Question
If a gas is suddenly compressed, its temperature increases, why?

Answer

Because sudden compression of a gas is an adiabatic process. According to the first law of thermodynamics,
$\Delta\text{Q}=\Delta\text{U}+\Delta\text{W}$
$\because\Delta\text{Q}=0$
$\therefore\Delta\text{U}=-\Delta\text{W}$
$\because\Delta\text{W}=$ negative because work done on the gas
Thus, $\Delta\text{U}$ increases and gas temperature rises.

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