Question

An ideal gas undergoes an adiabatic expansion from volume \( V \) to \( 2V \). If the initial temperature is \( T \), what is the final temperature? (Assume the ratio of specific heats \( \gamma = \frac{5}{3} \))

• A. \( T \)
• B. \( \frac{T}{2} \)
• C. \( \frac{T}{2^{2/3}} \)
• D. \( \frac{T}{2^{5/3}} \)

Hint:

\textbf{Tip:} For adiabatic processes, use \( TV^{\gamma - 1} = \text{const} \) to directly relate initial and final temperatures and volumes.