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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A fluid can be cooled by allowing for an expansion in an insulated cylinder against a constant pressure. For an ideal gas in Houston , TX, what is the lowest possible temperature that can be reached in such a process? We will assume a monatomic gas, and no friction.

Expert Solution

Step 1

The Joule–Thomson effect describes the temperature change of a gases when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment.

The Joule thompson coefficient of a gas is given by the formula

$\mu = \frac{\partial T}{\partial p}|_h = \frac{1}{c_p}(T\frac{\partial V}{\partial T}|_p-V)$

Now,

For an ideal gas,

pV = nRT

SO,

$\frac{\partial V}{\partial T}|_p = \frac{R}{p} = \frac{V}{T}$

Hence, we get

$\mu = 0$

The Joult thompson coefifcient of an ideal gas is zero.

It means that an ideal gas can not change temperature for such an expansion, and It is only possible for real gases.

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