Question

Explain why the temperature of a gas increases when it is compressed adiabatically.

Short answer

During compression, the work on the gas system and the change in internal energy are positive. As internal energy is a function of temperature, the temperature of the gas increases during adiabatic compression.

Step-by-step solution

Concept

By the first law of thermodynamics,\(\Delta U = Q - W\).

Now, for the adiabatic process, the change in heat energy is\(Q{\bf{ = 0}}\).

Explanation

For the adiabatic process,

\(\begin{aligned}{c}\Delta U = Q - W\\\Delta U = - W.\end{aligned}\)

During the adiabatic process, the change in the gas system's internal energy is equal to the opposite of the work done by the gas system or on the gas system.

During compression, the work on the gas system and the change in internal energy are positive. Internal energy is a function of temperature.

Hence, the temperature of the gas increases during adiabatic compression.