Two systems merging, what is final temp?

[mateomy]

Hi all,

I just want to see if my work is correct because it's not matching the answer in the book:


A tank has a volume of 0.1 m^3 and is filled with He gas at a pressure of 5x10^6 Pa. A second tank has a volume of 0.15 m^3 and is filled with He gas at a pressure of 6x10^6 Pa. A valve connecting the two tanks is opened...

(My problem references this question and asks...)

If the temperatures within the two tanks before opening the valve, had been T = 300K and 350 K respectively, what would the final temperature be?


So what I did was utilize this equation:
<br /> U = cNRT<br />
to find the energies of each. Based off of the 'adiabatic and rigid' statement given I know no energy is lost to heat flow or work on the walls.

I get energies for the respective systems of 3741 J and 4365 J. Adding those together I get 8106.
Now I just plug that number back into the former equation (this time manipulated):
<br /> T = \frac{U}{cNR}<br />

And I'm getting a temp of 324.9 K. The book says 330 K. Need some help, am I wrong or is this a misprint?

Thanks.

 

[gneill]

Using PV = nRT and assuming PV is proportional to the energy content I find that the book's value is reasonable...