2.1 Heat. Joule's experiment. Equivalence of heat and work

Heat is one of the most essential concepts of thermodynamics. By its nature the concept of heat is very close to the concept of work. Both heat and work are forms of transfer of energy. There is, therefore, no sense in saying that a body stores some heat or work. We can only state that a certain amount of heat or work has been imparted to, or taken away from, a body.

The difference between heat and work consists in that they are different forms of transfer of energy. Heat is such a form of transfer of energy which is associated either with direct contact between bodies (heat conductivity, convection) or with radiant transfer of energy. Work is regarded as another mechanism of energy transfer. Mechanical work is always associated with a change in the volume of the body involved.

It is customary to assume that addition of heat involves a rise in the temperature of the body, determined by the energy of the microparticles constituting the body, which is often the case. But, as it will be seen later on, it happens that not withstanding the addition of heat to a body its temperature decreases. All depends on the balance of the energy transferred to the body and removed from it. In the special but most widespread case the change in the temperature of a body is determined by the relation between the amounts of heat and work imparted to the body and removed from it.

In the course of the development of science the ideas about heat varied. From the lime of Aristotle the predominant idea of heat consisted in that heat was assumed to be one of the 'primary qualities" of matter, with this "primary quality" being inherent to every body to a different degree. As long ago as the seventeenth century, it was evident that in the works of Descartes and Bacon attempts were made to relate the idea of heat with the motion of particles of which bodies consist. In the eighteenth century, in connection with the wide development of calorimetry, a new scientific idea appeared of the so-called caloric or phlogiston, an inviscid (non-viscous) and invisible liquid passing from bodies at a higher temperature to bodies at a lower temperature when they come or are brought into contact; the increase in the temperature of a body was thought to be due to the increase in the content of the caloric or phlogiston in the body. It ought to be mentioned that as long ago as 1760 the famed Russian scientist M. V. Lomonosov rejected the theory of the phlogiston, postulating the idea of heat as a form of motion of particles.

At the end of the eighteenth centuries works appeared refuting the theory of the phlogiston. One of the first works in this field involved an experiment conducted by the English physicist Benjamin Thompson (Count Rumford) in 1798. During the experiment a blunt cutter was pressed to the internal surface of a barrel of a gun rotating about its axis. Rumford discovered that resulting from the friction between the cutter and barrel, the temperature of the barrel increased, due to the liberation, or release, of heat. It was also found that in the course of the experiment, heat was liberated as long as the barrel rotated. Analyzing the results, Rumford concluded that if an insulated body or a system of bodies is capable of an unlimited liberation of heat, then the heat is not a material substance and only motion is able to ensure a continuous "excitation and propagation of heat in our experiments". Simultaneously with Rumford s work, the experiments of another English scientist, Sir Humphry Davy, dealt a hard blow on the theory of the phlogiston. The scientist demonstrated that it is possible to melt two pieces of ice or fat or wax by simply rubbing them against each other, without bringing them in contact with a higher-temperature body.

In 1844-1854 the English scientist J. P. Joule conducted experiments which were destined to play an important role in science. The objective of Joule's experiment was to establish a relation between the amount of work spent to bring about the liberation of heat and the amount of the heat liberated. The layout of Joule's experiment was as follows (Fig. 2.1). Paddle wheel 2 was submerged in the heat-insulated vessel 1 to the walls of which vanes 3 were fastened, the vanes interfering with the motion of water due to rotation of the paddle. Rotation was imparted to the paddle (stirrer) by the falling load 4 of weight G, connected to the paddle by means of a rope and pulley 5. As the weight falls through a distance Δh, the work done by it (and, consequently, by the stirrer) is equal to the decrease in the potential energy of the weight GΔh. The heat liberated in the water-filled vessel is calculated from the rise in water temperature, measured with a thermometer.

Fig. 2.1

It should be noted that before the nature of heat was finally established, sufficiently accurate methods of measuring the amount of heat (calorimetry) were elaborated. The mass of water was measured in advance, and the absorption of heat by the walls of the vessel, vanes and the paddle wheel was taken into account. The heat capacities of water and metal (copper) were known. Based on the results of a series of thoroughly conducted experiments, Joule discovered a direct proportionality between the spent work L and the quantity of heat obtained Q:

Q = AL, (2.1)

where A is a proportionality factor.

Joule found that the proportionality factor A remains the same irrespective of the method of heat production, type of work, temperature of the body involved, etc.

In other words, Joule established that when one and the same amount of work is spent, one and the same amount of heat is liberated. Thus, the amount of liberated heat was shown to be equivalent to the amount of work spent; it is clear that this relationship is true for the case when work is accomplished at the expense of heat.

Using the results of these measurements, Joule calculated the magnitude of A, which is known as the thermal equivalent of work, and of J, referred to as the mechanical equivalent of heat:

A = 0.002345 kcal/(kgf·m)

and

J = 427 kgf·m/kcal.

It is obvious that

J = 1/A.

Later on the values of A and J, obtained by Joule, were somewhat improved; in accordance with the results obtained after very accurate up-to-date measurements,

J = 426.935 kgf·m/kcal.

As it was already mentioned, sufficiently accurate methods of measuring heat (calorimetry), based on using the notions of temperature and heat capacity of a body, had been elaborated as far back as the eighteenth century, i.e. long before the nature of heat was finally elucidated. In its time the most common unit of heat was the calorie, which was defined as the amount of heat required to raise the temperature of 1 g of water by l ^oC. However, it was found later that the heat capacity of water changes somewhat with temperature. Therefore, at different temperatures different amounts of heat are required to raise the temperature of 1 g of water by 1°C. In this connection it became necessary to define the calorie with a greater accuracy, and the so-called 15° calorie was introduced, defined as the amount of heat required to raise the temperature of water from 14.5 °C to 15.5 °C. At the present time work and heat are measured in different units; the relations between them are given in Table 2.1. The units most widely spread are the joule and the international calorie (4.1868 J = 1 cal).

Table 2.1 Relations between different units of work and heat

Unit	J	erg	kgf-m	kcal	kW-h
1 J	1	10^7	0.101972	2.38846×10^-4	2.7778×10^-7
1 erg	10^-7	1	10.1972×10^-9	23.8846×10^-12	27.778×10^-15
1 kgf-m	9.80665	98.0665×10^6	1	2.34228×10^-3	2.72407×10^-6
1 kcal	4186.8	41.868×10^9	426.935	1	1.163×10^-3
1 kW-h	3.6×10^6	36×10^12	367098	859.845	1

Shortly after Joule's experiments, the molecular-kinetic theory was elaborated, according to which heat is the energy of the chaotic thermal motion of the microparticles of a body.

From here on, to simplify notation the thermal equivalent of work A and the mechanical equivalent of heat J will not be used in the thermodynamic equations, heat and work will be measured in the same units.