Two cylinders and of equal capacity are connected to each other via a stopcock. contains a gas at standard temperature and pressure. is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
What is the final pressure of the gas in and ?
The final pressure of the gas in both A and B will be 0.5 atm (half of the initial STP pressure). Since both cylinders have equal capacity and the gas expands freely into vacuum, the volume doubles. For an ideal gas at constant temperature, pressure becomes half when volume doubles.
What is the change in internal energy of the gas?
The change in internal energy of the gas is zero. Since the system is thermally insulated, no heat is exchanged (Q = 0). Also, the gas expands into vacuum, so no work is done by the gas (W = 0). By the First Law of Thermodynamics: ΔU = Q - W = 0 - 0 = 0.
What is the change in the temperature of the gas?
The change in temperature of the gas is zero. For an ideal gas, internal energy depends only on temperature. Since the change in internal energy is zero, the temperature remains unchanged during this free expansion.
Do the intermediate states of the system (before settling to the final equilibrium state) lie on its surface?
No, the intermediate states do not lie on the P-V-T surface. As stated in the context, "The non-equilibrium states do not have well-defined pressure and temperature." During the sudden expansion, the gas passes through states that are not equilibrium states, and these cannot be described by well-defined thermodynamic variables.
Explanation
This question tests understanding of free expansion of gas into vacuum. Key concepts: (1) Free expansion into vacuum does no work since P_ext = 0, (2) Thermally insulated means adiabatic process with Q = 0, (3) For ideal gas, internal energy depends only on temperature, so ΔU = 0 implies ΔT = 0, (4) Non-equilibrium intermediate states cannot be represented on P-V-T surface as they lack well-defined pressure and temperature values.