Analysis
The process described is the expansion of an ideal gas into a vacuum (evacuated part B). This is known as Free Expansion.
Thermodynamics of Free Expansion
- Work Done ($W$): Since the gas expands against a vacuum ($P_{ext} = 0$), the work done is zero ($W = \int P_{ext} dV = 0$).
- Heat Transfer ($Q$): The vessel is perfectly heat insulating, so $Q = 0$.
- Internal Energy ($\Delta U$): According to the First Law of Thermodynamics, $\Delta U = Q – W = 0 – 0 = 0$.
For an ideal gas, internal energy depends only on temperature ($U \propto T$). Since $\Delta U = 0$, the temperature change $\Delta T = 0$.
This holds true for both the first opening (partial expansion) and the second opening (full expansion), as the system is isolated throughout.
Correct Option: (d) During both the first and the second openings, the temperature remains constant.