Thermodynamic Weirdness by Don S. Lemons;

Author:Don S. Lemons; [Lemons, Don]
Language: eng
Format: epub
Tags: thermodynamics; Classical thermodynamics; laws of thermodynamics; history of thermodynamics; energy; entropy; absolute temperature; thermometers; heat; caloric; system; conservation of energy
Publisher: MIT Press
Published: 2019-02-22T00:00:00+00:00

5.3 Mechanical Equivalent of Heat

Mayer concluded his 1842 paper with a sketch of a derivation of “the quantity of heat which corresponds to a given quantity of motion or falling force.” The ratio of these two quantities is what today we call the mechanical equivalent of heat. Mayer filled out his sketch three years later (in 1845) in a self-published pamphlet. These dates and circumstances became important in the priority dispute that developed between the partisans of Mayer and those of his near contemporary, James Joule (1818–1889).

Gases have two heat capacities: a heat capacity at constant volume and a somewhat larger heat capacity at constant pressure . Mayer reasoned that the latter is larger than the former because, if allowed, a heated gas expands by pushing against the constant pressure of the atmosphere. In this way, heat may not only raise the temperature of a gas; some of the heat is also converted into the work done in expanding the volume of the gas. Therefore, the difference between these two heat capacities should be a measure of the mechanical equivalent of heat.

The heat capacity at constant volume is the ratio of the heat added to a gas having constant volume to its consequent increase in temperature . Thus, , as diagrammed in figure 5.1a. According to Mayer, extra heat is needed to achieve the same temperature increase when the gas is allowed to expand against a constant pressure . Therefore, the heat capacity at constant pressure is given by , as illustrated in figure 5.1b.

Figure 5.1 (a) . (b) . In each case, the same temperature increment is realized. The container in panel (a) is rigid, while in panel (b) its top wall changes position in order to equalize the pressure on the container.

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