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### converting degrees Kelvin to Joules

Posted: Wed Mar 03, 2004 11:02 am
what is the relationship between temperature and energy?

### Re: converting degrees Kelvin to Joules

Posted: Wed Mar 03, 2004 11:46 pm
JJJ wrote:what is the relationship between temperature and energy?

A favorite Physics question!

Most people think that heat and temperature are the same thing. They're not. Knowing the difference between heat and temperature is important if one is to have a clear understanding of energy.

Temperature is a number that is related to the average kinetic energy of the molecules of a substance. If temperature is measured in Kelvin degrees, then this number is directly proportional to the average kinetic energy of the molecules.

Heat is a measurement of the total energy in a substance. That total energy is made up of not only of the kinetic energies of the molecules of the substance, but total energy is also made up of the potential energies of the molecules.

So, temperature is not energy. It is a number that relates to one type of energy possessed by the molecules of a substance. Temperature directly relates to the kinetic energy of the molecules. The molecules have another type of energy besides kinetic - potential energy. Temperature readings do not tell you anything directly about this potential energy.

Temperature can be measured in a variety of units. If you measure it in degrees Kelvin, then the temperature value is directly proportional to the average kinetic energy of the molecules in the substance. Mind you, it's directly proprotional, but not equal to. The relationship would be that if you double the Kelvin temperature of a substance, you double the average kinetic energy of its molecules.

Heat, on the other hand, is energy. Heat is the total amount of energy possessed by the molecules in a piece of matter. This energy is both kinetic energy and potential energy.

When heat, (i. e., energy), goes into a substance one of two things can happen:

First, the substance can experience a raise in temperature. That is, the heat can be used to speed up the molecules of the substance. Since Kelvin temperature is directly proportional to the average kinetic energy of molecules in a substance, an increase in temperature causes an equal increase in the average kinetic energy of the molecules. If the kinetic energy of the molecules increases, the speed of those molecules also increases, although these increases are not directly proportional. The kinetic energy of a body is proportional to the square of the speed of the body.

Secondly, the substance can change state. For example, if the substance is ice, it can melt into water. Perhaps surprisingly, this change does not cause a raise in temperature. The moment before melting the average kinetic energy of the ice molecules is the same as the average kinetic energy of the water molecules a moment after melting. Although heat is absorbed by this change of state, the absorbed energy is not used to speed up the molecules. The energy is used to change the bonding between the molecules. Changing the manner in which the molecules bond to one another constitutes a change in potential energy. Heat comes in and there is an increase in the potential energy of the molecules. Their kinetic energy remains unchanged.

So, when heat comes into a substance, energy comes into a substance. That energy can be used to increase the kinetic energy of the molecules, which would cause an increase in temperature, or that heat could be used to increase the potential energy of the molecules causing a change in state that is not accompanied by an increase in temperature.

Relating this to the subject you posted this question under, "converting degrees Kelvin to Joules", the relationship between kelvins and joules applies to the pricilple of Specific Heat.

Specific heat capacity is the slope (derivative) of the internal energy due to random motion of atoms in a sample as a function of temperature, normalized by dividing by the mass of the sample. Because the internal energy curve is normally almost linear, it can by approximated by measuring the heat required to raise the temperature of 1 kilogram of a substance by 1 °C (or one Kelvin). The SI unit of measurement for this is the Joule per kilogram-kelvin (J/(kg·K) or J·kg^-1·K^-1).