INTRODUCTION. XXIU 



HEAT UNITS. 



I. If heat be measured in dynamical units its dimensions are the same as those 

 of energy, namely ML^T~^. The most common measurements, however, are 

 made in thermal units, that is, in terms of the amount of heat required to raise 

 the temperature of unit mass of water one degree of temperature at some stated 

 temperature. This method of measurement involves the unit of mass and some 

 unit of temperature ; and hence, if we denote temperature-numbers by and their 

 conversion factors by 0, the dimensional formula and conversion factor for quan- 

 tity of heat will be M0 and mO respectively. The relative amount of heat com- 

 pared with water as standard substance required to raise unit mass of different 

 substances one degree in temperature is called their specific heat, and is a simple 

 number. 



Unit volume is sometimes used instead of unit mass in the measurement of 

 heat, the units being then called thermometric units. The dimensional formula 

 is in that case changed by the substitution of volume for mass, and becomes L^0, 

 and hence the conversion factor is to be calculated from the formula Pd. 



For other physical quantities involving heat we have : — 



2. Coefficient of Expansion. — The coefficient of expansion of a substance 

 is equal to the ratio of the change of length per unit length (linear), or change 

 of volume per unit volume (voluminal) to the change of temperature. These 

 ratios are simple numbers, and the change of temperature is inversely as the mag- 

 nitude of the unit of temperature. Hence the dimensional and conversion-factor 

 formulae are ©~^ and 6~^. 



3. Conductivity, or Specific Conductance. — This is the quantity of heat 

 transmitted per unit of time per unit of surface per unit of temperature gradient. 

 The equation for conductivity is therefore, with H as quantity of heat, 



,\=T 



and the dimensional formula 7:rr^ = r-n-, which gives m/~^i ^ for conversion factor. 



0LT LI' ^ 



In thermometric units the formula becomes UT~^, which properly represents 

 diffusivity. In dynamical units H becomes ML^T~*, and the formula changes to 

 MLT~*0~^. The conversion factors obtained from these are Pf~^ and m/t~^0~^ 

 respectively. 



