Question

Which of the following conditions is CORRECT for free expansion of an ideal gas under adiabatic condition? (q = heat, \(\Delta T = \) temperature difference, w = work)

• 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. \( q = 0, \Delta T = 0, w = 0 \)

Hint:

Free expansion means no heat exchange, no work done, and no change in temperature.

Answer 1

The Correct Option is D

Step 1: Understand free expansion.
In free expansion, the gas expands without doing work on the surroundings and without any heat exchange. This means:
- \( w = 0 \) (no work done by the gas).
- \( q = 0 \) (no heat is transferred).
Step 2: Analyze temperature change.
Since no work is done and no heat is transferred, the internal energy of the ideal gas does not change. For an ideal gas, if the internal energy remains unchanged, the temperature must also remain constant, so \( \Delta T = 0 \).
Step 3: Conclusion.
Thus, the correct conditions for free expansion are:
- \( q = 0 \),
- \( \Delta T = 0 \),
- \( w = 0 \).
Final Answer: \[ \boxed{\text{For free expansion, \( q = 0, \Delta T = 0, w = 0 \).}} \]