QUANTITY OF HEAT. SPECIFIC HEAT. 66 



by the containing vessel, that the final temperature of the mixture 

 is very nearly the mean of the two initial temperatures. If, for 

 example, we mix 50 grammes of water at 15 with 50 grammes at 17, 

 the resulting temperature is 16, within the limits of errors of observa- 

 tion. Then the heat given out by a gramme in cooling from 17 to 16 

 will raise another gramme from 15 to 16, or the same heat will raise 

 a given gramme from 15 to 16, and from 16 to 17. Or, if we take a 

 wider range, and have initial temperatures of and 30, the mixture 

 is exceedingly near to 15 ; or the heat required to raise 1 gramme from 

 to 15 is very nearly the same as the heat required to raise 1 gramme 

 from 15 to 30. Exact experiments, to be described later on, show that 

 the heat values of successive degrees in the rise of temperature in a 

 quantity of water are not quite the same, and we are therefore obliged 

 to specify the temperature range used. 



The most convenient range is 1 at the average laboratory tempera- 

 ture, viz., from 15 to 16, and we therefore choose the following 

 definition : 



The unit quantity of heat, or the calory, is the quantity which raises 

 1 gramme of water from 15 C. to 16 0.* 



But in rough work, sufficient for many purposes, we may neglect the 

 variation in the heat required for a rise of 1 at different parts of 

 the scale, and take the calory as simply the heat raising 1 gramme of 

 water 1 C. If m grammes of water are raised t, the heat gained 

 by the water is therefore mt calories. 



We are thus enabled to measure and express the heat given 

 up by any other substance in cooling through a definite range of 

 temperature. 



Let us suppose, for instance, that 50 grammes of iron are heated 

 to 100 and then plunged into 50 grammes of water at 15. The iron 

 and water will ultimately come to a common temperature of about 

 23 - 5. Hence, 50 gi-ammes of iron, in cooling 76'5, have given up heat 

 which raises the temperature of the 50 grammes of water 8 '5; or, 

 the iron has given up 50x8'5 = 425 calories. On the assumption (not 

 quite accurate) that each degree has the same heat value for the iron, 



each gramme of iron in cooling 1 has given up =- calory 



50 x 7oo 9 



nearly. 



Thus the iron in rising 1 requires - of the heat which will raise the 



i/ 



same mass of water 1. This is expressed by saying that the specific 

 heat of iron is -. 



Or, let us suppose that 50 grammes of lead at 100 are plunged into 

 50 grammes of water at 15. The common temperature will now be 

 about 17-5; or 50 grammes of lead in cooling 82*5 have raised 

 50 grammes of water 2*5, and have given up 50 x 2 "5 = 125 calories. 

 Assuming equality of value of each degree, 1 gramme of lead, in cooling 



* The unit of heat used by Regnault was defined as that raising 1 gramme of 

 water from to 1. Another unit is the -j-J^ part of the heat raising 1 gramme 

 of water from to 100. We may term the three calories respectively the 15, 

 the 0, and the mean calory. 



