A gas is compressed adiabatically, which one of the following statement is NOT true.

Solution

Physics sir · 4 steps

Adiabatic means no heat flows, so all the work you do on the gas goes straight into its internal energy.

1. Adiabatic means. No heat crosses the boundary, so Q = 0. That makes statement (a) true.

   Δ U = Q + Wₒₙ = 0 + Wₒₙ = Wₒₙ

2. Compression. In compression the surroundings push on the gas, so Wₒₙ > 0. The first law then gives Δ U = Wₒₙ, which is statement (d), and Δ U > 0.
3. Temperature rises. For an ideal gas Δ U = nC_VΔ T, so a positive Δ U means Δ T > 0. Statement (b) is true. You can also see it from TV^(γ-1) = constant: as V falls, T must rise.
4. So. The internal energy does change; it increases. Statement (c) is the one that is NOT true, so the answer is (c).

The idea to keep. In an adiabatic process Q = 0, so Δ U equals the work done on the gas. Compression heats the gas and expansion cools it. Zero change in internal energy belongs to isothermal processes, not adiabatic ones.

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