(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

n_1 moles of a monatomic gas and n_2 moles of a diatomic gas are mixed together in a container.

Derive an expression for the molar specific heat at constant volume of the mixture.

My answer can only use the variables n_1 and n_2, and I'm assuming constants.

2. Relevant equations

Monoatomic gas

E_th = (3/2)nRT

C_v = (3/2)R

Diatomic gas

E_th = (5/2)nRT

C_v = (5/2)R

First Law:

(Change)E_th = W + Q = (n)(C_v)(change in T)

3. The attempt at a solution

Honestly, I'm not sure where to begin.

I'm assuming:

Since volume is constant, that means this is an Isochoric process.

In which case W = 0

Which means (change in E_th) = 0 + Q = n(C_v)(change in T)

So...

for the monoatomic gas

E_1f = (n_1)(C_v)(T) = (3/2)(n_1)(R)(T_1f)

for the diatomic gas

E_2f = (n_2)(C_v)(T) = (5/2)(n_2)(R)(T_2f)

Now I figure this is a process going for thermal equilibrium...

so

T_1f = T_2f = T_f, so I can make the temperature variable T_f from now on.

E_1f = (n_1)/(n_1 + n_2)

E_2f = (n_2)/(n_1 + n_2)

E_tot = E_1f + E_2f

E_tot = (3/2)(n_1)(R)(T_f) + (5/2)(n_2)(R)(T_f)

I don't know where I'm going with this. Can someone tell me if I'm going in the right direction?

Thank you

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# Homework Help: Deriving Molar Specific Heat Equation

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