# Why do gas expand when heated?

So as a volume of gas is heated, the addition of energy increase the particles' kinetic energy. This only means that they are now moving faster right? I cannot relate this increase of kinetic energy to expansion. Do the particles grow or something?

• – anna v Jan 18 '19 at 7:08

The molecules that make up the gas are in random motion, bouncing off each other and off the walls of the container they are in. Their average speed between bounces tells us the temperature of the gas molecules. Adding energy to them (in the form of heat) makes them move faster, which raises the temperature of the gas. The added energy means when they hit the walls of their container, they hit harder. All those hits add up to pressure, which means the hotter the gas gets, the faster the molecules in it move, the more pressure they exert on the walls of the container.

• every good answer, i upvoted and one more thing, how can this expansion use to do work? Like i heard my teacher said if there is no change in volume for the system, that means there is no work. – Negrawh Jan 18 '19 at 7:38
• simple. You make one wall of the gas container moveable. when you heat the gas, it pushes on the wall and makes it move. You then connect the moving wall to your machine, where it turns a crank or pushes on a lever, etc. and performs work. this is how automobile engines operate. – niels nielsen Jan 18 '19 at 7:43
• sorry, Mr Nielsen, I got 1 more question. So the increase in volume for a system does not necessarily perform work if the moving wall is not attached to some kind of machines? For example a balloon alone? – Negrawh Jan 18 '19 at 8:07
• you are right, a "free" expansion only does work against the pressure of the atmosphere. These matters are explained in a first course in thermodynamics you would get in college. Are you working now from a textbook? college or high school? -Niels – niels nielsen Jan 18 '19 at 9:15
• Best of luck to you in your studies! – niels nielsen Jan 18 '19 at 16:43

A heated gas doesn’t expand if it is in, say, a steel container. Instead, its pressure rises due to the greater kinetic energy.

If it is in, say, a balloon, then the greater pressure pushes outward on the balloon and makes it expand.

I cannot relate this increase of kinetic energy to expansion.

The volume of a gas which has been heated does not necessarily increase.
If the gas is contained in a vessel with constant volume it will not expand but rather the pressure of the gas will increase.
This is because when heated the gas molecules will move faster and rebound off the wall of the container suffering a greater change in momentum and this will happen more often.
Thus the force (rate of change of momentum) exerted by the gas molecules on the walls per unit area of wall (pressure) will increase.

Now consider the gas heated in a container and the pressure of the gas is allowed to stay constant because the container can expand.
In this case the gas molecules will again rebound off the wall of the container suffering a greater change in momentum but now the area over which the molecules exert a force on the walls will have increased thus keeping the pressure constant.

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In a more formal way in terms of the kinetic theory of gasses, the pressure exerted by a gas is $$P =\frac 13\rho c^2_{\rm rms}$$ where $$\rho$$ is the density of the gas and $$c^2_{\rm rms}$$ is the mean square speed of the gas molecules.

If the gas is heated at constant volume the density of the gas stays the same but the mean square speed of the molecules increases so the pressure must increase.

On the other hand, if on heating the density of the gas decreases (due to an increase in volume) at the same rate as the mean square speed of the molecules increase the pressure of the gas will stay constant.