Page:International Library of Technology, Volume 93.djvu/48

for constant volume, the pressure changes in direct proportion to the temperature. The equation is commonly written

${\frac {pv}{T}}={\frac {p_{1}v_{1}}{T_{1}}}=R$(4)

in which $R$ is a constant. For air, the value of $R$ is .37.

Formula 4 may be applied when the quantity of gas considered is 1 pound. If some other quantity than 1 pound is taken, the formula to be used is

${\frac {pv}{T}}=GR$

or$pv=GRT$(5)

in which $G$ represents the weight of the quantity of gas, in pounds, and the other letters have the same significance as before.

39. Formula 4, Art. 38, which is true for any of the so-called permanent gases, is the broadest expression of the law of Gay-Lussac, since from it, when the pressure, volume, and temperature of a given weight of gas are known for any particular moment, the pressure, volume, or temperature can be calculated for any other case in which the other two factors are known.

40. Beginning with Mariotte's law, the several laws of gases may be recapitulated as follows:

I. The temperature remaining constant, the pressure of a given weight of a perfect gas varies inversely as its volume; or the product of the pressure and volume is a constant.

$pv=p_{1}v_{1}=$ a constant(1)

II. The pressure remaining constant, the volume of a given weight of a perfect gas varies directly as its absolute temperature.

${\frac {v}{v_{1}}}={\frac {T}{T_{1}}}$(2)

III. The volume remaining constant, the pressure of a given weight of a perfect gas varies directly as the absolute temperature.

${\frac {p}{p_{1}}}={\frac {T}{T_{1}}}$(3)