The Mechanical Equivalent of Heat

Enthalpy. Enthalpy is the thermodynamic property of a substance defined as the sum of its internal energy plus the quantity Pv//, where P = pressure of the substance, v = its specific volume, and J = the mechanical equivalent of heat. Enthalpy is also known as total heat and heat content. 

Definition.—The Mechanical Equivalent of Heat (J) is the number of ergs of work which, if completely converted into heat, would give rise to one calorie. 

J. R. Mayer (1842) made the first calculation of the mechanical equivalent of heat by comparing the work done on expansion of air with the heat absorbed. 

The entire agreement between the values of the mechanical equivalent of heat obtained by many different methods establishes the proposition that it is independent of the process in which the conversion of work into heat occurs, and depends solely on the choice of the units of these two magnitudes. This result was first established by Joule. 

The correctness of this statement is to be inferred from the exact agreement between the values of the mechanical equivalent of heat obtained by different methods. Thus, in Joule s second series of experiments, mechanical work is directly converted into heat in the first and third series, it is indirectly transformed through the medium of electro-magnetic energy in the fourth series, the energy of an electric current is converted into heat the identity of the values of J so obtained implies a complete conversion of the initial forms of energy into heat energy. 

The calculation of Mayer was thrown into a different form by Rankine (1850), who showed that, instead of estimating the mechanical equivalent of heat from the difference of the specific heats of air, one could take Joule s value of the mechanical equivalent and the known ratio of the specific heats, and thence determine the specific heats themselves. 

In all of these systems, by definition, the specific heat capacity of water is unity. It may be noted that, by comparing the definitions used in the SI and the mks systems, the kilocalorie is equivalent to 4186.8 J/kg K. This quantity has often been referred to as the mechanical equivalent of heat J. 

The subject of physics may be characterized as that Branch of Philosophy to which men look for exact information [my emphasis] . .. the difficulty of physical investigation can be realized when we reflect that an accurate determination, for instance, of the mechanical equivalent of heat would take all the time of the most competent physicist for at least a year.93... 

It is important to bear in mind that an electrophoresis gel is an element in an electrical circuit and as such obeys the fundamental laws of electricity. Each gel has an intrinsic resistance, R, determined by the ionic strength of its buffer (R changes with time in discontinuous systems). When a voltage V is impressed across the gel, a current I flows through the gel and the external circuitry. Ohm s law relates these three quantities V = IR, where V is expressed in volts, I in amperes, and R in ohms. In addition, power P, in watts, is given by P = IV. The generation of Joule heat, H, is related to power by the mechanical equivalent of heat, 4.18 J/cal, so that H = (PI4.18) cal/sec. 

Credit for the first recognizable statement of the principle of conservation of energy (heat plus work) apparently belongs to J. Robert Mayer (Sidebar 3.2), who published such a statement in 1842. Mayer also obtained a (slightly) improved estimate, approximately 3.56 J cal-1, for the mechanical equivalent of heat. Mayer had actually submitted his first paper on the energy-conservation principle two years earlier, but his treatment of the concepts of force, momentum, work, and energy was so confused that the paper was rejected. By 1842, Mayer had sufficiently straightened out his ideas to win publication,... 

He is remembered for Joule s Law lhat describes the rale at which heal is produced by an electric current. Joule s work showed there were different kinds or energy, which can be changed into each other. He established the mechanical equivalence of heat. His work led to the law of conservation of energy. Alsu, he collaborated with William Thomson (Lord Kelvin) and verified experimentally the Joule-Thomson refrigeration effect. 

Berthelot considered the characteristic product as a measure of the mechanical work per-formed by so osplosioo. This work) csliod pc lentiel de 1 explosif or action explosive in Fr, can also be calcd from the expression QeE, where E is the mechanical equivalent of heat. This is >iven hv MuraourfRef 8.0 76) as 428... 

One of the most intriguing achievements of the 19th century was James Joule s (1818-1889) determination of the mechanical equivalent of heat and, therefore, the first law of thermodynamics. There is a study of the background to this paper, through the analysis of Joule s work in electrochemistry.88... 

From this example, it is clear that both conservation laws broke down at once. In a process involving friction, energy is not conserved, but rather disappears continually. At the same time, however, heat is not conserved, but appears continually. Rumford essentially suggested that the heat which appeared was really simply the energy which had disappeared, observable in a different form. This hypothesis was not really proved for a good many years, however, until Joule made his experiments on the mechanical equivalent of heat, showing that when a certain amount of work or mechanical energy disappears, the amount of heat... 

Equation (2.1) is the mathematical statement of the first law of thermodynamics. It is to be noted that both sides of the equation should be expressed in the same units. Thus if internal energy and mechanical work are expressed in ergs, the heat absorbed must be converted to ergs by use of the mechanical equivalent of heat,... 

Joule spoke to the Greenock Philosophical Society in the Watt Institution on 19January 1865, On Some Facts in the Science of Heat Developed Since the Time of Watt .8 The bulk of the lecture was given over to a description of Joule s own, already famous, experimental demonstration of the mechanical equivalent of heat... 

The determination of the specific heat of water at various temperatures (that at 15°C. being the standard or unit of heat, 1 g.cal., 1,12.11) is equivalent to the determination of the mechanical equivalent of heat, and the methods have been mentioned ( 12,14.11). Its variation with temperature was first established by Rowland (1879-80). 

The question at once arises as to how much work must be done to produce this much heat. This question was answered by experiments carried out in Manchester, England, between 1840 and 1878 by James Prescott Joule (1818-1889), after Count Rumford (Benjamin Thompson, 1753-1814, an American Tory) had shown in 1798 that the friction of a blunt borer in a cannon caused an increase in temperature of the cannon. Joule s work led to essentially the value now accepted for the mechanical equivalent of heat, that is, the relation between heat and work ... 

This number E is called the mechanical equivalent of heat. The correctness of the preceding proposition is subordinate to the following conditions the bodies which constitute the system are movable, but the size, form, state, and temperature of each remains invariable W represents the work of all the forces that act upon the system, including the forces that originate in bodies exterior to the system as well as forces by which the various parts of the system act upon each other. 

Value of the mechanical equivalent of heat.—Depending on this principle and on the results of various experiments whose description is beyond the scope of this work, Robert Mayer, Joule, and a great number of other physicists have occupied themselves with the determination of the value of the mechanical equivalent of heat E they found that approximately... 

Evaluation of the mechanical equivalent of heat.—It is evident that Mayer s equation (14) may also be writtoi... 

We see then that equation (14 ) gives a means of calculating the mechanical equivalent of heat it is the method which led Robert Mayer to the first evaluation ever publi ed of this quantity before Mayer, Sadi Carnot had obtained a value of the mechanical equivalent, probably by the same method. 

Multiply the two members of equation (10) by the mechanical equivalent of heat E this equality becomes... 

The first member of this equation, product of a quantily of heat by the mechanical equivalent of heat, is a quantily of the same kind as work it is therefore the same for each of the two terms composing the second member. We shall give to the first,... 

The available mechanical effect of an adiabatic change is obtained by mvUiplying the mechanical equivalent of heat by the decrease sus- tained in the internal energy of the system during this change. 

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