[mcc]

Hi. I am trying to calculate Cp/v - the heat capacity at constant P/V or at T/V^2.

I have tried different scenarios (one in which one path was at constant temperature, the next at constant volume) that obey the above laws, calculated the heat associated with each path, summed them, divided them the dT of the system... and I haven't gotten the correct answer. (which supposedly is 2R).

Any ideas?

[enahs]

You will have to be more specific then trying to calculate the heat capacity at constant volume or pressure.

What are you given? What do you know? etc

[mcc]

Well... I'm not really given anything. It is for an ideal gas, and we can use the relation Cp-Cv=R.

[Dan]

Have you looked at the equipartition theorum? My pyschem is rusty, but I think that's the way to go.

[Donaldson Tan]

My pyschem is rusty, but I think that's the way to go.

Psychic Chemistry? LOL..

Btw are you calculating Cp and Cv for perfect gas?

[Dan]

yeah, everyone knows you have to be psychic to calculate heat capacities 

[mcc]

My pyschem is rusty, but I think that's the way to go.

Btw are you calculating Cp and Cv for perfect gas?

No, not Cp and Cv... I know what those are/how they are derived. I'm looking for "Cp/v"

I doubt it involves equipartition theory as we haven't learned that, and I *should* be able to do this.

Maybe you do have to be psychic to do this.... hehe..

Anyway, I've been going about it like this: calculating the heat for such a process, and dividing by DT. That's how we tried to do it in class (it took the whole period) and we coudln't come to a conclusion. My teacher says it is MUCH easier than what we tried, so I'm guessing that's not how I should be doing it.

I'm guessing it has something to do with entropy, and may involve some scary math (EEK) ... I spent a couple hours thinking about this yesterday evening. I'll be doing the same thing here in a bit.

[enahs]

What do you mean by "Cp/v" exactly then?

I read that as Heat Capacity at constant pressure divided by volume.
I thought the p/v meant you wanted both Cp and Cv.

Are you sure that is a “p” and not a greek rho?

[mcc]

Cv - heat capacity at constant volume
Cp - heat capacity at constant pressure

C(p/v) - heat capacity at constant P/V (constant 'pressure divided by volume') ...

[Yggdrasil]

It seems like a pretty hard question, and Cp/v doesn't seem well defined.  For example, Cp and Cv have definitions in terms of differentials, for example:

Cp = (dH/dT)_P and
Cv = (dU/dT)_V

whereas it doesn't seem obvious what the differential expression would be for Cp/v.  If you define it as the heat absorbed/released per unit change in temperature during a reversible process which proceeds through a path where P/V is constant, then it isn't easily apparent how you'd calculate that or whether Cp/v will even be a constant valued function.

I'll have to think about this some more...

[Donaldson Tan]

The most basic definition of heat capacity (C) is dQ/dT. In fact, you are seeking (dQ/dT)_(P/V)

Let's consider 1 mole of perfect gas: PV = RT

k = constant = P/V = RT/V²

For a close system, dQ = dU + P.dV
dQ/dT = dU/dT + P(dV/dT)

kV² = RT
2kV(dV/dT) = R
dV/dT = R/2kV

(dQ/dT)_(P/V) = dU/dT + P(dV/dT)_(P/V) = dU/dT + P(R/2kV) = dU/dT + R/2 = C_v + R/2

C_(P/V) = (dQ/dT)_(P/V) = C_v + R/2

[mcc]

The most basic definition of heat capacity (C) is dQ/dT. In fact, you are seeking (dQ/dT)_(P/V)

Let's consider 1 mole of perfect gas: PV = RT

k = constant = P/V = RT/V²

For a close system, dQ = dU + P.dV
dQ/dT = dU/dT + P(dV/dT)

kV² = RT
2kV(dV/dT) = R
dV/dT = R/2kV

(dQ/dT)_(P/V) = dU/dT + P(dV/dT)_(P/V) = dU/dT + P(R/2kV) = dU/dT + R/2 = C_v + R/2

C_(P/V) = (dQ/dT)_(P/V) = C_v + R/2

That's great. Cv + R/2 does in fact equal 2R. The only step I don't understand is when you equate dU/dT to C_v. This is true when the system is at constant volume. Does it still hold true for constant P/V? To me, it doesn't seem so..