Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. It only takes a minute to sign up.
Sign up to join this community
My teacher said that for ideal gases,
the lower the temperature, the lower the kinetic energy of a gas will be, and it will be easier to compress the gas.
Using the ideal gas equation $PV=nRT$, if the volume is constant, a decrease in temperature will cause a decrease in the pressure of the gas. That will make it easier to compress. Will the volume remain constant, or will it change?
Compressing a gas by applying an external force means to work against the force the gas exerts on the walls of its container, i.e. its pressure.
The definition of compressibility
$$\beta = -\frac{1}{V}\frac{\partial V}{\partial p} \tag{1}$$
for an ideal gas with the well-known equation of state
$$p V = n R T \tag{2}$$
gives
$$\beta = -\frac{1}{V}\frac{\partial V}{\partial p} = \frac{1}{V} \frac{n R T}{p^2} = \frac{1}{p} \tag{3}$$
which is independent of the temperature $T$.
For non-ideal gases there will be higher order terms that also depend on temperature.
It is also worth noting that at the critical point the compressibility of a real gas is infinite. So if you are below the critical temperature you will be able to compress the gas more easily at a state (the critical point) with higher temperature.
