• id: JTHERM-01-N07
• title: Adiabatic Process — No Heat Exchange
• tags: adiabatic, gamma, insulated

Condition: $\Delta Q = 0$ (thermally insulated system or very fast process). First Law: $\Delta U = -W$. Expansion cools the gas (W > 0, so $\Delta U < 0$, T drops). Compression heats it. Three relations: $PV^\gamma = C$, $TV^{\gamma-1} = C$, $TP^{(1-\gamma)/\gamma} = C$. Work: $W = nR(T_1-T_2)/(\gamma-1) = (P_1V_1-P_2V_2)/(\gamma-1)$. On P-V diagram, adiabatic curve is steeper than isothermal by factor $\gamma$ (since $dP/dV = -\gamma P/V$ vs $-P/V$). Adiabatic free expansion (into vacuum): W = 0, Q = 0, $\Delta U = 0$, T unchanged for ideal gas.