Question

At a pressure of 20 kPa, a sample of a gas has a volume of 50 liters. What pressure does it exert when the gas is compressed to 20 liters?

Answer 1

In order to solve the problem, one needs to assume that the temperature of the system doesn't change. The relationship between pressure and volume at constant temperature is described by Boyle's law:

$p\propto\frac{1}{V}$ ,

or pressure is inversely proportional to volume at $T=const$ .

Therefore, for two states of the same system at the same temperature, the pressures and volumes are linked as:

$p_1V_1 = p_2V_2$ .

In our case, $p_1$ is 20 kPa, $V_1$ is 50 L and $V_2$ is 20 L. Thus:

$p_2 = \frac{p_1V_1}{V_2} = \frac{20\text{ kPa}\cdot 50\text{ L}}{20\text{ L}} = 50$ kPa.

Answer: when the gas is compressed to 20 L, it exerts a pressure of 50 kPa.