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Question

Before we tackle a constant volume situation for an ideal gas let us think about an equivalent problem, where we keep the pressure constant, while volume is allowed to increase. If γ is the coefficient of volume expansion at a temperature T, which of the following is true?


A

γ is more or less constant, and independent of T.

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B

Insufficient data. Need to know the final temperature

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C

γ = T1

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D

γ = 1T2

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Solution

The correct option is C

γ = T1


The new volume upon expansion, V, is given as-

V = V(1+γΔT)

nRTV = nRTV(1+γΔT)

(where we have used the ideal gas equation, PV = nRT, for constant pressure P)

T = T(1+γΔT)

T = T+TγΔT

(TT) = TγΔT

TγΔT = ΔT

γ = T1.
Awesome! This suggests that, for an ideal gas at a temperature T, the volume expansion coefficient is just T1. See if you can do a similar analysis for the coefficient of pressure expansion at constant volume, in the earlier problem.


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