Adiabatic Process

As explained in NCERT Class 11, Chapter 12 (Thermodynamics), an adiabatic process is one in which no heat is exchanged with the surroundings, so $\Delta Q=0$. Two conditions favour this: thermal insulation, and a process that happens so rapidly that heat has no time to flow. A perfectly insulated cylinder with a fast-moving piston satisfies both. Applying the First Law with $\Delta Q=0$ gives $$\begin{gathered} 0=\Delta \\ cup+\Delta W \end{gathered}$$, so $$\begin{gathered} \Delta \\ cup=-\Delta W \end{gathered}$$. During compression the surroundings do work on the gas, making $\Delta W$ negative (work by gas), so $\Delta U$ is positive and the internal energy and temperature rise. The option about heat flowing out at constant temperature describes an isothermal compression, not adiabatic. The option about heat flowing in describes a heating process and contradicts $\Delta Q=0$. The option that internal energy stays constant is wrong because adiabatic compression must raise internal energy when work is done on the gas. A consistency check: since no heat escapes the insulated wall, the work input has nowhere to go but internal energy, so a temperature rise is physically required.