John C. Georgian1 Washington university
St. Louis, Missouri
I I
The MKS Temperature
I
T h e writer has recently proposed a temperature scale2-&to fit into the MKS system of units. This scale is based on the ideal gas law rather than on the properties of water, and is determined from the universal gas law by setting the soxalled universal gas constant R = 1.0. The equation of state of the ideal gas then becomes
PV=
(1)
T
where P is the volume of the gas in cubic meters per kmole, P is the pressure in newtons per square meter, and T is the absolute temperature in j per kmole. The scale for this temperature is found from the latest values of the fundamental constants given by NASNCR6as: POP. = To = 2,271,134 328 j/kmole for ideal gas at
*
0°C and Po
-
the student will see that specific heat defined as:
and entropy defined as
where dq is in j/kg and T and dT in j/kmole, are dimensionless quantities. It also can be seen that Boltzmann's constant, k = 1/N is now only the reciprocal of the Avogadro Number N. Its value and units will be k = 1.6604 X kilomole5in theMKS system. The ideal gas relations between specific heat at constant pressure and volume become
0.
For convenience, the conversion factor from the Celsius scale to the MKS scale is given as:
and the specific heat at constant pressure is
I T or K = 8,314.3 j/kmole
The MKS temperature unit is a small quantity when compared to the Celsius or Kelvin unit temperature. Accordingly, the MKS thermometer should be marked in units of lo4 j/kmole and the intervals on the MKS scale mercury thermometer will be only 1/0.83143 larger than the present Celsius scale. The adoption of this MKS temperature scale has several possible pedagogical advantages. First, the gas law becomes:
and:at constant volume
A short table of specific heats at constant pressure to use with MKS system of units and temperature scale has been computed from "Tables of Thermodynamic and Transport Properties."6 Specific Heat c, a t 1 Atmosphere and 241.11 ilkmole Temperature (290°K)
where v = meterS/kg, M is the molecular mass number (molecular weight) of the gas, and T is the MKS temperature. Hence the so-called gas constants, R, for various gases are seen to be only the reciprocal of the molecular mass number of the particular gas. I n addition, it is clearly evident that temperature has the units of specific energy, that is, meter2/sec2. Therefore in dimensional analysis, temperature will not be given a separate dimension. By understanding the proper units of temperature,
' Now on leave at the Instituto Teonol6gico de Aeron&uticn, University of Michigan AID Program, SBo Jose dos Crtmpos, S.P., Brazil. J. C., Nature, 201, 695 (1964). GEORGIAN, Nature, 203, 1158 (1964). GEORGIAN, J. C.,(Disc~~ssion) ' GEORGIAN, J. C., (Di~cus~ion)Natwe, 207,1285 (1965). NAS-NCR Committee on Fundamental Constants, Technical News Bulletin, National Bureau of Standards, USA 47, 175, Oct., 1963. 414
/
Journal o f Chemicol Education
Fluid Air Argon Hydrogen Nitrogen Oxygen Steam Carbon dioxide Carbon monoxide Water
X 10'
CP
0.1210 0.0627 1.717 0.1252 0.1105 0.2405 (r = 1.3) 0.1014 0.1253 0.5033
The author has had made for student laboratory use a series of laboratory thermometers using units of lo4 j per kmole as a scale. There was only a nominal surcharge for these thermometers, and with wide adoption of the scale the prices would be the same as present Celsius thermometers. For use with thermocouples, all that would be required would be the printing of new conversion tables. HILSENRATA, J., ET IL., "Tables of Thermodynamic and Transport Properties," Pergamon Press, London, 1960.
