. (A) \(30 \mathrm{~K}\) (B) \(42 \mathrm{~K}\) (C) \(18 \mathrm{~K}\) (D) \(50 \mathrm{~K}\)

The change in internal energy, when a gas is cooled from $927^{\circ} \mathrm{C}\( to \)27^{\circ} \mathrm{C}$ (A) \(200 \%\) (B) \(100 \%\) (C) \(300 \%\) (D) \(400 \%\)
See all solutions

Recommended explanations on English Textbooks

Summary Text

Read Explanation

Rhetoric

Read Explanation

International English

Read Explanation

Email

Read Explanation

Rhetorical Analysis Essay

Read Explanation

Essay Writing Skills

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