Assume there are two different kind of monoatomic ideal gas A and B. n moles of A are placed in a insulated compartment while m moles of B are placed in another insulated compartment. There is an insulated partition to join this two compartment. If the initial temperature and pressure of A is known (Ta, P) and the initial temperature and pressure of B is know (Tb, P), find the final temperature after the partition was removed. Assuming Tb>Ta, two initial volume for each compartment are the same.
2. The attempt at a solution
I know I should apply the energy relation to find out final temperature. That is, the energy absorbed by the low temperature gas is identical to the energy released by the high temperature gas. If we know the capacity heat, it is easily to write down some thing like
n C (Tf-Ta) + m C (Tf-Tb) = 0
I think this relation is correct, right?
Now, I just wondering how to solve for C in this case. There is two different capacity for ideal gas: isobar (Cp) or isovolumn (Cv). However, since while the gas is mixing the pressure must change and volume will also be change, it seems that both Cp or Cv is not suitable. How to find the capacity heat?