How Does Entropy Influence Final Temperature in Gas Mixtures?

[roam]

Homework Statement

http://img812.imageshack.us/img812/1874/entropy.jpg

The Attempt at a Solution

First, not sure if this is an adequate explanation but I think for both gases in both partitions, regardless of whether it starts off colder or warmer, the total entropy will increase in order to reach thermal equilibrium.

To find the final temprature, I have an equation in my notes for the final temprature when an object and its environment come in contact and reach a final temperature:

$T_f = \frac{C_oT_o + C_eT_e}{C_o+C_e}$

Is this the correct equation for this situation? And what kind of heat capacities are the C's (C_v or C_p)?

For the total entropy I would use the equation which gives the total change of entropy by the object+environment:

$\Delta S_{o+e} = \Delta S_o + \Delta S_e = Q_{tot} \left( \frac{1}{T_o} - \frac{1}{T_e} \right)$

And there is another equation:

$\Delta S_{o+e} = C_o \ln \left( \frac{T_f}{T_o} \right) + C_e \ln \left( \frac{T_f}{T_e} \right)$

I want to use the second one. But again how do I find the C_e and C_o? The only info I am given is the number of moles. Any guidance is appreciated.

 

[roam]

My question really is what formulas need to be used for finding these particular heat capacities?

 

[Andrew Mason]

To find the final temprature, I have an equation in my notes for the final temprature when an object and its environment come in contact and reach a final temperature:

$T_f = \frac{C_oT_o + C_eT_e}{C_o+C_e}$

Where does the number of moles factor into your equation?

Is this the correct equation for this situation? And what kind of heat capacities are the C's (C_v or C_p)?

Will the final temperature be closer to 300 or 500 K? Why?

If volume constant? Is pressure constant?

AM

 

[roam]

Where does the number of moles factor into your equation?

How can I use the number of moles for finding C? Because that equation doesn't directly take the number of moles into account...

Will the final temperature be closer to 300 or 500 K? Why?

If volume constant? Is pressure constant?

How can I find that out? Intuitively, I think the final temprature would be somewhere between 300 and 500 K.

If volume is constant then the pressure would be constant as long as the number of moles don't change (we can see that from the equation P=nRT/V).

 

[roam]

Since the hotter gas will lose some heat and the colder gas would gain that much heat I could use the equation $Q=mc\Delta T$ for finding T_f:

$m_1 C_1 (T_f - 300) = m_2 C_2 (T_f - 500)$

Since it is the same type of gas in both partitions, is it okay to cancel out the C's on both sides (i.e C₁=C₂)?

To find the masses using the number of moles we can use use m=nM... but we don't know the molar mass of the gas. But would it be okay to also cancel out the M's on both sides?