Question

Which of the following is correct option for free expansion of an ideal gas under adiabatic condition ?

• A. $q = 0, \Delta T < 0, w \neq 0$
• B. $q = 0, \Delta T \neq 0, w = 0$
• C. $q \neq 0, \Delta T = 0, w = 0$
• D. $q = 0, \Delta T = 0, w = 0$

Answer 1

The Correct Option is D

Free expansion of an ideal gas under adiabatic conditions is an important concept in thermodynamics. To understand why the correct answer is $q = 0, \Delta T = 0, w = 0$, we need to break down the terms and the process:

1. Adiabatic Process: In an adiabatic process, there is no heat exchange with the surroundings. This implies that the heat transfer $q = 0$.
2. Free Expansion: During free expansion, the gas expands into a vacuum without any external pressure opposing it. This means that no work is done by or on the system, which implies $w = 0$.
3. Change in Temperature: For an ideal gas undergoing free expansion, the internal energy remains constant due to no work done and no heat exchange. In terms of the ideal gas law and internal energy equation, this results in no change in temperature, so \Delta T = 0.

Therefore, combining all these considerations, the correct option for the free expansion of an ideal gas under adiabatic conditions is indeed $q = 0, \Delta T = 0, w = 0$. Let's summarize why other options are incorrect:

• $q = 0, \Delta T < 0, w \neq 0$: This is incorrect as work w is zero and there's no change in temperature.
• $q = 0, \Delta T \neq 0, w = 0$: This is incorrect because there is no temperature change \Delta T = 0.
• $q \neq 0, \Delta T = 0, w = 0$: This is incorrect because, in an adiabatic process, q is always zero.

The correct understanding of these concepts solidifies the answer as $q = 0, \Delta T = 0, w = 0$.