Two vessels A and B with rigid walls containing ideal gases are shown in the figure. The pressure, temperature, and volume are p_A, T_A, and V in vessel A , and p_B, T_B, and V in vessel B . The vessels are subsequently connected through a small tube. When equilibrium is achieved, which of the following relations is satisfied by the final pressure p and temperature T ?

Step-by-step solution

From the ideal gas equation, the initial number of moles in vessel A and vessel B are: n_A = p_A V R T_A n_B = p_B V R T_B The total number of moles before mixing is: n_ initial = n_A + n_B = V R ( p_A T_A + p_B T_B ) After the vessels are connected, the total volume becomes V + V = 2V . For the final equilibrium state with pressure p and temperature T , the total number of moles is: n_ final = p(2V) RT Since the total number of moles is conserved, n_ initial = n_ final : p(2V) RT = V R ( p_A T_A + p_B T_B ) Dividi