Final answer:
To determine the final temperature of an ideal gas returning to its original pressure after expansion, we can utilize the ideal gas law and the initial conditions to find that the final temperature will be 400 K (127°C).
Step-by-step explanation:
The question presents a scenario involving an ideal gas which is initially contained in half of a rigid tank, with the other half being evacuated. Upon removal of the partition, the gas expands to fill the entire tank. To find the final temperature after the gas returns to its initial pressure upon heating, we can apply the ideal gas law PV=nRT for both the initial state (state 1) and the final state (state 2) and use the fact that the number of moles and the gas constant remain unchanged.
Initial state (V1, T1, P1): V1 is unknown, T1 = 927°C ( = 1200 K after converting from Celsius to Kelvin), P1 is the initial pressure.
Final state (V2, T2, P2): V2 = 3V1 (since the evacuated side is twice as large as the gas-containing side), T2 is the final temperature we want to find, P2 = P1 (after heating the gas back to its original pressure).
Since P1V1 = nRT1 and P2V2 = nRT2, and P1 = P2, we can say that V1/V2 = T1/T2. Plugging in V2 = 3V1 and T1 = 1200 K, we find T2 = (1/3) * 1200 K, so the final temperature T2 is 400 K or 127°C.