PRESSURE, TEMPERATURE, AND DENSITY. 103 



By means of (4) we may determine the volume which a 

 gas will assume at a given temperature ; or, conversely, the 

 temperature it will have under a given volume, if the volume 

 it has at any given temperature is known, the pressure re- 

 maining constant. 



EXAM PLES. 



1. If 100 cubic inches of gas at 68 F. be heated to 

 120 F., find the volume, the pressure being constant. 



Ans. 109.85 cu. ins. 



2. A mass of air at 50 F. is raised to 51 F. What is 

 the increase of its volume under a constant pressure ? 



Ans. - of its volume. 



54. Law of the Pressure, Temperature, and 

 Density of a Mass of Gas. Let ;;, p, and v be the 

 pressure, density, and volume of a mass of gas at the tem- 

 perature t, vo and po t\\e volume and density at 0. 



Then, when p remains constant, we have, from (1) of 

 Art. 53, 



v = v (1 + erf). (1) 



Now, if t remains constant while the gas is compressed 

 from v to t> , the volume varies inversely as the density 

 (Boyle"s Law) ; that is, 



v : v :: p : p, 



which in (1) gives, 



Pi =p(l + 0. (2) 



Substituting in (2) of Art. 48, we have 



p = k Po = Jcp (1 + at). (3) 



COR. 1. If p', p' be the pressure and density of the same 

 gas at a temperature t', we have 



