Question

What happens when an ideal gas undergoes isothermal expansion into vacuum?

• A. \(w=0,\;Q=0\)
• B. \(Q=+ve,\;w=-ve\)
• C. \(w=-ve,\;Q=+ve\)
• D. \(w=0\)

Hint:

For free expansion of an ideal gas: \[ \boxed{ \begin{aligned} P_{\text{ext}}&=0\\ w&=0\\ \Delta U&=0\;(\text{isothermal})\\ Q&=0 \end{aligned} } \] Always remember: \[ \boxed{\Delta U=Q+w} \] is the First Law of Thermodynamics.

Answer 1

The Correct Option is A

When an ideal gas expands isothermally into a vacuum, $p_{ext} = 0$, so work done $w = 0$. Because the internal energy of an ideal gas depends only on temperature and $\Delta T = 0$, we have $\Delta U = 0$, and from the first law $q = 0$ as well. Consequently $\Delta H = \Delta U + nR\Delta T = 0$.