Farwell and Stifler — Common Laboratory Experiments. 535 



Art. XLVI. — Some Variations in Ttvo Common Laboratory 

 Experiments ; by H. W. Farwell and W. W. Stifler. 



Fig. 1. 



1. A Simple Form of Hot Wire Ammeter. 



An electric current passing through a wire develops in the 

 wire heat at the rate of PR watts. If the wire is enclosed in 

 a perfect heat insulator it will of course rise in temperature 

 with the time. Ordinarily, however, it will attain a steady 

 state in a short time if conditions outside are maintained con- 

 stant, and in this steady state will lose heat to its surroundings 

 at the same rate as it is received. Suppose the wire to be sur- 

 rounded by, but not in contact with, a good heat conductor 

 with large heat capacity. This w il 

 give the same conditions as those to 

 which Newton's law of cooling may 

 be applied, provided the wire is not 

 raised to a temperature greatly differ- 

 ent from that of the surrounding heat 

 conductor. It will lose heat then at 

 a rate equal to KCTj — T ) where T 1 is 

 the temperature of the wire and T 

 is that of the heat conductor and K 

 is a constant depending on the mate- 

 rial and nature of the surface of the 

 wire. In the steady state then 



FR = JK(T\ - T ) 



where J is the mechanical equivalent 

 of heat. 



If the wire has at the temperature 

 of the surroundings a length L it will 

 have at temperature T, a length 



L + AL = L[l + a(T x - T.)] 



where a is the coefficient of expan- 

 sion of the wire. Or 



AL = La(T, - 

 pR= JKAL 



La 



T ). That is 

 AT FRLa 



That AL may be large a long wire 

 of small cross-section of a material 

 with a large coefficient of thermal 

 expansion would be necessary. 



These conditions are usually found in the apparatus used in 

 every laboratory for the measurement of Young's modulus. 



