A container has two chambers of volumes $V_1=3$ litres and $V_2=2$ litres separated by a partition m

Question

A container has two chambers of volumes $V_1=3$ litres and $V_2=2$ litres separated by a partition made of a thermal insulator. The chambers contain ideal gas at pressures $p_1=2 \mathrm{~atm}$ and $p_2=3 \mathrm{~atm}$, respectively. When the partition is removed, the mixture attains an equilibrium pressure of

Professor PC Thomas Classes · Answer

(a) : When the partition is removed, the total number of moles is conserved, and assuming the system is isolated, the internal energy is conserved. For an ideal gas at equilibrium, $P_{eq}(V_1 + V_2) = P_1 V_1 + P_2 V_2$. Therefore, $P_{eq} = \frac{P_1 V_1 + P_2 V_2}{V_1 + V_2} = \frac{2 	imes 3 + 3 	imes 2}{3 + 2} = \frac{12}{5} = 2.4 \mathrm{~atm}$.