Question

When a gas surrounded by air is compressed adiabatically, its temperature rises even though there is no heat input to the gas. Where does the energy come from to raise the temperature?

Short answer

The increase in the temperature in the adiabatic compression is due to the work done by the air on the gas.

Step-by-step solution

Understanding the adiabatic process

In this process, there is no heat exchange observed. The heat change value remains zero in this case. No heat gain or loss occurs with in the system. No heat transfer between specific system and surrounding.

Explanation of the energy required to raise the temperature

As the air compresses the gas, the air applies force, so work done W on the gas, where this work done converted into energy and increases its internal energy$∆U$ as no heat transfer (Q = 0), according to the first law of thermodynamics.

Also, the change in internal energy$∆U$ depends on the system's temperature change$∆T$ ; the internal energy of a particular system increases, then the temperature$∆T$increases.

It can be given as:

$∆U=n{C}_v∆T$

Here, n is the number of moles, and $C_v$is the specific heat.

Hence, the increase in the temperature in the process of adiabatic compression is due to work done by the air on the gas.