There are two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and volume are P_A , T_A and V in the vessel A and P_B , T_B and V in vessel B. The vessels are now connected through a small tube. In equilibrium, pressure is P and temperature is T, then P T is number of moles of gas in vessel A = number of moles of gas in vessel B

Step-by-step solution

Using the ideal gas equation, the initial number of moles in vessel A is: n_A = P_A V R T_A The initial number of moles in vessel B is: n_B = P_B V R T_B When the vessels are connected, the total volume becomes V_ total = V + V = 2V . Let the equilibrium pressure be P and the equilibrium temperature be T . The total number of moles in the system remains conserved: n_ total = n_A + n_B P(2V) RT = P_A V RT_A + P_B V RT_B Dividing the entire equation by V R : 2P T = P_A T_A + P_B T_B P T = 1 2 ( P_A T_A + P_B T_B ) An