At constant volume the volume expansivity 1 K-1, isothermal compressiblity 1 bar1 and thechange in temparature is 1K. Calculate the change in pressure.

Answered: At constant volume the volume…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

See similar textbooks

Related questions

Question

At constant volume the volume expansivity 1 K-1, isothermal compressiblity 1 bar1 and the
change in temparature is 1K. Calculate the change in pressure.

Expert Solution

Step 1

Write the expressions for volume expansivity and isothermal compressibility as follows:

volume expansivity,

$β = \frac{1}{V} {(\frac{\partial V}{\partial T})}_{P} {(\frac{\partial V}{\partial T})}_{P} = β V . . . . . . (1)$

isothermal compressibility,

$k = - \frac{1}{V} {(\frac{\partial V}{\partial P})}_{T} {(\frac{\partial V}{\partial P})}_{T} = - k V . . . . . . (2)$

Step 2

For an ideal gas, the cyclic property is

${(\frac{\partial P}{\partial T})}_{V} {(\frac{\partial T}{\partial V})}_{P} {(\frac{\partial V}{\partial P})}_{T} = - 1$

Substitute the corresponding values in the above equation

${(\frac{\partial P}{\partial T})}_{V} = - \frac{{(\frac{\partial V}{\partial T})}_{P}}{{(\frac{\partial V}{\partial P})}_{T}} {(\frac{\partial P}{\partial T})}_{V} = - \frac{β V}{(- k V)} {(\frac{\partial P}{\partial T})}_{V} = \frac{β}{k} {(\frac{∆ P}{∆ T})}_{V} = \frac{β}{k} . . . . . (3)$

Step by step

Solved in 4 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemical-engineering and related others by exploring similar questions and additional content below.

Similar questions