Chapter 8-INTRODUCTION TO THERMODYNAMICS 



One is the general conduction equation 



Q = kTA 



4-^2 



where, as we have seen, Q may be expressed 

 in calories or in Btu. In this example, we are 

 using the metric CGS system and must therefore 

 express ^in calories. The second equation we 

 will use gives us a second way of calculating 

 Q— that is, by determining the amount of heat 

 absorbed by the circulating water. Thus, 



Q = mass of water x temperature change 

 of water x specific heat of water 



Substituting some of our known values in 

 this second equation, we find that 



Q = (1300) (10) (1) = 13,000 calories 



Using this value of Q and substituting other 

 known values in the general conduction equation, 

 we find that 



13,000 = k (360) (20) ( 



80 - 60 ) 



10 



= k (360) (20) (2) 

 = 14,400 k 

 0.9 = k 



It should be noted that the general conduction 

 equation applies only when there is a steady- 

 state thermal gradient— that is, after a uniform 

 flow of heat has been established. It should be 

 noted also that k_ varies slightly as a function of 

 temperature, although for many purposes the 

 rise in }^that goes with a rise in temperature 

 is so slight that it can safely be disregarded. 



In considering the experimental determina- 

 tion of thermal conductivity, why do we include 

 "specific heat of water = 1.00" as one of the 

 known data? What is specific heat, and what is 

 its utility? Specific heat (also called heat capac- 

 ity or specific heat capacity) is, like thermal 

 conductivity, a thermal property of matter that 

 must be determined experimentally for each 

 substance. In general, we may say that specific 

 heat is the property of matter that explains why 

 the addition of equal quantities of heat to two 

 different substances will not necessarily produce 

 the same temperature rise in the two substances. 

 We may define the specific heatof any substance 



as the quantity of heat required to raise the 

 temperature of unit mass of that substance 1 

 degree. ^ In the metric CGS system, specific 

 heat is expressed in calories per gram per 

 degree Celsius; in the metric MKS system, it 

 is expressed in kilocalories per kilogram per 

 degree Celsius; and in British systems, it is 

 expressed in Btu per pound per degree Fahren- 

 heit. The specific heat of water is 1.00 in any 

 system, and the numerical value of specific 

 heat for any given substance is the same in all 

 systems (although the units are, of course, dif- 

 ferent). 



Specific heat is determined experimentally 

 by laboratory procedures which are extremely 

 complex and difficult in practice, although 

 basically simple in theory. One of the common- 

 est methods of determining specific heat is 

 known as the method of mixtures. In this pro- 

 cedure, a known mass of finely divided metal is 

 heated and then mixed with a known mass of 

 water. The temperatures of the metal before 

 mixing, of the water before mixing, and of the 

 mixture just as it reaches thermal equilibrium 

 are measured. Then, on the simple premise that 

 the heat lost by one substance must be gained 

 by the other substance, the specific heat of the 

 metal can be found by using the equation 



m^c^ (tl -*3^ = '"2^2^*3- V 



where 



m- = mass of metal 



m„ = mass of water 



c^ - specific heat of metal 



c„ = specific heat of water (known to be 1.00) 



t- . temperature of metal before mixing 



t„ = temperature of water before mixing 



t„ = temperature at which water and metal 

 reach thermal equilibrium 



Specific heat as defined here should not be confused 

 with the relatively useless concept of specific heat 

 ratio , by which the heat capacity of each substance is 

 compared to the heat capacity of water (taken as 1.00). 

 The specific heat ratio is, obviously, a pure number 

 without units. 



165 



