Chapter 15, Problem 5Q

To determine

To find: The temperature of a gas increases when it is adiabatically compressed.

Explanation of Solution

Introduction:

No heat is allowed to flow into or out of the system in an adiabatic phase, $Q=0.$

Accordingly, $\Delta U=-W$

The change in internal energy = opposite work by gas, or $=$ work by gas.

The internal energy of the gas increased and that leads to an increase in temperature after positive work was done on the gas.

The work performed on the gas becomes the gas particles' inner energy, and the temperature increases accordingly.

As we know, in adiabatically process change in heat zero.

From first law of thermodynamics

  $\Delta U=\Delta Q+W,$ If $\Delta Q=0$ then $\Delta U=W$

  $\Rightarrow$ When piston is moving the gas molecules

  $\Rightarrow$ gain moAdd re kinetic energy as before

  $\Rightarrow$ due to collision with piston. As we know gain of kinetic energy leads to increase temperature and also gained heat due to collision cannot be lost because of adiabatic wall hence temperature increases.