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As a general rule thermometers are graduated to read correctly for total immersion, that is, with bulb and stem of the thermometer at the same temperature, and they should be used in this way when compared with a standard thermometer. If the stem emerges into space either hotter or colder than that in which the bulb is placed, a "stem correction" must be applied to the observed temperature in addition to any correction that may be found in the comparison with the standard. For instance, for a particular thermometer, comparison with the standard with both fully immersed made necessary the following corrections:

Temperature Correction 40°F 0.0 100 0.0 200 0.0 300 +2.5 400 −0.5 500 −2.5

When the sign of the correction is positive (+) it must be added to the observed reading, and when the sign is a negative (-) the correction must be subtracted. The formula for the stem correction is as follows:

Stem correction = 0.000085 × n (T-t)

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 ¼91.64 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:

1 Calorie = 3.968 B. t. u. 1 B. t. u. = 0.252 Calories.

Unit Water Temperature Rise 1 B. t. u. 1 Pound 1 Degree Fahrenheit 1 Calorie 1 Kilogram 1 Degree centigrade

But 1 kilogram = 2.2046 pounds and 1 degree centigrade = 9/5 degree

Fahrenheit.

Hence 1 calorie = (2.2046 × 9/5) = 3.968 B. t. u.

The heat values in B. t. u. are ordinarily given per pound, and the heat values in calories per kilogram, in which case the B. t. u. per pound are approximately equivalent to 9/5 the calories per kilogram.

As determined by Joule, heat energy has a certain definite relation to work, one British thermal unit being equivalent from his determinations to 772 foot pounds. Rowland, a later investigator, found that 778 foot pounds were a more exact equivalent. Still later investigations indicate that the correct value for a B. t. u. is 777.52 foot pounds or approximately 778. The relation of heat energy to work as determined is a demonstration of the first law of thermo-dynamics, namely, that heat and mechanical energy are mutually convertible in the ratio of 778 foot pounds for one British thermal unit. This law, algebraically expressed, is W = JH; W being the work done in foot pounds, H being the heat in B. t. u., and J being Joules equivalent. Thus 1000 B. t. u.'s would be capable of doing 1000 × 778 = 778000 foot pounds of work.

Specific Heat—The specific heat of a substance is the quantity of heat expressed in thermal units required to raise or lower the temperature of a unit weight of any substance at a given temperature one degree. This quantity will vary for different substances For example, it requires about 16 B. t. u. to raise the temperature of one pound of ice 32 degrees or 0.5 B. t. u. to raise it one degree, while it requires approximately 180 B. t. u. to raise the temperature of one pound of water 180 degrees or one B. t. u. for one degree.

If then, a pound of water be considered as a standard, the ratio of the amount of heat required to raise a similar unit of any other substance one degree, to the amount required to raise a pound of water one degree is known as the specific heat of that substance. Thus since one pound of water required one B. t. u. to raise its temperature one degree, and one pound of ice requires about 0.5 degrees to raise its temperature one degree, the ratio is 0.5 which is the specific heat of ice. To be exact, the specific heat of ice is 0.504, hence 32 degrees × 0.504 = 16.128 B. t. u. would be required to raise the temperature of one pound of ice from 0 to 32 degrees. For solids, at ordinary temperatures, the specific heat may be considered a constant for each individual substance, although it is variable for high temperatures. In the case of gases a distinction must be made between specific heat at constant volume, and at constant pressure.

Where specific heat is stated alone, specific heat at ordinary temperature is implied, and mean specific heat refers to the average value of this quantity between the temperatures named.

The specific heat of a mixture of gases is obtained by multiplying the specific heat of each constituent gas by the percentage by weight of that gas in the mixture, and dividing the sum of the products by 100. The specific heat of a gas whose composition by weight is CO_{2}, 13 per cent; CO, 0.4 per cent; O, 8 per cent; N, 78.6 per cent, is found as follows:

CO_{2} : 13 × 0.217 = 2.821 CO : 0.4 × 0.2479 = 0.09916 O : 8 × 0.2175 = 1.74000 N : 78.6 × 0.2438 = 19.16268———— 100.0 23.82284

and 23.8228 ÷ 100 = 0.238 = specific heat of the gas.

The specific heats of various solids, liquids and gases are given in

Table 4.

Sensible Heat—The heat utilized in raising the temperature of a body, as that in raising the temperature of water from 32 degrees up to the boiling point, is termed sensible heat. In the case of water, the sensible heat required to raise its temperature from the freezing point to the boiling point corresponding to the pressure under which ebullition occurs, is termed the heat of the liquid.

Latent Heat—Latent heat is the heat which apparently disappears in producing some change in the condition of a body without increasing its temperature If heat be added to ice at freezing temperature, the ice will melt but its temperature will not be raised. The heat so utilized in changing the condition of the ice is the latent heat and in this particular case is known as the latent heat of fusion. If heat be added to water at 212 degrees under atmospheric pressure, the water will not become hotter but will be evaporated into steam, the temperature of which will also be 212 degrees. The heat so utilized is called the latent heat of evaporation and is the heat which apparently disappears in causing the substance to pass from a liquid to a gaseous state.