34 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



The factor y9 is called the temperature coefficient of resistance 

 of the given metal. It is equal to the increase of resistance of 

 the metal for one degree rise in temperature expressed as a frac- 

 tional part of the resistance of the metal at o C. Its value for 

 pure metals is approximately 0.0037 P er degree centigrade. For 

 pure commercial copper wire its value is about 0.004 per degree 

 centigrade. 



It is to be remembered that equation (5) is based on the as- 

 sumption that the temperature-resistance curve is a straight line. 

 If the actual resistances of any wire or substance at o C. and 

 at t C. are substituted in equation (5) for R Q and R t , respec- 

 tively, the value of /3 may be calculated. The value of /3 so 

 calculated is called the mean temperature coefficient of resistance 

 of the given substance for the given range of temperature. 



The value of the temperature coefficient of a substance depends 

 upon the choice of the standard temperature in a way that may 

 be most easily explained by considering the thermal expansion 

 of a gas. A gas at constant pressure undergoes a certain definite 

 increment of volume for one degree rise of temperature. Thus, 

 a gas at constant pressure undergoes the same increment of volume 

 when heated from 10 C. to 1 1 C., or when heated from 50 C. 

 to 51 C., or when heated from 200 C. to 201 C. This incre- 

 ment of volume per degree rise of temperature is equal to ^|^ of 

 the volume of the gas at o C., to ^-^ of the volume of the gas 

 at i C, to 3^3- of the volume of the gas at 100 C., and so on, 

 and this fraction is the temperature coefficient of expansion of 

 the gas. In order to avoid ambiguity, the increment of volume 

 of a gas for i rise of temperature is always expressed as a frac- 

 tional part of the volume of the gas at o C., and the coefficient 

 of expansion of a gas at constant pressure is therefore equal to 

 ^^ (equals 0.00366). Similarly, the temperature coefficient ot 

 resistance of a metal should always refer to a definite standard 

 temperature, say, o C. It is interesting to note that the temper- 

 ature coefficient of resistance of most pure metals is very nearly 

 the same in value as the temperature coefficient of expansion of a 



