Two rigid vessels A and B , each having a volume of 200 cm ^3 , contain an ideal gas ( C_V = 12.5 J K ⁻¹ mol ⁻¹ ). These vessels are connected to a manometer tube containing mercury. Initially, the pressure in both vessels is 75 cm of mercury and the temperature is 300 K . Subsequently, 5.0 J of heat is supplied to the gas in vessel A and 10 J to the gas in vessel B . Assuming no appreciable transfer of heat from A t

Step-by-step solution

For a constant volume process, the heat supplied is Q = n C_V T . From the ideal gas equation PV = nRT , the change in pressure at constant volume is P = n R T V . Substituting n T = Q C_V , we get P = R Q V C_V . The difference in pressure between vessel B and vessel A is: P_ net = P_B - P_A = R V C_V (Q_B - Q_A) Substituting the given values ( R = 8.3 J K ⁻¹ mol ⁻¹ , V = 200 10⁻⁶ m ^3 , C_V = 12.5 J K ⁻¹ mol ⁻¹ , Q_B - Q_A = 5.0 J ): P_ net = 8.3 5.0 2 10⁻⁴ 12.5 = 16600 N m ⁻² To convert this pressure difference