# Does lowering temperature of a gas make it easier to compress?

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?

• Why gas molecules will come closer on lowering the temperature?? – Vidyanshu Mishra Nov 5 '16 at 14:02
• The kinetic energy decreases and they cannot move freely anymore. It is similar to the way water molecules come closer and form ice when temperature is lowered – Abhishek Mhatre Nov 5 '16 at 14:04
• Since you are saying that water molecules come closer to form ice then why don't volume of water decreases (i don't see any decrease) – Vidyanshu Mishra Nov 5 '16 at 14:06
• Sorry I actually gave a wrong example since "Water is the only known non-metallic substance that expands when it freezes; its density decreases and it expands approximately 9% by volume". Source:lpi.usra.edu/education/explore/ice/activities/ice_action/… – Abhishek Mhatre Nov 5 '16 at 14:08
• So,give me a suitable answer of "Why gas molecules will come closer on lowering the temperature" so that i can write my answer – Vidyanshu Mishra Nov 5 '16 at 14:10

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.