Chapter 8-INTRODUCTION TO THERMODYNAMICS 



Although three modes of heat transfer- 

 conduction, radiation, and convection— are com- 

 monly recognized, we will find it easier to 

 understand heat transfer if we make a distinction 

 between conduction and radiation, on the one 

 hand, and convection, on the other. Conduction 

 and radiation may be regarded as the primary 

 modes of heat flow. Convection may best be 

 thought of as a related but basically different 

 and special kind of process which involves the 

 movement of a mass of fluid from one place to 

 another. 



CONDUCTION.— Conduction is the mode by 

 which heat flows from a hotter to a colder re- 

 gion when there is physical contact between the 

 two regions. For example, consider a metal bar 

 which is held so that one end of it is in boiling 

 water. In a very short time the end of the bar 

 which is not in the boiling water will have be- 

 come too hot to hold. We say that heat has been 

 conducted from molecule to molecule along the 

 entire length of the bar. The molecules in the 

 layer nearest the source of heat become in- 

 creasingly active as they receive thermal 

 energy. Since each layer of molecules is bound 

 to the adjacent layers by cohesive forces, the 

 motion is passed on to the next layer which, in 

 turn, sets up increased activity in the next layer. 

 The process of conduction continues as long as 

 there is a temperature difference between the 

 two ends of the bar. 



The total quantity of heat conducted depends 

 upon a number of factors. Let us consider a bar 

 of homogeneous material which is uniform in 

 cross-sectional area throughout its length. One 

 end of the bar is kept at a uniformly high tem- 

 perature, the other end. is kept at a uniformly 

 low temperature. After a steady and uniform 

 flow of heat has been established, the total quan- 

 tity of heat that will be conducted through this 

 bar depends upon the following relationships: 



1. The total quantity of heat passing through 

 the conductor in a given length of time is di- 

 rectly proportional to the cross-sectional area 

 of the conductor. The cross-sectional area is 

 measured normal to (that is, at right angles to) 

 the direction of heat flow. 



2. The total quantity of heat passing through 

 the conductor in a given length of time is pro- 

 portional to the thermal gradient— that is, to the 

 difference in temperature between the two ends 

 of the bar, divided by the length of the bar. 



3. The quantity of heat is directly propor- 

 tional to the time of heat flow. 



4. The quantity of heat depends upon the 

 thermal conductivity of the material of which 

 the bar is made. Thermal conductivity (k) is 

 different for each material. 



These relationships may be expressed by 

 the equation 



Q = kTA 



^1-^2 



where 



Q = quantity of heat, in Btu or calories 



k = coefficient of thermal conductivity 

 (characteristic of each material) 



T = time during which heat flows 



A = cross-sectional area, normal to the path 

 of heat 



t. = temperature at the hot end of the bar 

 t„ = temperature at the cold end of the bar 



L = distance between the two ends of the bar 



This equation, which is sometimes called the 

 general conduction equation , applies whether we 

 are using a metric system or a British system. 

 Consistency in the use of units is, of course, 

 vital. 



t. - t„ 

 The quantity ^5^ =- is called the thermal 



gradient or the temperature gradient. In the 

 metric CGS system, the temperature gradient is 

 expressed in degrees Celsius per centimeter of 

 length; the cross-sectional area is expressed in 

 square centimeters; and the time is expressed 

 in seconds. In British units, the temperature 

 gradient is expressed in Btu per inch (or some- 

 times per foot) of length; the cross-sectional 

 area is expressed in square feet; and the time is 

 expressed in seconds or in hours. (As may be 

 noted, some caution is required in using the 

 British units; we must know whether the tem- 

 perature gradient indicates Btu per inch or Btu 

 per foot, and we must know whether the time is 

 expressed in seconds or in hours.) 



From the general conduction equation, we 

 may infer that the coefficient of thermal 



163 



