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: {Ideal Gas Free Expansion Fundamentals}
In free expansion, a gas expands without performing work or exchanging heat with its environment. Because the process is adiabatic, \( q = 0 \), indicating no heat transfer occurs. 
Step 2: {Work Calculation for Free Expansion} 
As the expansion occurs against a vacuum, no work is done by or on the system. Therefore, \( w = 0 \). 
Step 3: {Temperature Variation During Free Expansion} 
An ideal gas undergoing free expansion experiences no temperature alteration, thus \( \Delta T = 0 \). Consequently, option (D) is the correct selection.