HEAT AND ITS MEASUREMENT

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HEAT AND ITS MEASUREMENT

The usual conception of heat is that it is a form of energy produced by the vibratory motion of the minute particles or molecules of a body. All bodies are assumed to be composed of these molecules, which are held together by mutual cohesion and yet are in a state of continual vibration. The hotter a body or the more heat added to it, the more vigorous will be the vibrations of the molecules.

As is well known, the effect of heat on a body may be to change its temperature, its volume, or its state, that is, from solid to liquid or from liquid to gaseous. Where water is melted from ice and evaporated into steam, the various changes are admirably described in the lecture by Mr. Babcock on “The Theory of Steam Making”, given in the next chapter.

The change in temperature of a body is ordinarily measured by thermometers, though for very high temperatures so-called pyrometers are used. The latter are dealt with under the heading “High Temperature Measurements” at the end of this chapter.

By reason of the uniform expansion of mercury and its great sensitiveness to heat, it is the fluid most commonly used in the construction of thermometers. In all thermometers the freezing point and the boiling point of water, under mean or average atmospheric pressure at sea level, are assumed as two fixed points, but the division of the scale between these two points varies in different countries. The freezing point is determined by the use of melting ice and for this reason is often called the melting point. There are in use three thermometer scales known as the Fahrenheit, the Centigrade or Celsius, and the Réaumur. As shown in Fig. 11, in the Fahrenheit scale, the space between the two fixed points is divided into 180 parts; the boiling point is marked 212, and the freezing point is marked 32, and zero is a temperature which, at the time this thermometer was invented, was incorrectly imagined to be the lowest temperature attainable. In the centigrade and the Réaumur scales, the distance between the two fixed points is divided into 100 and 80 parts, respectively. In each of these two scales the freezing point is marked zero, and the boiling point is marked 100 in the centigrade and 80 in the Réaumur. Each of the 180, 100 or 80 divisions in the respective thermometers is called a degree.

Table 3 and appended formulae are useful for converting from one scale to another.

In the United States the bulbs of high-grade thermometers are usually made of either Jena 58 III borosilicate thermometer glass or Jena 16 III glass, the stems being made of ordinary glass. The Jena 16 III glass is not suitable for use at temperatures much above 850 degrees Fahrenheit and the harder Jena 59 III should be used in thermometers for temperatures higher than this.

Below the boiling point, the hydrogen-gas thermometer is the almost universal standard with which mercurial thermometers may be compared, while above this point the nitrogen-gas thermometer is used. In both of these standards the change in temperature is measured by the change in pressure of a constant volume of the gas.

In graduating a mercurial thermometer for the Fahrenheit scale, ordinarily a degree is represented as 1 ⁄ 180 part of the volume of the stem between the readings at the melting point of ice and the boiling point of water. For temperatures above the latter, the scale is extended in degrees of the same volume. For very accurate work, however, the thermometer may be graduated to read true-gas-scale temperatures by comparing it with the gas thermometer and marking the temperatures at 25 or 50 degree intervals. Each degree is then 1 ⁄ 25 or 1 ⁄ 50 of the volume of the stem in each interval.

Every thermometer, especially if intended for use above the boiling point, should be suitably annealed before it is used. If this is not done, the true melting point and also the “fundamental interval”, that is, the interval between the melting and the boiling points, may change considerably. After continued use at the higher temperatures also, the melting point will change, so that the thermometer must be calibrated occasionally to insure accurate readings.

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:

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.

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.

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:

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:

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.

Latent heat is not lost, but reappears whenever the substances pass through a reverse cycle, from a gaseous to a liquid, or from a liquid to a solid state. It may, therefore, be defined as stated, as the heat which apparently disappears, or is lost to thermometric measurement, when the molecular constitution of a body is being changed. Latent heat is expended in performing the work of overcoming the molecular cohesion of the particles of the substance and in overcoming the resistance of external pressure to change of volume of the heated body. Latent heat of evaporation, therefore, may be said to consist of internal and external heat, the former being utilized in overcoming the molecular resistance of the water in changing to steam, while the latter is expended in overcoming any resistance to the increase of its volume during formation. In evaporating a pound of water at 212 degrees to steam at 212 degrees, 897.6 B. t. u. are expended as internal latent heat and 72.8 B. t. u. as external latent heat. For a more detailed description of the changes brought about in water by sensible and latent heat, the reader is again referred to the chapter on “The Theory of Steam Making”.

