Page:International Library of Technology, Volume 93.djvu/46

 constant, the increase in volume is $1⁄492$ cubic foot for each degree rise of temperature and the total increase of volume is $1⁄492$ (2,000 - 32) = 1,968 ÷ 492 = 4 cubic feet. Hence, the final volume of the gas is $$1 + 4 = 5$$ cubic feet.

36. The volume of a gas at constant pressure is, from the foregoing, proportional to its temperature on the absolute scale. For this reason, when the expansion or the contraction of a gas, due to changes in temperature, is to be calculated, only the absolute temperature is considered. For convenience, the absolute temperature is generally represented by T, while the ordinary temperature is represented by t. Throughout the remainder of this Section, the word pressure will be used to signify absolute pressure in pounds per square inch, and v the volume in cubic feet, unless otherwise stated.

37. In all that has been said, it has been supposed that the pressure of the gas is constant. If, however, the gas is restrained from expanding or contracting by keeping the volume constant, and heat is added as before, it is found that the pressure of the gas increases at a rate proportional to the rise in temperature, just as the volume did when the pressure was maintained constant, the increase in pressure for a rise of 2° being twice that for 1°.

38. The statement just made follows directly from a consideration of Mariotte's and Gay-Lussac's laws, and is a combination of the two, as may be seen from the following: Let $$v_0, p_0$$ and $$T_0$$ be the volume, pressure, and absolute temperature, respectively, of a given weight of gas under standard conditions, as, for example, 32° F. and 14.7 pounds pressure. Also, let $$v_0 $$ and $$p_0$$ be the corresponding volume and pressure at some other temperature $$T_0$$. Now compress (or expand) this gas from the pressure $$p_0$$ to $$p$$ without change of temperature. To do this, as will be shown later, heat will have to be abstracted from the gas if it is compressed, or added if it is expanded, since compressing a gas heats it, and expansion cools it. The new volume of the gas will be denoted by $$v'$$ but the temperature remains $$T_0$$.