Is confined to one side of a rigid container divided by a pa

Is confined to one side of a rigid container divided by a partition. as shown in the figure. the other side is initially evacuated, The air is initially at p_1=5 bar, T_1 = 500 K, and V_1 = 0.2 m^3. When the partition is removed, the air expands to fill the entire chamber. Measurements show that V_2 = 2V_i and p_2 = p_1/4. Assuming the air behaves as an ideal gas. determine (a) the final temperature, in K, and (b) the heat transfer, kJ.

Solution

It is a case of free expansion for this case the heat transfer would be zero.

for first part using P1V1/T1 = P2V2/T2 it can be deduced that T2 = 0.5 T1

therefore the final temperature would be half of intial i.e. 250 K