Computing work in an isothermal process

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Homework Help Overview

The discussion revolves around computing work in an isothermal process, specifically within the context of the Carnot cycle and the behavior of ideal gases. Participants are exploring the relationship between pressure, volume, and temperature during this thermodynamic process.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning how to determine the pressure value for the integral used to compute work, given that pressure is not constant during an isothermal process. There is a discussion about using the ideal gas law to express pressure in terms of other variables.

Discussion Status

The discussion is ongoing with participants exploring different interpretations of pressure behavior in isothermal versus isobaric processes. Some guidance has been offered regarding the use of the ideal gas law, but no consensus has been reached on the treatment of pressure in the integral.

Contextual Notes

There is a focus on the assumptions related to ideal gases and the conditions of isothermal processes, with participants highlighting the need to clarify the distinction between isothermal and isobaric conditions.

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I was reviewing some notes on the Carnot cycle and noticed that to compute the work done along an isotherm you take the integral of PdV from the initial to final volume. What value do you use for P since P is not held constant on an isothermal curve? Why is P treated as a constant?
 
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If the gas being compressed in the Carnot engine is an ideal gas, then you may simply use the ideal gas law to express P in terms of temperature, particle number and volume:

P dV = nRT dV/V
 
But during that process,the volume is rising,so pressure remains constant.
 
R A V E N said:
But during that process,the volume is rising,so pressure remains constant.

It's an isothermal process being considered, not an isobaric process - the temperature (in an ideal gas) remains constant because the pressure changes to compensate for the change in volume. If the pressure were constant the temperature would have to change as the volume changed.
 

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