Page 32 - Entrophy Analysis in Thermal Engineering Systems

Birth and evolution of thermodynamics 23

However, the above proposed scale did not prevail. Using the experi-
ments of Regnault on the pressure and latent heat of saturated steam at tem-
peratures between 0°C and 230°C, Thomson found large discrepancy
between the values of temperature determined based on this hypothesis
and that of an air thermometer. In 1854, Thomson proposed a modified def-
inition for the absolute temperature scale: “the numerical measure of temperature
shall be not founded on the expansion of air at a particular pressure, but shall be simply
the mechanical equivalent of the thermal unit divided by Carnot’s function … the
formula for the action of a perfect thermo-dynamic engine expresses that the heat used
is to the heat rejected in the proportion of the temperature of the source to the temper-
ature of the refrigerator” [21]. According to this latter definition, the absolute
temperature in units of Kelvin is equal to temperature measured in Centi-
grade plus a numerical constant.

2.4 Theoretical developments
The theoretical development and formulation of the fundamental laws
of thermodynamics is primarily due to Rankine, Thomson, and Clausius. In
1849, a year after proposing a foundation for the absolute temperature scale,
Thomson extended Clapeyron’s investigation and arrived at the following
relation for the amount of work required for production of a unit of heat
evolved during the compression of air [22].
μ 1+ EtÞ
ð
W
¼ (2.11)
Q E
where W is the amount of work spent to compress the air, Q the heat
evolved by the compression, μ Carnot’s function, t the temperature, and
E the expansion coefficient of air.
Like Carnot and Clapeyron, the theoretical analysis of Thomson was
based on the combined gas laws, which he expressed in the following form.

pV ¼ p 0 V 0 1+ Etð Þ (2.12)
The functional form of μ adopted by Thomson [23] is

(2.13)
E
μ ¼ J
1+ Et
where J denotes the mechanical equivalent of a thermal unit.
In explanation of Eq. (2.13), Thomson writes “It was suggested to me by Mr
Joule, in a letter dated December 9, 1848, that the true value of μ might be inversely
at the temperatures from zero … This formula [Eq. (2.13)] is also adopted by