302 HEAT. 



and expansion from high densities there appears to be great cooling in 

 all cases, even in that of hydrogen. And this we might expect, for with 

 the high densities the molecules are, in much larger proportion, within 

 each other's sphere of action, and work is needed to separate them.* 

 Generalisation of the Indicator Diagram for any Stresses and 



the Corresponding Strains. If we take abscissae to represent strains 

 and ordinates stresses, so measured that areas represent work done on or 

 by the quantity of matter considered, we may use the indicator diagram 

 for any corresponding stresses and strains and draw isothermals and 

 adiabatics just as with pressure and volume. 



As an illustration let us suppose we have a wire under an end pull 

 and let the relation between stretch ds per length 1 and pull P per 

 square centimetre section be given by 



where Y is Young's modulus. This implies that we are dealing with unit 

 cube of the material. 



If Y is constant for a given temperature, the isothermal for, say, 0. 

 may be represented by a straight line going through the origin as OH 

 (Fig. 171), the tangent of the slope representing Y. Now as the tempera- 

 ture rises the length under zero pull in general increases. Let a be the 

 ordinary coefficient of length expansion. Drawing OP = a, PK will 

 represent the 1 isothermal, and since Y in general decreases with rise of 

 temperature it is at a slightly less slope than OH. Similarly QL will 

 represent the 2 isothermal. 



It may be noted that these isothermals, if straight lines, will meet 

 beyond O, at a point in the lower quadrant to the left, say at T. Draw 

 TM to represent the pressure. If Young's modulus at any temperature 



is given by Y = Y ( 1 - A*) 



then Y 



TM TM 



OM + OP~OM + o 



Y OM + a 



ana -ff- = A -t- A = x-^-..- = i + 



OM " OM 

 whence OM = y. 



11 2 



With iron a is of the order -y^- 6 , while A is of the order . 4> so that 



T = OAA a compression which is never approached. But if it could be 



A Z(JO 



reached without disintegration, and if the isothermals were straight lines 

 as supposed, the interpretation would be that at this compression the 

 increase in yielding due to rise of temperature would just neutralise the 

 expansion due to the same rise of temperature. 



* For a full discussion see Callendar, "On the ThermodTnamical Correction of 

 the Gas Thermometer." Phil. Mag. v., 1903, p. 48. 



