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Which of the following is correct option for free expansion of an ideal gas under adiabatic condition?
A
$q = 0,\ \Delta T < 0,\ w \neq 0$
B
$q = 0,\ \Delta T \neq 0,\ w = 0$
C
$q \neq 0,\ \Delta T = 0,\ w = 0$
D
$q = 0,\ \Delta T = 0,\ w = 0$
Detailed Solution
Adiabatic condition means no heat is exchanged with the surroundings: q = 0.
Free expansion means expansion against zero external pressure: $w = -p_{ext}\Delta V = 0$.
First law: $\Delta U = q + w = 0 + 0 = 0$
For an ideal gas the internal energy depends only on temperature, so $\Delta U = 0$ gives $\Delta T = 0$.
Hence q = 0, $\Delta T = 0$ and w = 0.
Free expansion means expansion against zero external pressure: $w = -p_{ext}\Delta V = 0$.
First law: $\Delta U = q + w = 0 + 0 = 0$
For an ideal gas the internal energy depends only on temperature, so $\Delta U = 0$ gives $\Delta T = 0$.
Hence q = 0, $\Delta T = 0$ and w = 0.