/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 How much of a triatomic gas with... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 18: Problem 65

How much of a triatomic gas with \(C_{V}=3 R\) would you have to add to 10 mol of monatomic gas to get a mixture whose thermodynamic behavior was like that of a diatomic gas?

Short Answer

Expert verified
Therefore, 20 mol of a triatomic gas needs to be added to the 10 mol of monatomic gas to get a mixture that behaves like a diatomic gas.

Step by step solution

01

Understand the given data and the aim

Given: Amount of monoatomic gas, \(n_1 = 10\) mol. Heat capacity at constant volume for a monoatomic gas, \(C_{V1} = 3R\), for a diatomic gas, \(C_{V2} = 5R\) and for a triatomic gas, \(C_{V3} = 3R\). Aim: To find the amount of triatomic gas (\(n_{3}\)) having heat capacity \(C_{V3}\) required to mix with the given monoatomic gas such that this mixture displays thermodynamic behavior of the diatomic gas.
02

Formulate the Equation

The heat capacity at constant volume of a mixture of gases is given by \(C_{Vmix} = (n_{1}C_{V1} + n_{3}C_{V3})/(n_{1} + n_{3})\). This (\(C_{Vmix}\)) needs to be equal to the heat capacity of a diatomic gas (\(C_{V2}\)). So, we set up the following equation, \(5R = (10mol * 3R + n_{3} * 3R)/(10 mol + n_{3})\)
03

Solve the Equation

Simplify the equation to find \(n_3\). Multiply through by 10 + \(n_{3}\), then collect terms and isolate \(n_{3}\) to find that \(n_{3} = 20\) mol.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Why is specific heat at constant pressure greater than at constant volume?

A \(25-\) L. sample of ideal gas with \(\gamma=1.67\) is at \(250 \mathrm{K}\) and \(50 \mathrm{kPa} .\) The gas is compressed adiabatically until its pressure triples, then cooled at constant volume back to \(250 \mathrm{K},\) and finally allowed to expand isothermally to its original state. (a) How much work is done on the gas? (b) What is the gas's minimum yolume? (c) Sketch this cyclic process a \(p V\) diagram.

During cycling, the human body typically releases stored energy from food at the rate of \(500 \mathrm{W},\) and produces about \(120 \mathrm{W}\) of mechanical power. At what rate does the body produce heat during cycling?

In a certain automobile engine, \(17 \%\) of the total energy released in burning gasoline ends up as mechanical work. What's the engine's mechanical power output if its heat output is \(68 \mathrm{kW} ?\)

By what factor must the volume of a gas with \(\gamma=1.4\) be changed in an adiabatic process if the pressure is to double?
See all solutions

Recommended explanations on Physics Textbooks

Kinematics Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Fluids

Read Explanation

Electric Charge Field and Potential

Read Explanation

Physics of Motion

Read Explanation

Medical 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.