Internal Energy, Heat and Temperature

An important characteristic of all matter, as described above, is that its molecules are in continuous motion, either travelling around, as in gases and liquids, or simply vibrating, as in solids. They may also possess energy by virtue of internal vibrations or rotations. Clearly they possess kinetic energy because of these different activities. So, any substance possesses an internal energy due to this motion of its component molecules. They will be travelling around in gases and liquids with all sorts of speed and in all sorts of direction, and in a solid the vibrations will again be very varied in their amplitudes and directions. These motions, in other words, are entirely random in nature. However, in all cases there will be an average value of this kinetic energy per molecule which is simply the total internal kinetic energy of a piece of matter divided by the number of molecules in it. This quantity is proportional to the temperature of the substance. Temperature, in other words, is simply a measure of the kinetic energy of the molecules of a substance: the higher the temperature the faster they are moving about; the lower the temperature the stiller they become. This latter statement has the inevitable implication that there must be a lowest possible temperature that at which all the component molecules are at rest and have no energy. This temperature is known as absolute zero and, on the Celsius scale (freezing point of water, 0 ^oC, boiling point, 100°C), is -273.16^oC. In physics it is usual to use what are known as absolute temperatures, first introduced by Lord Kelvin in the latter part of the 19th century, on which the basic temperature interval (known as one kelvin or 1 K) is identical with that on the Celsius scale (i.e. 1K = 1°C). However, zero temperature on the Kelvin scale is taken to be the absolute zero so

bsolute temperature = Celsius temperature + 273.16.

The boiling point of water, for example, is then 373.16K since, on the Celsius scale, this boiling point (100 ^oC) is 373.16 degrees higher than absolute zero. It must be stressed here that temperature is a physical quantity that only has meaning at a statistical level it is related to the average kinetic energy of a large number of molecules. It has no meaning to talk about the temperature of a single atom or molecule or, for that matter, of a small number. In the light of the concept of internal energy, let us now return to the law of conservation of energy. There, in considering the conservation of energy in pushing a trolley or when a car brakes, it was pointed out that the heat created through friction was embodied in the increased kinetic energy of the atoms and molecules involved leading, as we have now understood, to a rise in temperature. Another way of raising the temperature of a body is for it to derive heat from a hotter body; we then think of heat flowing from the hotter body to the cooler body energy is transferred between them. Such a transfer of heat can, in fact, take place in three quite different ways. Conduction is the process in which heat travels, for example, from the hot end of an object (e.g. a rod) to the cold end; there is no transfer of matter along the rod, just a transfer of energy. On the other hand with convection, in which, for example, hot air rises or hot liquid moves to the top in a heated pan, the substance as a whole moves. Finally, there is radiation, in which energy travels across space as an electromagnetic wave and heats up the objects on which it falls, for example the heat we experience from the sun or the heat generated in a microwave cooker. If heat is supplied to a body we have seen that its internal energy increases. There is also another possible result: the body may actually do some work. Suppose gas in a cylinder confined by a piston is heated. There must be a force on the piston to withstand the pressure of the gas. When heated, because of the increased kinetic energy and, therefore, higher speeds of the molecules, the pressure on the piston will increase. The piston will be pushed out against the restraining force, thereby doing some work as in a steam engine. So the heat energy supplied can be transformed into two forms of energy internal energy and external work. The law of conservation of energy then tells us that

heat energy supplied = increase in internal energy + external work done.

This is simply a particular formulation of the law of conservation of energy but it is also dignified by being known as the first law of thermodynamics. Thinking of this in practical terms means that not all of the heat energy supplied (say to a steam engine) can be converted into useful external work. Some, inevitably, increases the internal energy and, therefore, the temperature of the system. On the other hand the reverse process, in which work is converted into heat, can be carried out with 100% efficiency as was first shown by James Prescott Joule (whose name is now used as the unit of energy) in the middle of the 19th century. There is here a fundamental asymmetry: a given amount of work can all be converted into heat, but a given amount of heat cannot all be converted into work-there is always some loss of heat to the surroundings. This asymmetry leads us on to what is known as the second law of thermodynamics.