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The correct option for free expansion of an ideal gas under adiabatic condition is:
A
$q=0,\ \Delta T0$
B
$q<0,\ \Delta T=0$ and $w=0$
C
$q>0,\ \Delta T>0$ and $w>0$
D
$q=0,\ \Delta T=0$ and $w=0$
Detailed Solution
Free expansion: $P_{ext} = 0 \Rightarrow w = -P_{ext}\Delta V = 0$
Adiabatic process: q = 0
$\Delta U = q + w = 0$; since the internal energy of an ideal gas depends only on temperature, $\Delta T = 0$.
So q = 0, $\Delta T$ = 0 and w = 0.