Page:Elementary Text-book of Physics (Anthony, 1897).djvu/237

§ 213] that is, if the volume of a given mass of gas be multiplied by the corresponding pressure and divided by the factor of expansion, the quotient is constant.

Let us represent this constant by $$C$$ and write $$\tfrac{1}{273}$$ for $$\alpha$$ and $$v$$ for $$V_{pt}.$$ Then we have $$\frac{vp}{273 + t} = \frac{C}{273} = R,$$ where $$R$$ is a constant.

If the temperatures of the gas be reckoned from a zero point which is 273° below the melting-point of ice, or the zero of the centigrade thermometer, we may set $$273 + t = T,$$ where $$T$$ is the temperature reckoned from the new zero, and have finally as the equation which embodies Boyle's and Gay-Lussac's laws. The temperature $$T$$ is called the temperature on the scale of the air-thermometer, and the zero from which it is reckoned is called the zero of the air-thermometer. For reasons which will subsequently appear, it is also called the absolute temperature, and its zero the absolute zero.

213. Elasticity of Gases.—It has been shown (§ 105) that the elasticity of a gas obeying Boyle's law is numerically equal to the pressure. This is the elasticity for constant temperature. But when a gas is compressed it is heated (§158); and heating a gas increases its pressure. Under ordinary conditions, therefore, the ratio of a small increase of pressure to the corresponding decrease of unit volume is greater than when the temperature is constant. It is important to consider the case when all the heat generated by the compression is retained by the gas. The elasticity is then a maximum, and is called the elasticity when no heat is allowed to enter or escape.

Let $$mn$$ (Fig. 70) be a curve representing the relation between volume and pressure for constant temperature, of which the abscissas represent volumes and the ordinates pressures. Such a curve is called an isothermal line. It is plain that to each temperature must correspond its own isothermal line. If, now, we suppose the gas to be compressed, and no heat to escape, it is plain