Heat and Temperature
The terms 'hot' and 'cold' are familiar to most people; they are the subjective sensations that accompany exposure to different degrees of heat. An ice cube is 'cold' and a flame is 'hot'. Our bodies quickly tell us the difference between a day in summer and a day in winter and our mouths respond differently to a warm cup of tea and a hot cup of tea.
Temperature is a scale or degree of 'hotness' that we detect in a object or situation, but temperature is more than just a subjective sensation of the human body; temperature is also an important property of inanimate objects. A hot bar of iron is longer than a cold bar of iron and very cold water is a solid, where very hot water is gas.
One property that changes with different degrees of temperature is the volume of liquids. Hot liquids have larger volumes than cold liquids. This property change gives us a way of measuring temperature. If a small amount of colored liquid is enclosed in a long thin tube so that it can expand and contract, we have a way of accurately determining the temperature surrounding the tube. As the surroundings heat up, the liquid in the tube expands and fills more of the tube. As the surroundings cool down, the liquid contracts and so the column of liquid in the tube will becomes shorter.
Of course such a 'heat-measure' was invented a long time ago. A German physicist called Gabriel Daniel Fahrenheit did so in 1714. He enclosed mercury in a tube that had a reservoir at the bottom and a very narrow tube extending from the reservoir, along which the mercury could expand. This thermometer could measure the temperature of its surroundings by responding to the heat it absorbed.
Using a thermometer, it became possible to measure temperature-dependent phenomena such as expansion of solids, liquids or gasses and find out how they behave as the temperature varies. These investigations eventually led to the atomic theory of gas structure (Boyle's Law), and the idea that gases were composed of separate particles (we now call them molecules) that were in constant, free, random motion.
Temperature, therefore is an important property of an object or system. But 'temperature' and 'heat' must not be confused. They are not the same thing.
It is perhaps natural, but totally wrong, to assume that a glass of water at 90 degrees centigrade (a temperature scale) has more heat than a bath of water at 30 degrees centigrade. But allow them both to cool and the glass of water will reach room temperature long before the bath of water. There are a couple of reasons for this, but one of them is the fact that the bath of water holds far more heat than the glass of water.
The molecules in water are moving randomly and at a variety of different velocities, some fast, some slower. The heat content of any volume of liquid is the total internal energy of all these molecules added together (because they are in motion, a lot of this energy is in the form of kinetic energy). But temperature is simply a measure of the average kinetic energy of an individual molecule.
If there are 10 molecules of water in a given volume and they have kinetic energies 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units, the amount of heat in this volume of water would be 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10, which equals 55 units. The temperature of this water, however would be the average of these values, which is 55/10 or 5.5.
If we double the number of water molecules in our sample, so that two molecules have kinetic energies of 1 unit, two with 2 units, two with 3 units, and so on, then the amount of heat doubles to 110 units for this water, but the temperature, determined by the calculation 110/20, still stays at 5.5 degrees.
Heat and temperature are linked properties of an object or system, but they are not the same.