What Is the Heat Capacity in an Isothermal Process?

AI Thread Summary
In an isothermal process, the heat capacity is questioned due to the definition C = ΔQ/ΔT, where ΔT equals zero, leading to an indeterminate form. The discussion highlights that while work is done (ΔQ > 0), the internal energy change remains zero, complicating the calculation of heat capacity. The attempt to solve involves setting various parameters equal, but participants struggle to derive a clear expression for heat capacity under these conditions. The key point is that despite the isothermal nature, the concept of heat capacity remains relevant but requires careful consideration of the definitions involved. The conversation emphasizes the need for clarity on how to handle the zero change in temperature while accounting for heat transfer.
maurice2705
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Homework Statement


The question is presented as picture.


Homework Equations


What is the expression of this 'heat capacity C'?
The x-process is isothermal then C=nCΔT=0?
Please give me some ideas.

The Attempt at a Solution


set V1=V2, V3=V4, T1=T4, T2=T3, p1+p0=p2, p3-p0=p4
constant volume process:ΔU=n*Cv*(T2-T1)=Cv*V1*p0/R where p0=p2-p1
isothermal process:W=nRT1*ln(V3/V2)=nRT1*ln(p2/p3)
Then I can't go any further.
 

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maurice2705 said:

Homework Statement


The question is presented as picture.

Homework Equations


What is the expression of this 'heat capacity C'?
The x-process is isothermal then C=nCΔT=0?
Please give me some ideas.

The Attempt at a Solution


set V1=V2, V3=V4, T1=T4, T2=T3, p1+p0=p2, p3-p0=p4
constant volume process:ΔU=n*Cv*(T2-T1)=Cv*V1*p0/R where p0=p2-p1
isothermal process:W=nRT1*ln(V3/V2)=nRT1*ln(p2/p3)
Then I can't go any further.
Heat capacity is defined as: C = ΔQ/ΔT. Since work is being done but there is no change in internal energy, ΔQ > 0. However, since it is isothermal, ΔT = 0. So what is the heat capacity, ΔQ/ΔT at all pressures (points) on the isothermal curve?

AM
 

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