Page:Elementary Text-book of Physics (Anthony, 1897).djvu/236

the pressure becomes constant for any further diminution of volume, and the gas assumes the liquid state. The less the pressure and density of the ^as, the more nearly it obeys Boyle's law.

211. Gay-Lussac's Law.—It has been stated already that gases expand as the temperature rises. The law of this expansion, called, after its discoverer, Gay-Lussac's law, is that, for each increment of temperature of one degree, every gas expands by the same constant fraction of its volume at zero. This is equivalent to saying that a gas has a constant coefficient of expansion, which is the same for all gases.

Let $V_{0},V_{t}$ represent the volumes at zero and $t$ respectively, and $\alpha$ the coefficient of expansion. Then, the pressure remaining constant, we have

$V_{t}=V_{0}(1+\alpha t).$

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If $d_{0},d_{t}$ represent the densities at the same two temperatures we have, since densities are inversely as volumes,

$d_{t}={\frac {d_{0}}{1+\alpha t}}\cdot$

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Later investigations, especially those of Regnault, show that this simple law, like the law of Boyle, is not rigorously true, though it is very nearly so for all gases and vapors which are not too near their points of saturation. The common coefficient of expansion is $\alpha =0.003666={\tfrac {1}{273}}$ very nearly.

212. Boyle's and Gay-Lussac's Laws.—From the law of Boyle we have, for a given mass of gas, if the temperature remain constant, $V_{p}p=V_{p'}p'=$ volume at pressure unity, where $V_{p},V_{p'}$ represent the volumes at pressure $p$ and $p'$ respectively.

From the law of Gay-Lussac we have, if the pressure remain constant, $V_{0}={\frac {V_{t}}{1+\alpha t}}={\frac {V_{t'}}{1+\alpha t'}}\cdot$ If the temperature and pressure both vary, we have

${\frac {V_{pt}p}{1+\alpha t}}={\frac {V_{p't}p'}{1+\alpha t'}};$

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