Question

the volume of a sample of air in a cylinder with a movable piston is 2.0 l at a pressure p1, as shown in the diagram above. the volume is increased to 5.0 l as the temperature is held constant. the pressure of the air in the cylinder is now p2. what effect do the volume and pressure changes have on the average kinetic energy of the molecules in the sample?
a the average kinetic energy increases.
b the average kinetic energy decreases.
c the average kinetic energy stays the same.
d it cannot be determined how the kinetic energy is affected without knowing p1 and p2.

Explanation:

Step1: Recall kinetic - energy relationship

The average kinetic energy of gas molecules is directly proportional to the temperature of the gas, given by the formula $\overline{K.E.}=\frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the absolute temperature.

Step2: Analyze temperature condition

In the problem, it is stated that the temperature is held constant during the volume and pressure changes. Since the average kinetic energy depends only on temperature and temperature is constant, the average kinetic energy of the molecules does not change.

Answer:

C. The average kinetic energy stays the same.