Question #43909

2 Answers
Sep 9, 2015

Its volume will decrease as well.


When pressure is kept constant, and assuming that the number of moles of gas is kept constant as well, temperature and volume have a direct relationship.

More specifically, if temperature decreases, volume decreases, and if temperature increases, volume increases as well. This is known as Charles' Law.

This happens because gas pressure is actually caused by the collisions that take place between the molecules and the walls of the container.

The temperature of the gas determines the average kinetic energy of the gas molecules, which in turn determines the frequency and force with which they hit the wall.

When temperature decreases, the average kinetic energy of the gas molecules decreases as well. This means that in order for the pressure to be constant, the volume needs to decrease, to compensate the lower average kinetic energy of the molecules.

Think of it like this - in order for the force and frequency of the collisions to remain unchanged, the volume needs to be smaller.

Likewise, if the temperature is increased, the molecules will have more kinetic energy, which means that the volume needs to increase to keep pressure constant.

Sep 9, 2015

You could mathematically state it this way, using the ideal gas law:

#PV = nRT#

We know that #n# and #R# are constants, so let's ignore them for now and call them #c_1#.

#PV = c_1T#

where #c_1# will never change in a closed container since nothing escapes. Since #P# is a constant as well, we can do this:

#color(blue)(V) = c_1/PT = c_2color(blue)(T)#

where #c_2# is a different constant, but again, it'll never going to change in a closed container, since nothing escapes and we have a constant pressure.

That means to keep the equality true, when temperature decreases, volume must decrease with it.

Or, conceptually, you could state it this way:

Since lower temperature describes lower average kinetic energy, and kinetic energy describes motion, the motion of molecules becomes slower at lower temperatures. That just means the molecules are less excited and so they move around less.

The less they move around, the less likely they occupy a large space, and the more controlled they are. Therefore, they occupy a smaller volume.

It is also worth noting that in a closed container, the pressure will not change if no one manually changes it since there is theoretically no contact with the outside atmosphere, and so, no air flow could change the pressure.