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Chapter 18: Problem 42

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?

Short Answer

Expert verified
The volume of the gas must be changed by a factor of \((1/2)^{1/1.4}\) or approximately 0.64 in an adiabatic process if the pressure is to double.

Step by step solution

01

Identify the known values

We know that the pressure \(P\) doubles (\(P_2 = 2P_1\)), and the specific heat ratio (\(\gamma\)) is given as 1.4.
02

Apply the adiabatic process formula

For an adiabatic process, \(P_1V_1^\gamma = P_2V_2^\gamma\). Substituting the known values into this equation, we get \(P_1V_1^{1.4} = 2P_1V_2^{1.4}\). Here, the pressure initially \(P_1\) cancels out from both sides giving \(V_1^{1.4} = 2V_2^{1.4}\). Now we express \(V_2\) from this equation.
03

Solve for \(V_2/V_1\)

Dividing both sides by \(V_1^{1.4}\) and take the reciprocal we obtain \(V_2/V_1 = (1/2)^{1/1.4}\)

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Most popular questions from this chapter

A gas mixture contains monatomic argon and diatomic oxygen. An adiabatic expansion that doubles its volume results in the pressure dropping to one- third of its original value. What fraction of the molecules are argon?

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