# Calculating Kinetic Energy in an Ideal Gas

Molecules have very little mass, but gases contain many, many molecules, and because they all have kinetic energy, the total kinetic energy can pile up pretty fast. Using physics, can you find how much total kinetic energy there is in a certain amount of gas? Yes! Each molecule has this average kinetic energy:

To figure the total kinetic energy, you multiply the average kinetic energy by the number of molecules you have, which is *nN*_{A}*,* where *n* is the number of moles:

*N*_{A}*k* equals *R,* the universal gas constant, so this equation becomes the following:

If you have 6.0 moles of ideal gas at 27 degrees Celsius, here’s how much internal energy is wrapped up in thermal movement (make sure you convert the temperature to kelvin):

This converts to about 5 kilocalories, or *Calories* (the kind of energy unit you find on food wrappers).

Suppose you’re testing out your new helium blimp. As it soars into the sky, you stop to wonder, as any physicist might, just how much internal energy there is in the helium gas that the blimp holds. The blimp holds 5,400 cubic meters of helium at a temperature of 283 kelvin. The pressure of the helium is slightly greater than atmospheric pressure,

So what is the total internal energy of the helium?

The total–kinetic energy formula tells you that *KE** _{total}* = (3/2)

*nRT.*You know

*T,*but what’s

*n,*the number of moles? You can find the number of moles of helium with the ideal gas equation:

*PV = nRT*

Solving for *n* gives you the following:

Plug in the numbers and solve to find the number of moles:

So you have

Now you’re ready to use the equation for total kinetic energy:

Putting the numbers in this equation and doing the math gives you

So the internal energy of the helium is

That’s about the same energy stored in 94,000 alkaline batteries.