Feel a working fluorescent light bulb. The gas inside is at a temperature of over 11,000 degrees Kelvin, which is hotter than the surface of the Sun. However, it only feels slightly warm to the touch.
Dinner is ready. It has been baking in a hot oven for an hour. Opening the oven door, the air feels warm on the cook's hand but will not burn it. Touching the metal baking pan at the same temperature will, however, burn the cook's hand.
Why? The answer requires understanding the difference between temperature and heat content. They are related but distinctly different concepts.
Temperature
An object's temperature is a measure of the random molecular motions. Individual atoms and molecules are never still. They move around randomly. The molecular motion is highly constrained in a solid object, so the object can keep its shape. On the other hand in the gaseous or liquid states the molecules and atoms have fewer constraints on their motion, so gasses and liquids have no specific shape, and the individual molecules can move more rapidly.
In either case as an object's temperature increases, the average speed of the random motions of individual atoms or molecules increases. If an object were to reach a temperature of absolute zero, random molecular motions would be at their minimum possible level. However the third law of thermodynamics says that it is not possible to reach a temperature of absolute zero.
The gas atoms in the fluorescent light bulb are at a high temperature, so they are on the average flying around randomly inside the light bulb at a very high speed. However there are relatively few gas atoms in the bulb. Therefore the total random kinetic energy contained in the gas atoms is small. This random kinetic energy in the atoms is the total amount of heat, or thermal, energy contained in the gas, its heat content.
Heat Content
The heat content of an object, sometimes called the internal energy, is the total amount of heat energy in the object. The thermal energy is the total random kinetic energy of all the individual atoms or molecules in the object. As the temperature increases the heat content also increases by an amount dependent on the specific object.
The gas in a fluorescent light bulb or the air in an oven has a relatively low heat capacity. Therefore it does not take a large amount of heat energy to raise the temperature of either one. On the other hand, the metal baking dish containing dinner has a larger total heat capacity. It is no hotter than the air in the oven, but it has a greater heat content.
The baking dish contains enough thermal energy to burn the hand of anyone touching it directly. Using an oven mitt or hot pad is necessary to provide thermal insulation. The air in the oven, at the same temperature, or the gas in the fluorescent light bulb, at a much higher temperature, have low heat capacities and therefore low heat content. They will not burn the hand of anyone touching them.
Heat content and temperature are related but different quantities. Depending on an object's heat capacity, it is possible for one of these quantities to be high while the other is low.
Further Reading
Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.
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