The ratio of expansion on the Fahrenheit scale is derived from the absolute temperature below the freezing-point of water (32°) to correspond with the Centigrade scale; therefore 1⁄492.66 = .0020297, the ratio of expansion from 32° for each degree rise in temperature on the Fahrenheit scale. As an example, if the temperature of any volume of air or gas at constant volume is raised, say from 60° to 2000° F., the increase in temperature will be 1940°. The ratio will be 1⁄520.66 = .0019206. Then by the formula:
Ratio × acquired temp. × initial pressure = the gauge pressure; and .0019206 × 1940° × 14.7 = 54.77 lbs.
By another formula, a convenient ratio is obtained by (absolute pressure)/(absolute temp.) or 14.7⁄520.66 = .028233; then, using the difference of temperature as before, .028233 × 1940° = 54.77 lbs. pressure.
By another formula, leaving out a small increment due to specific heat at high temperatures:
| I. | Atmospheric pressure × absolute temp. + acquired temp. | = |
| Absolute temp. + initial temp. |
absolute pressure due to the acquired temperature, from which the atmospheric pressure is deducted for the gauge pressure. Using the foregoing example, we have
| 14.7 × 460.66° + 2000° | = 69.47 - 14.7 = 54.77, the gauge pressure, |
| 460.66 + 60° |
460.66 being the absolute temperature for zero Fahrenheit.
For obtaining the volume of expansion of a gas from a given increment of heat, we have the approximate formula: