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

Solution

Chemistry ma’am · 4 steps

Into a vacuum, w = 0; insulated, q = 0. So Δ U = 0 and an ideal gas keeps its temperature.

1. Adiabatic. The gas is insulated, so no heat crosses the boundary: q = 0.
2. Free expansion. The gas expands into a vacuum, so the external pressure is zero. Work done is w = -pₑₓₜΔ V = 0, even though the volume grows.

   Δ U = q + w = 0 + 0 = 0

3. Link to temperature. For an ideal gas, U depends only on temperature, since Δ U = nC_VΔ T. With Δ U = 0, it follows that Δ T = 0.
4. So. All three are zero: q = 0, Δ T = 0, w = 0. That is option (a).

The idea to keep. Free expansion means pₑₓₜ = 0, so w = 0. For an ideal gas, Δ U = 0 always means Δ T = 0, because its internal energy depends on temperature alone.

Answer from the NTA final answer key. Solution by PrepWiser.