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An adiabatic process has no heat exchange with the surroundings ($\Delta Q = 0$). This occurs when the system is perfectly insulated or the process is so rapid that heat has no time to flow. The First Law becomes $\Delta U = -W$: work done by the gas comes entirely at the expense of internal energy.

During adiabatic expansion, $W > 0$ so $\Delta U < 0$ and the gas cools. During compression, the gas heats up. Three equivalent relations describe the process: $PV^\gamma = C$, $TV^{\gamma-1} = C$, and $TP^{(1-\gamma)/\gamma} = C$, where $\gamma = C_p/C_v$.

Work done: $W = nR(T_1 - T_2)/(\gamma - 1) = (P_1V_1 - P_2V_2)/(\gamma - 1)$. On a P-V diagram, the adiabatic curve is steeper than the isothermal by a factor of $\gamma$ (slope $= -\gamma P/V$ versus $-P/V$). This steeper slope is a frequently tested comparison.

Adiabatic free expansion (into vacuum) is a special case: $W = 0$ (no opposing pressure), $Q = 0$, so $\Delta U = 0$ and temperature is unchanged for an ideal gas. Despite no temperature change, entropy increases — this process is irreversible.