Page:Elementary Text-book of Physics (Anthony, 1897).djvu/265

§ 232] the engine, or $$\frac{eBCf}{bBCc},$$ equals $$\frac{gi}{gh}\cdot$$ Now $$gh$$ represents the pressure of the gas at the temperature $$t$$ of the source, when its volume is $$Oh,$$ and $$gi$$ represents the diminution of pressure caused by a fall of temperature to $$\theta,$$ the temperature of the refrigerator, when the volume is kept constant. The efficiency of the engine is therefore $$\frac{p_{t} - p_{\theta}}{p_{t}}\cdot$$ And since the efficiency is also given by $$\frac{S - R}{S},$$ where $$S$$ and $$R$$ are the temperatures of source and refrigerator on the absolute scale, $$\frac{S - R}{S} = \frac{p_{t} - p_{\theta}}{p_{t}}$$ or $$\frac{R}{S} = \frac{p_{\theta}}{p_{t}}\cdot$$ We know, from the experiments of Gay-Lussac, that if $$t$$ and $$\theta$$ be measured on the Centigrade scale, and if $$p_{0}$$ represent the pressure of the gas at the Centigrade zero on the condition that the volume is constant, $$p_{t} = p_{0}(1 + \alpha t)$$ and $$p_{\theta} = p_{0}(1 + \alpha \theta)$$ where $$\alpha = \frac{1}{273}$$ is the coefficient of expansion. Using these values in the above equation we obtain $$\frac{R}{S} = \frac{1 + \alpha \theta}{1 + \alpha t} = \frac{273 + \theta}{273 + t}\cdot$$ If the pressure or volume of a gas, the two being interchangeable by Boyle's law, be used as a measure of its temperature, the pressure or volume and the temperature will always be directly proportional, provided the zero of temperature be taken at -273° Centigrade; this temperature is the zero of the perfect gas thermometer. From the equation just obtained it is clear that the absolute scale of temperatures is the same as the one given by the perfect gas thermometer, and that the absolute zero is the zero of the perfect gas thermometer.

No gases conform precisely to the laws of Boyle and Gay-Lussac, and consequently no gas thermometer can be constructed which will accurately indicate the absolute scale of temperatures. Nevertheless, some gases depart only slightly from the conditions of a perfect gas, and the temperature determinations given by thermometers in which such gases are employed may be converted by suitable corrections into the corresponding absolute temperatures.