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I have this question:

You have two insulated nitrogen tanks. The first tank is at a pressure $P$ with a volume $V$ and at the temperature $T$. The second tank is at a pressure of 2P with a volume of 3V and at the temperature 1.5T. The two tanks are then connected and the gases are allowed to mix insulated from the outside. Assume the two gases have the same molar specific heat. In terms of P, what is the final pressure of the mixture?

I'm at a loss for what I need to do to find the final temperature, I've been working one step at a time. Finding $n_f$, $V_f$, $P_f$, and $T_f$. I got the first two, but after that I don't know where to go.

$$P_1V_1=nRT \\n_1={PV\over RT}\\2P_13V_1=n_2R(1.5T)\\n_2={2P3V\over R(1.5T)}={4PV\over RT}=4n_1$$

$$V_f=v_1+3v_1=4V_1$$

How do I find the final temperature?

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    $\begingroup$ This is an interesting question. You have to obey the ideal gas law, and simultaneously conserve energy (enthalpy). From your equations, I don't see any energy conservation. $\endgroup$
    – David White
    Commented Jan 30, 2017 at 0:18

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You should assume energy conservation; IE, the energy of the gases before mixing is the same as the energy after. This is what the problem is hinting at by saying the containers are insulated - insulated containers can't lose any energy as heat.

See "Molecular Constants" at http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/idegas.html for more.

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