Mixing of two gasses. Find the temperature and pressure

[Xyius]

Homework Statement

A rigid insulated tank is separated into two rooms by a stiff plate. Room A of 0.5 m3 contains air at 250 kPa, 300 K and room B of 1 m3 has air at 150 kPa, 1000 K. The plate is removed and the air comes to a uniform state without any heat transfer. Find the final pressure and temperature.

Homework Equations

I am pretty sure these are the ones I am going to use.
$$PV=mRT$$
$$/delta u = c_{v}/delta T$$

The Attempt at a Solution

Well I figured I would find the mass of each gas in their rooms first. So I just used the ideal gas law on both of them..

$$m=\frac{PV}{RT} \rightarrow m_{1}=1.452kg,m_{2}=0.523kg$$

Therefore, at the final state the ideal gas equation is known except for T and P. I figured the equation $$/delta u = c_{v}/delta T$$ might be useful but I do not understand how I could get temperature from this. All I need is one and I can find the other via the ideal gas law.

Thanks! :]

 

[Xyius]

Ohh I think I have figured it out! But I will post my solution for anyone else with the same problem. :]

The internal energy lost from the hotter has, is equal to the internal energy gained from the cooler gas. Using the formula for specific heats..

$$C_{v1}(T_{f}-T_{i})+C_{v2}(T_{f}-T_{i})=0$$

Then I just got the C values from the tables and got a final temp of 680.5K. :]