Question

If an ideal gas, in an insulated vessel, is allowed to expand into another similar evacuated vessel through a valve then:

• A. External work is done on the gas
• B. The pressure of the gas is doubled
• C. The volume of the gas is doubled
• D. The pressure of the gas remains same
• E. The temperature of the gas is increased

Hint:

In free expansion, the gas expands into a vacuum without any work being done and without heat exchange. The only change in the system is an increase in volume, while the temperature and pressure generally decrease.

Answer 1

The Correct Option is C

This scenario describes a process known as free expansion. In free expansion, the gas expands into a vacuum (another vessel that is evacuated), and the system is insulated, meaning no heat is exchanged with the surroundings (adiabatic process).

In an adiabatic process with an ideal gas, there is no heat exchange (\( Q = 0 \)) and no work done by or on the gas if there is no external pressure opposing the expansion.

• External work is not done on the gas since it is expanding into an evacuated space (a vacuum).
• The pressure of the gas will not remain the same during the expansion. As the gas expands into a larger volume, the pressure will decrease according to Boyle's law (for an isothermal process), but this expansion is adiabatic, so pressure decreases due to the increase in volume.
• The volume of the gas will indeed double because the gas expands into an equally sized evacuated vessel. The total volume will be the sum of the volumes of both vessels, effectively doubling the initial volume.
• The temperature of the gas generally decreases during free expansion (in a real gas), as the gas does not do work on the surroundings, and no heat is added to the system. However, in this case, the temperature of an ideal gas remains constant.

Therefore, the correct answer is:

\[ \boxed{\text{C) The volume of the gas is doubled}} \]