in which T is the observed temperature, t is the mean temperature of the
emergent column, n is the number of degrees of mercury column emergent,
and 0.000085 is the difference between the coefficient of expansion of
the mercury and that in the glass in the stem.
Suppose the observed temperature is 400 degrees and the thermometer is
immersed to the 200 degrees mark, so that 200 degrees of the mercury
column project into the air. The mean temperature of the emergent column
may be found by tying another thermometer on the stem with the bulb at
the middle of the emergent mercury column as in Fig. 12. Suppose this
mean temperature is 85 degrees, then
Stem correction = 0.000085 × 200 × (400 - 85) = 5.3 degrees.
As the stem is at a lower temperature than the bulb, the thermometer
will evidently read too low, so that this correction must be added to
the observed reading to find the reading corresponding to total
immersion. The corrected reading will therefore be 405.3 degrees. If
this thermometer is to be corrected in accordance with the calibrated
corrections given above, we note that a further correction of 0.5 must
be applied to the observed reading at this temperature, so that the
correct temperature is 405.3 - 0.5 = 404.8 degrees or 405 degrees.
[Illustration: Fig. 12]
[Illustration: Fig. 13]
Fig. 12 shows how a stem correction can be obtained for the case just
described.
Fig. 13 affords an opportunity for comparing the scale of a thermometer
correct for total immersion with one which will read correctly when
submerged to the 300 degrees mark, the stem being exposed at a mean
temperature of 110 degrees Fahrenheit, a temperature often prevailing
when thermometers are used for measuring temperatures in steam mains.
Absolute Zero--Experiments show that at 32 degrees Fahrenheit a perfect
gas expands 1/491.64 part of its volume if its pressure remains constant
and its temperature is increased one degree. Thus if gas at 32 degrees
Fahrenheit occupies 100 cubic feet and its temperature is increased one
degree, its volume will be increased to 100 + 100/491.64 = 100.203 cubic
feet. For a rise of two degrees the volume would be 100 + (100 × 2) /
491.64 = 100.406 cubic feet. If this rate of expansion per one degree
held good at all temperatures, and experiment shows that it does above
the freezing point, the gas, if its pressure remained the same, would
double its volume, if raised to a temperature of 32 + 491.64 = 523.64
degrees Fahrenheit, while under a diminution of temperature it would
shrink and finally disappear at a temperature of 491.64 - 32 = 459.64
degrees below zero Fahrenheit. While undoubtedly some change in the law
would take place before the lower temperature could be reached, there is
no reason why the law may not be used within the range of temperature
where it is known to hold good. From this explanation it is evident that
under a constant pressure the volume of a gas will vary as the number of
degrees between its temperature and the temperature of -459.64 degrees
Fahrenheit. To simplify the application of the law, a new thermometric
scale is constructed as follows: the point corresponding to -460 degrees
Fahrenheit, is taken as the zero point on the new scale, and the degrees
are identical in magnitude with those on the Fahrenheit scale.
Temperatures referred to this new scale are called absolute temperatures
and the point -460 degrees Fahrenheit (= -273 degrees centigrade) is
called the absolute zero. To convert any temperature Fahrenheit to
absolute temperature, add 460 degrees to the temperature on the
Fahrenheit scale: thus 54 degrees Fahrenheit will be 54 + 460 = 514
degrees absolute temperature; 113 degrees Fahrenheit will likewise be
equal to 113 + 460 = 573 degrees absolute temperature. If one pound of
gas is at a temperature of 54 degrees Fahrenheit and another pound is at
a temperature of 114 degrees Fahrenheit the respective volumes at a
given pressure would be in the ratio of 514 to 573.
[Illustration: Ninety-sixth Street Station of the New York Railways Co.,
New York City, Operating 20,000 Horse Power of Babcock & Wilcox Boilers.
This Company and its Allied Companies Operate a Total of 100,000 Horse
Power of Babcock & Wilcox Boilers]
British Thermal Unit--The quantitative measure of heat is the British
thermal unit, ordinarily written B. t. u. This is the quantity of heat
required to raise the temperature of one pound of pure water one degree
at 62 degrees Fahrenheit; that is, from 62 degrees to 63 degrees. In the
metric system this unit is the _calorie_ and is the heat necessary
to raise the temperature of one kilogram of pure water from 15 degrees
to 16 degrees centigrade. These two definitions lead to a discrepancy of
0.03 of 1 per cent, which is insignificant for engineering purposes, and
in the following the B. t. u. is taken with this discrepancy ignored.
The discrepancy is due to the fact that there is a slight difference in
the specific heat of water at 15 degrees centigrade and 62 degrees
Fahrenheit. The two units may be compared thus: