CHAPTER IV MEASUREMENT OF TEMPERATURES W HEN the finger is inserted into a cup of warm water and then again into water formed by the melting of ice a distinct sensation is felt in each case. Many years ago scientists and philosophers attempted to explain this sensation by assuming that a substance existed which they called "caloric" whose entrance into our bodies caused the sensation of warmth and whose egress therefrom gave the sensation of cold. But heat, if a substance at all, cannot be similar to those substances with which we are familiar, since a hot body weighs no more than one which is cold. The discussion in this article is not concerned directly with FIG. 21.—A thermocouple for high heat but rather with one of its temperature measurement. effects, namely, that of change in temperature. From the above it is readily seen that temperature is an indicator of the physical effect of heat rather than a quantitative means of heat measurement. This statement is easily proved, for when we place our fingers alternately upon a piece of cold and hot iron at the temperatures mentioned for water in the opening paragraph of this discussion, the same physical sensation is experienced. Yet to transform the iron from a temperature of freezing water to that of boiling water takes far less heat than for the transfer of water under similar conditions. Fixed Points for Thermometer Calibration.-Since water is the most generally distributed substance through out nature and one of the most convenient for handling in the laboratory its freezing point and boiling point are used by common consent as two definite marks for temperature calibration. Thus in the Centigrade scale the freezing point of water is the zero point and the boiling point of water under standard conditions of atmospheric pressure is the one hundred unit point. Again, in the Fahrenheit scale the freezing point of water is the thirty-second division point and the boiling point of water the two hundred and twelfth division point. Similarly for the Reaumur scale, the freezing point of water is the zero division point and the boiling point of water, the eightieth division point. The Various Temperature Scales Employed. The Centigrade scale as described above has grown into rapid use in scientific investigation and now may be said to be universally adopted throughout the world for such practice. The Fahrenheit scale, on the other hand, has so ingrained itself into engineering practice that engineers are loath to part with it in spite of its cumbersome and unscientific divisions. In this work, then, we shall be compelled to express temperature measurement in the Fahrenheit scale. The Reaumer scale, mentioned above, finds slight application in this country and in such places where it is employed it is used for measurement in stills and breweries. All three of these scales are often for scientific purposes transformed to a socalled absolute zero which is 459.4°F. below the ordinary zero on the Fahrenheit scale. A free discussion of this absolute scale will be set forth in a discussion on thermodynamic laws of gases which will be found in another chapter. Relationship of Fahrenheit and Centigrade Values.-In order that transfers from one thermometer scale to another may be conveniently and rapidly accomplished, it now becomes necessary to develop some simple mathematical relationships whereby this may be done. Since all of the scales are graduated uniformly between the freezing and boiling point of water, their relationship may be said to be linear. In the study of analytical geometry we find that such relationships may be expressed by the straight line formula: wherein x and y represent any simultaneous temperatures expressed in different scale readings and the subscripts 1 and 2 represent definitely known points in correspondence. In order then to find a relationship between the Fahrenheit and Centi grade scale, if x represents the Fahrenheit and y the Centigrade, we find that 1 would be 32 when y1 is 0, and x2 would be 212 when y2 is 100. Consequently we derive a relationship thus: FIG. 23. The linear relationship of temperature scales. As an example, if the entering water in a boiler test is 84°F., this value is converted at once to the Centigrade scale by substituting in the formula Relationship of Fahrenheit and Reaumur Values.-A relationship between the Fahrenheit and Reaumur scales is similarly established. Thus in order to illustrate the application of this formula a temperature of 84°F. reduces to the Reaumur scale as follows: Relationship of Centigrade and Reaumur Values. To develop a relationship between the Centigrade and Reaumur scales the same reasoning is involved. Thus to convert a Centigrade reading of 28.9° into the Reaumur scale, we substitute directly In case that rapidity is necessary in the conversion of one scale to another and extreme accuracy is not required, a conversion chart is easily constructed whereby these three scales may be converted graphically from one to the other. Methods of Temperature Measurement. The ascertaining of correct temperatures is of extreme importance. Due to the wide range of temperatures that occur in practice, a number of different methods of temperature measurement are necessary. The method to be employed depends upon the range of temperature involved and often too upon the accessibility of the object whose temperature is desired. We shall describe first the approximate methods that are used in the ascertaining of temperatures. Estimation by Flame Color.-A number of years ago in the steel industry, it was found that a flame emitted definite gradations of color depending upon its temperature. In 1905 the Bureau of Standards issued a bulletin covering this point and made a statement that one may ascertain temperatures with an accuracy of 100 to 150°F. by means of eye judgment. It is stated, however, that it is impossible to ascertain temperatures above 2200°F. As this is the upper limit of furnace heating in steam engineering, we need not then be concerned with exceeding the limit. In a booklet published by the Halcomb Steel Company, 1908, the following tabulation is given to aid eye judgment in estimating temperatures: |