Free expansion of Real Gases - Dieterici EoS, Change in Temperature

Thread starter curious_mind
Start date Nov 20, 2022
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Change Expansion Free expansion Gases Temperature

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The discussion revolves around the free expansion of real gases using the Dieterici equation of state. The user derives expressions for internal energy changes and attempts to solve a differential equation related to the temperature change during the expansion. They face difficulties in obtaining a separable form for the equation and seek verification of their calculations. The conversation highlights the need to apply Hess's Law for integrating the internal energy changes along a defined path and emphasizes that the heat capacity must be treated as a function of volume. Ultimately, the conclusion suggests that the provided answer options in the original question may be incorrect based on dimensional analysis.

Oct 20, 2024

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mani_09 said:

I think this should have only been the answer. But the problem is V0 is not given in the question and we used this symbol on our own.

Vo is the initial volume of the gas. The full volume of the container V is equal to 2Vo, and V is given.

Also, this equation is only the limiting result (in the limit of small a) of our more comprehensive analysis.