Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following:

• A

  $\mathrm{q}=0, \Delta \mathrm{~T} \neq 0, \mathrm{w}=0$
• B

  $q=0, \Delta T \lt 0, w \neq 0$
• C

  $\mathrm{q}=\neq 0, \Delta \mathrm{~T}=0, \mathrm{w}=0$
• Correct answer
  D

  $\mathrm{q}=0, \Delta \mathrm{~T}=0, \mathrm{w}=0$

Solution

$\Delta U=q+w$ For a adiabatic process, $\Delta \mathrm{U}=\mathrm{w}=-\mathrm{p}_{\mathrm{ex}} \Delta \mathrm{v}$ For free expansion of ideal gas $\mathrm{p}_0=0$ As $\Delta \mathrm{U}=\mathrm{C} \Delta \mathrm{T}=0$

Hence, the correct answer is option: 'D'.