THE MAGNETIC CIRCUIT ELECTROMAGNETS 47 



only rare intervals of time, with long periods allowed for cooling, 

 so that the factor of importance is the capacity for heat. 



Case (a). During a period of 1 hr., the current is passing 

 through the magnet coil for a known short interval of time, 

 and is then switched off for another known period, so that out of 

 a total of 60 min., the current flows through the coil during h 

 min. only; the temperature rise can then be caculated, as 

 previously explained, by making the assumption that the watts 



to be dissipated are not W = PR', but W h = -^* * 



This method cannot safely be used if the "on" and "off" 

 periods are long; but no general rule can be formulated in this 

 connection because the size of the magnet is an important 

 factor. 



Case (6). If used only at rare intervals of time, with long 

 periods allowed for cooling down, a magnet coil can be worked 

 at very high current densities. 'The temperature rise is then 

 determined solely by the specific heat of the copper, and its total 

 weight or volume. 



The specific heat of a substance is the number of calories re- 

 quired to raise the temperature of 1 gram, 1C. The specific 

 heat of water at ordinary temperatures being taken as unity, 

 that of copper is about 0.09. One calorie will raise 1 gram of 

 water 1C.; and since 1 calorie is equivalent to 42 X 10 6 ergs 

 (or dyne-centimeters), it follows that, to raise 1 gram of copper 

 1C. in 1 sec., work must be done at the rate of 0.09 X 42 X 10 6 

 ergs per second. But 1 watt is the rate of doing work equal to 

 10 7 ergs per second; and 1 Ib. = 453.6 grams; this leads to the 

 conclusion that the power to be expended to raise 1 Ib. of copper 

 1C. in 1 sec. is 



0.09 X 42 X 10* X 458.6 = m 



A cubic inch of copper weighs 0.32 Ib., and (171.5 X 0.32) or 

 55 watts will therefore raise the temperature of 1 cu. in. of copper 

 1C. in 1 sec. assuming no heat to be radiated or conducted 

 away from the surface of the coil. 



In this manner it is possible to calculate how long an electro- 

 magnet for occasional use can be left in circuit without damage 

 to insulation. A temperature rise of 50 to 55C. is generally 

 permissible in making calculations on the heat-capacity basis. 



