What Is the Heat Capacity in an Isothermal Process?

[maurice2705]

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.

 

[Andrew Mason]

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