# Statistical physics (thermal)

Hi

I'm having a bit of trouble with 2 homework questions.

Firstly, I need to show that (Heat Capacity/Specific Heat) = 1+2f

using the fact that Cp= (1+f/2)Nk
and Cv= (f/2)Nk

I've tried to work this out by cross multiplying these, but I don't think I'm doing the maths right.

Secondly, I need to compute the entropy change for, adiabatic,isothermal,isochoric and isobaric processes. I have done the one for isothermal processes, but I can't find any clear info for the others - nb, my lecturer hasn't really covered these in any depth.

Can anyone help me with either of these ??

Thanks
Kel

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Andrew Mason
Homework Helper
kel said:
Hi

I'm having a bit of trouble with 2 homework questions.

Firstly, I need to show that (Heat Capacity/Specific Heat) = 1+2f

using the fact that Cp= (1+f/2)Nk
and Cv= (f/2)Nk

I've tried to work this out by cross multiplying these, but I don't think I'm doing the maths right.
You have to get the terms straight first. I am not sure what you are using for heat capacity. Specific heat is the heat required to raise 1 kilogram of the substance one K an is in units of joules / kg - K . Heat capacity is usually in joules / mole - K ie.the amount of heat required to raise one mole one degree K.

Secondly, I need to compute the entropy change for, adiabatic,isothermal,isochoric and isobaric processes. I have done the one for isothermal processes, but I can't find any clear info for the others - nb, my lecturer hasn't really covered these in any depth.

dS = dQ/T
and the first law:

dQ = dU + PdV = nCvdT + PdV

For isothermal, T is constant so it is just a matter of using TdS = PdV. Substitute P/T = nR/V (ideal gas law) and integrate.

For isochoric, dV = 0 so dQ = nCvdT, which means that dS = dQ/T = nCvdT/T. Just integrate that.

I will leave it up to you to work out isobaric.

AM

Last edited:
Thanks

That's a great help.

By the way, I'm just working on a proof for cp/cv= 1+2f

there are no other values other than the ones that I gave, I can get the 1, but I'm not sure how to get 2f as I always seem to end up with something like 1+f/2

cheers

Andrew Mason
Homework Helper
kel said:
Thanks

That's a great help.

By the way, I'm just working on a proof for cp/cv= 1+2f

there are no other values other than the ones that I gave, I can get the 1, but I'm not sure how to get 2f as I always seem to end up with something like 1+f/2

cheers
f appears to be the degrees of freedom. Cp/Cv does not equal 1 + 2f. But Cp/Cv is not the ratio of heat capacity to specific heat. It is heat capacity at constant pressure/ heat capacity at constant volume. Why don't you just give us the exact wording of the question.

AM

Ok, the question is in 3 parts

1-show that the heat capacity at constant pressure

Cp=dQ/dT= (1+f/2)Nk (nb: where dq and dt are partial derivitives)

2-show that the specific heat at constant volume

Cv=(dQ/dT) = (f/2)NK (nb: where dq and dt are partial derivitives)

and part 3 - which I'm stuck on

show that

Cp/Cv = gamma = 1+2f

Andrew Mason
Homework Helper
kel said:
Ok, the question is in 3 parts

1-show that the heat capacity at constant pressure

Cp=dQ/dT= (1+f/2)Nk (nb: where dq and dt are partial derivitives)

2-show that the specific heat at constant volume

Cv=(dQ/dT) = (f/2)NK (nb: where dq and dt are partial derivitives)

and part 3 - which I'm stuck on

show that

Cp/Cv = gamma = 1+2f
but Cp/Cv is not equal to 1 + 2f. Cp/Cv = 1 + 2/f

AM