Does potential energy increase with temperature?

- - The potential energy of a 12-lb bowling ball up on the shelf

doesn't have anything to do with the temperature of the ball or

the shelf.

- - The potential energy of a jar full of gas does depend on the

temperature of the gas. The warmer it is, the greater its pressure

is, and the more work it can do if you let it out through a little hole

in the jar. If it gets hot enough, it'll have enough potential energy

to blow the jar to smithereens.

When a solid melts and becomes a liquid, we say it changes phase from a solid to a liquid. In this change, the bonding between the atoms or molecules changes. You have to "break" some bonds to go from a solid to a liquid. This requires energy. The liquid is a "higher" potential energy state than the solid, even at the same temperature. (It is slightly more complicated than this, but this is good enough for this class.) To convert 1kg of solid water at 0oC (273K) to liquid water at 0oC (273K) requires about 330,000J of energy. Note that the temperature of the liquid is the same as the solid’s, i. e. you added heat without changing the temperature, instead the phase changed. The heat added went into "breaking" bonds and increasing its potential energy, not into increasing the average translational KE of the molecules. (It is slightly more complicated than this, but this explanation is good enough for this class.) If you go the other way, and convert 1kg of liquid water at 0oC (273K) to ice at 0oC (273K) releases 330,000J of heat. This heat comes from the energy given off when bonds form, i. e. it goes to a state of lower potential energy. The same type of thing occurs when a liquid changes to a gas. Then more bonds are broken as the molecules move apart, and it requires energy to break the bonds and move to a higher potential energy. To convert 1kg of liquid water at 100oC (373K) to 1kg of water vapor at 100oC (373K) requires 2,260,000J (almost 2.3 million Joules) of energy. That is, the water absorbs energy to change from a liquid to a gas ... If 1kg of water vapor conde