Gas Molecule Motion
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At a low temperature gas molecules travel, on the average, at slower speeds than they travel at a high temperature. So, at a low temperature the molecules have, on the average, less kinetic energy than they do at a high temperature due to their lower speeds.
Temperature, when measured in Kelvin degrees, is a number that is directly proportional to the average kinetic energy of the molecules in a substance. So, when the molecules of a substance have a small average kinetic energy, then the temperature of the substance is low.
This animation shows all of the molecules of a gas traveling at the same speed. This is not a perfect representation of their motion, however. Actually, these gas molecules would all travel at different speeds. However, for any temperature there is an average speed of molecular motion which would correspond to an average kinetic energy. The Kelvin temperature of the gas would be proportional to this average kinetic energy. This animation is meant to show that at a low temperature, gas molecules travel slowly.
Lower Temperature
Below is a simulation of gas molecules at a higher temperature than those shown above. Compare them carefully, their speed is not too much greater, but is in fact greater. These are faster by a factor of the square root of two, 1.414. This makes the average kinetic energy of these molecules to be twice that of those above, since the kinetic energy of a body is proportional to the square of the speed of the body. Consequently, this lower animation represents a gas at twice the Kelvin temperature than the gas above.
The area of this animation is twice as large as the area above so that the pressure of the gas is properly simulated as being equal to the pressure above. This allows us to properly see the effect of a temperature change on the speed of gas molecules without concerns about other effects due to pressure changes.
Higher Temperature
What you should notice in this lower animation is that the higher temperature is tied to a higher average kinetic energy. This results in the molecules having a higher average speed.
The potential energies present in the lower animation are very close to the potential energies in the upper animation. The substance, a gas in both cases, has not undergone a phase change, or, as it is also often called, a change of state. That is, the molecules in the low and high temperature situation bond to each other with about the same strength. One could imagine a very small increase in potential energy with the higher temperature gas due to the fact that the molecules are indeed, on the average, farther apart. Gas molecules are attracted to one another by a very weak Van der Waals force, so, some work had to be done push them farther apart at the higher temperature. This, though, is a very tiny amount of energy. Basically, there is not much of an increase in potential energy in the bottom diagram over the top diagram.
In the bottom diagram, however, there is a noticeable increase in kinetic energies.
Heat, as stated earlier, is the sum of all potential and kinetic energies possessed by the molecules of a substance. If the potential energies stay about the same and the kinetic energies go up, then the heat has gone up. Therefore, in the example which we have examined here, an increase in heat has caused an increase in temperature because the increase in heat has been realized as an increase in the kinetic energies of the gas molecules. When the kinetic energies of the gas molecules goes up, the temperature goes up.
An increase in heat is not always accompanied by an increase in temperature, however. That is very important to understand. The heat, or energy, could be used to change the bonding between the molecules rather than be used to speed up the molecules. This would be a situation where heat goes into a substance, and the temperature does not rise, as when ice melts or water boils. In these cases the increase in heat, or the increase in energy, shows up as an increase in potential energies and not as an increase in kinetic energies.
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