Question

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following:

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

Hint:

In an adiabatic free expansion of an ideal gas, there is no heat transfer, no work done, and no change in temperature, as the gas expands into a vacuum.

Answer 1

The Correct Option is D

Step 1: {Understanding Free Expansion of an Ideal Gas} 
In free expansion, the gas expands without doing work and without heat exchange with the surroundings. Since the process is adiabatic, \( q = 0 \), meaning no heat is exchanged. 
Step 2: {Work Done in Free Expansion} 
Since the expansion is against a vacuum, no work is done on or by the system. Hence, \( w = 0 \). 
Step 3: {Temperature Change in Free Expansion} 
For an ideal gas undergoing free expansion, there is no change in temperature, so \( \Delta T = 0 \). Thus, the correct answer is (D).