Temperature Computations
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:
II. Volume × absolute temp. + acquired temp. = heated volume.
Absolute temp. + initial temp.
In applying this formula to the foregoing example, the figures become:
I. × 460.66° + 2000° = 4.72604 volumes.
460.66 + 60°
From this last term the gauge pressure may be obtained as follows:
III. 4.72604 × 14.7 = 69.47 lbs. absolute - 14.7 lbs. atmospheric pressure = 54.77 lbs. gauge pressure; which is the theoretical pressure due to heating air in a confined space, or at constant volume from 60° to 2000° F.
By inversion of the heat formula for absolute pressure we have the formula for the acquired heat, derived from combustion at constant volume from atmospheric pressure to gauge pressure plus atmospheric pressure as derived from Example I., by which the expression
absolute pressure × absolute temp. + initial temp.
initial absolute pressure
= absolute temperature + temperature of combustion, from which the acquired temperature is obtained by subtracting the absolute temperature.
Then, for example,
69.47 × 460.66 + 60 = 2460.66, and 2460.66 - 460.66 = 2000°,
14.7
the theoretical heat of combustion. The dropping of terminal decimals makes a small decimal difference in the result in the different formulas.