Two thermally insulated vessels are filled with an ideal gas. The pressure, volume and temperature in the two vessels are `P_(1), V_(1), T_(1)` and `P_(2), V_(2), T_(2)` respectively. Now, the two vessels are connected using a short insulating tube.
(a) Find final temperature of the gas.
(b) Express the final pressure of the gas in terms of `P_(1), V_(1), P_(2)` and `V_(2)` only.

Answer

(a) `(T_(1)T_(2)(P_(1)V_(1)+P_(2)V_(2)))/((P_(1)V_(1)V_(2)+P_(2)V_(2)T_(2)))` , (b) `(P_(1)V_(1) + P_(1)V_(2))/(V_(1) + V_(2))`