Ebullition —The temperature of ebullition of any liquid, or its boiling point, may be defined as the temperature which exists where the addition of heat to the liquid no longer increases its temperature, the heat added being absorbed or utilized in converting the liquid into vapor. This temperature is dependent upon the pressure under which the liquid is evaporated, being higher as the pressure is greater.

Total Heat of Evaporation —The quantity of heat required to raise a unit of any liquid from the freezing point to any given temperature, and to entirely evaporate it at that temperature, is the total heat of evaporation of the liquid for that temperature. It is the sum of the heat of the liquid and the latent heat of evaporation.

To recapitulate, the heat added to a body is divided as follows:

Where water is converted into steam, this total heat is divided as follows:

The steam tables given on pages 122 to 127 give the heat of the liquid and the total latent heat through a wide range of temperatures.

Gases —When heat is added to gases there is no internal work done; hence the total heat is that required to change the temperature plus that required to do the external work. If the gas is not allowed to expand but is preserved at constant volume, the entire heat added is that required to change the temperature only.

Linear Expansion of Substances by Heat —To find the increase in the length of a bar of any material due to an increase of temperature, multiply the number of degrees of increase in temperature by the coefficient of expansion for one degree and by the length of the bar. Where the coefficient of expansion is given for 100 degrees, as in Table 6 , the result should be divided by 100. The expansion of metals per one degree rise of temperature increases slightly as high temperatures are reached, but for all practical purposes it may be assumed to be constant for a given metal.

High Temperature Measurements —The temperatures to be dealt with in steam-boiler practice range from those of ordinary air and steam to the temperatures of burning fuel. The gases of combustion, originally at the temperature of the furnace, cool as they pass through each successive bank of tubes in the boiler, to nearly the temperature of the steam, resulting in a wide range of temperatures through which definite measurements are sometimes required.

Of the different methods devised for ascertaining these temperatures, some of the most important are as follows:

1st. Mercurial pyrometers for temperatures up to 1000 degrees Fahrenheit.

2nd. Expansion pyrometers for temperatures up to 1500 degrees Fahrenheit.

3rd. Calorimetry for temperatures up to 2000 degrees Fahrenheit.

4th. Thermo-electric pyrometers for temperatures up to 2900 degrees Fahrenheit.

5th. Melting points of metal which flow at various temperatures up to the melting point of platinum 3227 degrees Fahrenheit.

6th. Radiation pyrometers for temperatures up to 3600 degrees Fahrenheit.

7th. Optical pyrometers capable of measuring temperatures up to 12,600 degrees Fahrenheit. [6] For ordinary boiler practice however, their range is 1600 to 3600 degrees Fahrenheit.

Table 7 gives the degree of accuracy of high temperature measurements.

Mercurial Pyrometers —At atmospheric pressure mercury boils at 676 degrees Fahrenheit and even at lower temperatures the mercury in thermometers will be distilled and will collect in the upper part of the stem. Therefore, for temperatures much above 400 degrees Fahrenheit, some inert gas, such as nitrogen or carbon dioxide, must be forced under pressure into the upper part of the thermometer stem. The pressure at 600 degrees Fahrenheit is about 15 pounds, or slightly above that of the atmosphere, at 850 degrees about 70 pounds, and at 1000 degrees about 300 pounds.

Flue-gas temperatures are nearly always taken with mercurial thermometers as they are the most accurate and are easy to read and manipulate. Care must be taken that the bulb of the instrument projects into the path of the moving gases in order that the temperature may truly represent the flue gas temperature. No readings should be considered until the thermometer has been in place long enough to heat it up to the full temperature of the gases.

