Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 12

Three identical gas-cylinder systems are compressed from the same initial state to final states that have the same volume, one isothermally, one adiabatically, and one isobarically. Which system has the most work done on it? The least?

Short Answer

Expert verified
The most work is done on the isothermally compressed system. The least work is done on the isobarically compressed system.

Step by step solution

01

Understanding the problem

Recognize that we are asked to compare the work done on the three different processes. Work done, \(W\), on a system can be calculated as the area under the pressure-volume curve. The more the area under the curve, the greater the work done. In an isothermal process, the curve is hyperbolic (since \(PV=nRT\), where \(nRT\) is constant), in an adiabatic process, the curve is steeper than the isothermal, and in an isobaric process, the curve is a straight horizontal line.
02

Comparing the work done in each process

Comparing the pressure-volume (PV) diagrams of each process, we can rank the processes by the amount of work done. An isothermal process has more area under the curve (thus more work done) compared to an adiabatic process which itself has more area under the curve when compared with an isobaric process. So, the most work is done on the isothermally compressed system, the least on the isobarically compressed system and the adiabatically compressed system falls somewhere in between these two.

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

When you let air out of a tire, the air seems cool. Why? What kind of process is occurring?

Blow on the back of your hand with your mouth wide open. Your breath will feel hot. Now tighten your lips into a small opening and blow again. Now your breath feels cool. Why?

A 25 -L sample of ideal gas with \(\gamma=1.67\) is at \(250 \mathrm{K}\) and \(50 \mathrm{kPa} .\) The gas is compressed isothermally to one-third of its original volume, then heated at constant volume until its state lies on the adiabatic curve that passes through its original state, and then allowed to expand adiabatically to that original state. Find the net work involved. Is net work done on or by the gas?

A \(40-\) W heat source is applied to a gas sample for 25 s, during which time the gas expands and does 750 J of work on its surroundings. By how much does the internal energy of the gas change?

A quasi-static process begins and ends at the same temperature. Is the process necessarily isothermal?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Fundamentals of Physics

Read Explanation

Rotational Dynamics

Read Explanation

Torque and Rotational Motion

Read Explanation

Particle Model of Matter

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