218 THE REALITIES OF MODERN SCIENCE 



We may deal always with the same number of mole- 

 cules, whatever the substance may be, by taking 1 

 mole of it as explained on page 85. The quantity 



Nw is then independent of the substance. Hence for 



2 

 1 mole let us write 5 Nw=R where R is constant. 1 



o 



Hence PV=RT (2) 



This equation gives the relation between the three 

 variables of pressure, volume, and temperature which 

 determine the " state" of a gas. For example suppose 



the temperature is main- 

 tained constant at a value 

 represented by T, then the 

 points corresponding to all 

 the possible pairs of values 

 may be represented by a 

 hyperbolic curve like that 



" v marked PV=RT in Figure 

 23. If the temperature is 



increased to TI the values of P and V will lie on a new 

 hyperbola like that marked PV=RTi. These curves 

 are called isothermals. 



In developing equation (2) we tacitly assumed that 

 the volume actually occupied by the molecules is 

 small as compared to the volume V in which they are 



1 The numerical value of R may be found from the following 

 data : Under standard conditions of pressure and temperature, 

 namely 76 cm. of mercury and C., the volume of 2.016 gm., that 

 is 1 mole, of hydrogen is 22,410 c. c. Since the density of mercury is 

 13.6 and g is 980, the pressure in dynes of a column 76 cm. high is 

 13.6X76X980 or 1.013X10 6 dynes per sq. cm. The temperature 

 T is 273. Substituting these values of P, 7, and T in equation (2) 

 gives R as 83.2 X 10 6 ergs per degree. 



