Question

In an adiabatic process, no transfer of heat takes place between the system and surroundings. Choose the correct option for free expansion of an ideal gas under adiabatic conditions from the following:

• A. \( q = 0, \Delta T \neq 0, W = 0 \)
• B. \( q \neq 0, \Delta T = 0, W = 0 \)
• C. \( q = 0, \Delta T = 0, W = 0 \)
• D. \( q = 0, \Delta T<0, W \neq 0 \)

Hint:

In free expansion, there is no work done, and the temperature of the ideal gas remains constant as there is no heat transfer.

Answer 1

The Correct Option is C

In an adiabatic process, by definition, there is no heat transfer between the system and its surroundings, so: \[ q = 0 \] For free expansion of an ideal gas, the gas expands without doing work on the surroundings because it is allowed to expand into a vacuum. Hence, the work done is zero: \[ W = 0 \] Since the expansion is free, there is no change in the internal energy of the gas (no work done, and no heat transferred). For an ideal gas undergoing an adiabatic process, the temperature would not change in the case of free expansion: \[ \Delta T = 0 \] Thus, the correct option is: \[ q = 0, \Delta T = 0, W = 0 \]