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Vo is the initial volume of the gas. The full volume of the container V is equal to 2Vo, and V is given.mani_09 said:
Also, this equation is only the limiting result (in the limit of small a) of our more comprehensive analysis.
Free expansion of Real Gases - Dieterici EoS, Change in Temperature
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Homework Help Overview
The discussion revolves around the free expansion of a real gas described by the Dieterici equation of state. The original poster explores the implications of internal energy changes during this process, particularly focusing on the temperature change resulting from the gas expanding into a larger volume without heat transfer or work being done.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking
Approaches and Questions Raised
- The original poster attempts to derive a differential equation relating volume and temperature changes during free expansion, questioning the separability of the equation. They express uncertainty about their calculations and seek verification of their approach.
- Some participants question the treatment of the number of moles in the equations and suggest that the specific heat capacity may depend on volume, prompting further exploration of the relationships between variables.
- Others suggest applying Hess's Law and integrating along a convenient path to find the temperature change, while also discussing the potential need to consider enthalpy instead of internal energy.
Discussion Status
The discussion is ongoing, with participants exploring various interpretations and approaches to the problem. Some guidance has been offered regarding the application of Hess's Law and the integration of internal energy changes, but no consensus has been reached on the method to obtain the final temperature change.
Contextual Notes
The problem involves specific constraints related to the Dieterici equation of state and the conditions of free expansion, including the assumption of no heat transfer and no work done during the process. Participants are navigating the complexities of these assumptions while attempting to derive a solution.
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