An adiabatic vessel of total volume V is partitioned into two equal parts by a fixed, conducting separator. The left part holds one mole of an ideal gas ( U = 1.5 nRT ) and the right part contains two moles of the same gas. Initially, the pressure on each side is p . The system is allowed to rest for sufficient time until a steady state is achieved. Determine the increase in the internal energy of the gas in the left

Step-by-step solution

Let the initial volume of each part be V 2 . The initial internal energy of a gas is given by U = 1.5 nRT = 1.5 pV_ part . For the left part: U_ L,i = 1.5 p ( V 2 ) = 3pV 4 For the right part: U_ R,i = 1.5 p ( V 2 ) = 3pV 4 Total initial internal energy of the system: U_ i = U_ L,i + U_ R,i = 3pV 4 + 3pV 4 = 3pV 2 Since the vessel is adiabatic and the separator is fixed, the total internal energy of the system remains conserved. The conducting separator allows heat exchange until a common final temperature T_f is r