The work done in an adiabatic change in an ideal gas depends upon only :

Solution

Physics sir · 3 steps

No heat goes in or out, so all the work comes from internal energy, and that depends only on temperature.

1. First law. In an adiabatic change Q = 0. So Δ U = Q - W becomes W = -Δ U: the gas does work only by spending its own internal energy.
2. Internal energy. For an ideal gas, internal energy depends on temperature alone: Δ U = nC_V Δ T. Using C_V = R/(γ - 1) gives the work directly.

   W = -nC_V Δ T = (nR (T₁ - T₂))/(γ - 1)

3. So. For a given amount of a given gas, n, R and γ are fixed. The only thing that changes the work is T₁ - T₂, the change in temperature, which is option (b).

The idea to keep. In an adiabatic process, W = -Δ U. For an ideal gas U depends only on T, so the work is set entirely by the temperature change.

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