Question

A container has two chambers of volumes \(V_1 = 2\) litres and \(V_2 = 3\) litres separated by a partition made of a thermal insulator. The chambers contain \(n_1 = 2\) moles and \(n_2 = 3\) moles of ideal gas at pressures \(p_1 = 1\) atm and \(p_2 = 2\) atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of :

• A. \( 1.6 \text{ atm} \)
• B. \( 1.4 \text{ atm} \)
• C. \( 1.8 \text{ atm} \)
• D. \( 1.3 \text{ atm} \)

Hint:

Since the container is insulated, assume no heat exchange. Use the ideal gas law \(PV = nRT\) for each chamber to find the initial temperatures (in terms of \(R\)). After mixing, the total number of moles is \(n = n_1 + n_2\) and the total volume is \(V = V_1 + V_2\). Use conservation of internal energy \(n_1 C_v T_1 + n_2 C_v T_2 = (n_1 + n_2) C_v T_f\) to find the final temperature \(T_f\). Finally, use the ideal gas law for the mixture \(P_f V = n R T_f\) to find the equilibrium pressure \(P_f\).