# 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?? Nov 5, 2016 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 Nov 5, 2016 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) Nov 5, 2016 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/… Nov 5, 2016 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 Nov 5, 2016 at 14:10

## 1 Answer

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.