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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SUMMARY

The discussion focuses on the free expansion of real gases using the Dieterici equation of state (EoS) and the calculation of temperature change during this process. The participants derive the internal energy change equation and explore the implications of the first internal energy equation, leading to a differential equation that describes the relationship between volume and temperature. The final goal is to determine the temperature at equilibrium after the gas expands, with the expected result being T = T0 - (na/CV)ln(2). However, discrepancies in the calculations and the interpretation of variables such as n and CV are highlighted, leading to a debate on the correctness of the provided answer.

PREREQUISITES

Understanding of the Dieterici equation of state for real gases.
Familiarity with the concepts of internal energy and specific heat (C_V).
Basic knowledge of differential equations and their applications in thermodynamics.
Proficiency in applying Hess's Law in thermodynamic calculations.

NEXT STEPS

Study the derivation and applications of the Dieterici equation of state in real gas behavior.
Learn how to solve differential equations relevant to thermodynamic processes.
Explore Hess's Law and its application in calculating changes in internal energy.
Investigate the relationship between specific heat and temperature in real gases.

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Students and professionals in thermodynamics, chemical engineering, and physical chemistry who are dealing with real gas behavior and internal energy calculations during free expansion processes.

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.