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Chapter 8: Problem 1133

For free expansion of the gas which of the following is true ? (A) \(\mathrm{Q}=0, \mathrm{~W}>0\) and \(\mu \operatorname{Eint}=-\mathrm{W}\) (B) \(\mathrm{W}=0, \mathrm{Q}>0\) and \(\Delta\) Eint \(=\mathrm{Q}\) (C) \(\mathrm{W}>0, \mathrm{Q}<0\) and \(\Delta\) Eint \(=0\) (D) \(\mathrm{Q}=\mathrm{W}=0\) and \(\Delta \operatorname{Eint}=0\)

Short Answer

Expert verified
\( \mathrm{D} \) is the correct answer since during a free expansion, no heat exchange occurs (\( \mathrm{Q} = 0 \)), no work is done (\( \mathrm{W} = 0 \)), and the change in internal energy is also zero (\( \Delta \operatorname{Eint} = 0 \)).

Step by step solution

01

Analyze Statement A

Statement A states that the heat exchange, Q, is equal to 0, work done, W, is greater than 0, and the internal energy change is equal to the negative work done. In a free expansion, no work is done, which means W = 0. Because this statement suggests W > 0, statement A is incorrect.
02

Analyze Statement B

Statement B says that the work done, W, is equal to 0, heat exchange, Q, is greater than 0, and the change in internal energy, ΔEint, is equal to Q. In a free expansion, W = 0, which is correct. However, since a free expansion is an adiabatic process with no heat exchange, we have Q = 0, contradicting the claim that Q > 0. Therefore, statement B is incorrect.
03

Analyze Statement C

Statement C states that the work done, W, is greater than 0, heat exchange, Q, is less than 0, and the change in internal energy, ΔEint, is equal to 0. Since a free expansion's work done is zero (W = 0), statement C is incorrect.
04

Analyze Statement D

Statement D states that the heat exchange, Q, is equal to 0, the work done, W, is equal to 0, and the change in internal energy, ΔEint, is equal to 0. For a free expansion, both Q and W are indeed zero, which is correct. Moreover, ΔEint for an ideal gas solely depends on changes in temperature, and no change in temperature occurs during a free expansion. Hence, ΔEint is also zero. Statement D is therefore consistent with the properties of a free expansion, and it is the correct choice.

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