Expansion Pyrometers —Brass expands about 50 per cent more than iron and in both brass and iron the expansion is nearly proportional to the increase in temperature. This phenomenon is utilized in expansion pyrometers by enclosing a brass rod in an iron pipe, one end of the rod being rigidly attached to a cap at the end of the pipe, while the other is connected by a multiplying gear to a pointer moving around a graduated dial. The whole length of the expansion piece must be at a uniform temperature before a correct reading can be obtained. This fact, together with the lost motion which is likely to exist in the mechanism connected to the pointer, makes the expansion pyrometer unreliable; it should be used only when its limitations are thoroughly understood and it should be carefully calibrated. Unless the brass and iron are known to be of the same temperature, its action will be anomalous: for instance, if it be allowed to cool after being exposed to a high temperature, the needle will rise before it begins to fall. Similarly, a rise in temperature is first shown by the instrument as a fall. The explanation is that the iron, being on the outside, heats or cools more quickly than the brass.

Calorimetry —This method derives its name from the fact that the process is the same as the determination of the specific heat of a substance by the water calorimeter, except that in one case the temperature is known and the specific heat is required, while in the other the specific heat is known and the temperature is required. The temperature is found as follows:

A given weight of some substance such as iron, nickel or fire brick, is heated to the unknown temperature and then plunged into water and the rise in temperature noted.

If X = temperature to be measured, w = weight of heated body in pounds, W = weight of water in pounds, T = final temperature of water, t = difference between initial and final temperatures of water, s = known specific heat of body. Then X = T + W t ÷ w s

Any temperatures secured by this method are affected by so many sources of error that the results are very approximate.

Thermo-electric Pyrometers —When wires of two different metals are joined at one end and heated, an electromotive force will be set up between the free ends of the wires. Its amount will depend upon the composition of the wires and the difference in temperature between the two. If a delicate galvanometer of high resistance be connected to the “thermal couple”, as it is called, the deflection of the needle, after a careful calibration, will indicate the temperature very accurately.

In the thermo-electric pyrometer of Le Chatelier, the wires used are platinum and a 10 per cent alloy of platinum and rhodium, enclosed in porcelain tubes to protect them from the oxidizing influence of the furnace gases. The couple with its protecting tubes is called an “element”. The elements are made in different lengths to suit conditions.

It is not necessary for accuracy to expose the whole length of the element to the temperature to be measured, as the electromotive force depends only upon the temperature of the juncture at the closed end of the protecting tube and that of the cold end of the element. The galvanometer can be located at any convenient point, since the length of the wires leading to it simply alter the resistance of the circuit, for which allowance may be made.

The advantages of the thermo-electric pyrometer are accuracy over a wide range of temperatures, continuity of readings, and the ease with which observations can be taken. Its disadvantages are high first cost and, in some cases, extreme delicacy.

Melting Points of Metals —The approximate temperature of a furnace or flue may be determined, if so desired, by introducing certain metals of which the melting points are known. The more common metals form a series in which the respective melting points differ by 100 to 200 degrees Fahrenheit, and by using these in order, the temperature can be fixed between the melting points of some two of them. This method lacks accuracy, but it suffices for determinations where approximate readings are satisfactory.

The approximate melting points of certain metals that may be used for determinations of this nature are given in Table 8 .

Radiation Pyrometers —These are similar to thermo-electric pyrometers in that a thermo-couple is employed. The heat rays given out by the hot body fall on a concave mirror and are brought to a focus at a point at which is placed the junction of a thermo-couple. The temperature readings are obtained from an indicator similar to that used with thermo-electric pyrometers.

Optical Pyrometers —Of the optical pyrometers the Wanner is perhaps the most reliable. The principle on which this instrument is constructed is that of comparing the quantity of light emanating from the heated body with a constant source of light, in this case a two-volt osmium lamp. The lamp is placed at one end of an optical tube, while at the other an eyepiece is provided and a scale. A battery of cells furnishes the current for the lamp. On looking through the pyrometer, a circle of red light appears, divided into distinct halves of different intensities. Adjustment may be made so that the two halves appear alike and a reading is then taken from the scale. The temperatures are obtained from a table of temperatures corresponding to scale readings. For standardizing the osmium lamp, an amylacetate lamp, is provided with a stand for holding the optical tube.

Determination of Temperature from Character of Emitted Light —As a further means of determining approximately the temperature of a furnace, Table 9 , compiled by Messrs. White & Taylor, may be of service. The color at a given temperature is approximately the same for all kinds of combustibles under similar conditions.

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