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(B) For free expansion of an ideal gas,the external pressure $P_{ext} = 0$. Since $w = -P_{ext} \Delta V$,it follows that $w = 0$. For an adiabatic pr

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$q = 0, \Delta T = 0$ and $w = 0$

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(B) For free expansion of an ideal gas,the external pressure $P_{ext} = 0$. Since $w = -P_{ext} \Delta V$,it follows that $w = 0$. For an adiabatic process,the heat exchange $q = 0$. According to the first law of thermodynamics,$\Delta U = q + w$. Substituting the values,$\Delta U = 0 + 0 = 0$. For an ideal gas,internal energy change $\Delta U = n C_{v,m} \Delta T$. Since $\Delta U = 0$,it implies $\Delta T = 0$. Therefore,the correct conditions are $q = 0, \Delta T = 0, w = 0$.

The correct option for free expansion of an ideal gas under adiabatic condition is

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