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roam
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Homework Statement
I need some help with the following problem:
Consider a thermally insulated enclosure containing an ideal gas initially separated by a thermally insulated partition into two separate regions. One region is at pressure p1=100 Pa, temprature T1=200 K, and volume V1 = 10 m3. The other is at p2=50 Pa, T2=300 K, and V2=20 m3.
If the partition is removed and the gas from each region is allowed to mix freely, what is the final temprature of the mixture?
Homework Equations
Ideal gas law:
PV=NKT
p=ρRT
The Attempt at a Solution
I've first found the final pressure as follows
[itex]U_i \propto P_1 V_1 + P_2 V_2[/itex]
[itex]U_f \propto P_f (V_1+V_2)[/itex]
[itex]P_1 V_1 + P_2 V_2 = P_f (V_1 + V_2)[/itex]
[itex]P_f = \frac{V_1}{V_1 + V_2} P_1 + \frac{V_2}{V_1 + V_2} P_2 = 66.66 \ Pa[/itex]
Now to find the temprature, I wrote
[itex](N_1 + N_2) k T_f = (N_1T_1 + N_2T_2) k = P_f(V_1+V_2) = 66.66[/itex]
But how can I solve for "Tf"? The problem is that I do not know the number of moles of gas in each partition. Is there a way to calculate the number of moles, or should I use a different method to find Tf? Any helps is appreciated.
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