CORRECTION OF THERMOMETER Thermometer readings require, in general, to be corrected: (1) For change in the zero-point. (2) For the cooling of that portion of the thread not immersed in the heating medium (the emergent thread). For the most accurate work a correction is also applied for the want of uniformity of the bore of the capillary stem, generally by means of a table formed by calibration of the tube or by comparison of the individual thermometer with a standard instrument. Finally, the mercurialthermometer readings, to be comparable, should all be reduced to air-thermometer readings by means of Table VII. (Appendix). = = An approximate correction for the emergent thread may be obtained by means of the expression 8 (t − t')n, where d the co-efficient of apparent expansion of mercury in glass '000154, t the observed temperature on the thermometer, t the mean temperature of the cooled column as determined by an attached thermometer, and n = the length in degrees of the cooled column. = == In ordinary cases d *000143 gives a result nearer the truth than the actual coefficient; a useful table calculated by means of this constant is appended (Table VIII).* EXAMPLES. I. In the determination of the boiling-point of a sample of ethyl formate a thermometer is used indicating o°8 when plunged into melting ice. When the stem is entirely surrounded by vapour the reading taken is 55°. What is the corrected boiling-point? * Several other formulæ have been proposed to calculate the correction required, but neither these nor the one given above give the true correction in all cases; for moderate values of n Table VIII. is fairly true if thermometers of the ordinary type are employed. See the article Zur Korrection der Thermometerablesungen für den herausragenden Faden," by Dr. E. Rimbach, in the Zeitschrift für Instrumentenkunde, May 1890. The zero of this thermometer has risen o°.8, hence all readings must be diminished by this amount and we have 55°-0°8 = 54°2 BP required. 2. With a thermometer reading o°2 in melting ice, the BP of propionic acid is indicated as 139°2; the column is immersed in the vapour to the 70° mark and the temperature of the exposed part is 26°; what is the corrected BP? What is the corresponding H - thermometer temperature? = Correction for change of zero-point -0°*2. Correction for cooled column +1°13 for n = 139°270=69°2 (70 nearly), and t-t' = 139°2 – 26 = 113'2, while from Table VIII. for n = 70 and t-t' = = IIO and 120 the corrections are +1°10 and + 1°20 respectively. The required BP is therefore 139'2-0°2+1°13 = 140°13. From Table VII. 139.85° mercury thermr. hydrogen thermr.; hence 140°•13 = 140° (140 - 13985)° 140°*13 +0°*15 140° 28 is the corresponding hydrogenthermometer temperature. QUESTIONS. 30. The indicated temperature of the vapour of boiling methyl acetate is 57°9 when the thermometer is immersed in the vapour to the 100° mark; the same instrument reads o°5 in melting snow; what is the corrected boiling point? 31. During a fractionation of isobutyric acid 4 portions are collected (a) from 149°5 to 150°3 (6) from 150°3 to 150°9 (c) from 150°9 to 151°1 (d) 151°1 to 151°5 as indicated by a thermometer (standing at o°4 in clean melting ice), having 55° immersed in the vapour, temperature of outside column as given by a second thermometer being 27°. What are the corrected temperatures between which the four fractions pass over? 32. A sample of ethene dibromide distils over mostly between 1306 and 130°7, n = 55 and ' 11°3. What is the corrected BP of this fraction? What is the corresponding temperature on the hydrogen thermometer scale? 33. Reduce the indicated BP's given below to temperatures on the hydrogen-thermometer scale. NgO4 2I°85 (n = 22, t' = I3°5) SiCl4 58°20 (n = 0) Observed barometric heights are reduced to the height of a column of mercury at o° and at the level of the sea in latitude 45°, which would produce the same pressure. The corrections needed for this reduction are: I. Correction for temperature, due to expansion of the mercury and the material of the scale. Let m = coefficient of expansion of Hg, S = coefficient of linear expansion of the substance of the scale, h = the observed height of the barometer, and H corrected height; then H = h ( 1 + st I+mt or approximately H= h {1-(m-s)t} Hence the required correction is – (m − s)t.h. = the With a brass scale we have H = h (1−0·000162t) and with a glass scale similarly H = h (10'000157t) and the correction is -o'000157.t.h. II. Correction for height above the sea-level and latitude, obtained as follows:: If λ be the latitude, and the height expressed in metres of the place of observation above the sea-level, the length of the column of mercury which produces the standard pressure is 760'000 1'946 cos 2 λ +0000149r. mm. therefore if the observed height of the barometer be ʼn the true or reduced height H = = h x 760 760+ 1946 cos 2λ +0'000149 x If x be less than 100m. the term o'000149x may be omitted. As these corrections are small, a result approximately true is obtained by taking H = h - 1946 cos 2λ — 0'000149 x. the greatest error so made being o'04 mm. A further correction is required for the combined effects of error in adjustment of the scale and the depression of the column produced by capillarity, this correction should be given by the maker from comparison with a standard instru ment. EXAMPLE. A Fortin barometer at latitude 52° and 21m. above sea-level stands at 754'34 mm. The instrument has a brass scale, the correction for index-error and capillarity is +0 26 mm., and the temperature at time of observation is 16° C.; what is the reduced reading? Neglecting quantities beyond the second place of decimals. I. H = 754 34 (1 −0·000162. †) mm. = = 754 34-754°34 X 0'000162 X 16 mm. Hence true height of barometer, reduced to o°C, sealevel, and latitude 45° = 752.84 + 26 mm. = 753'10 mm. QUESTIONS. 34. The barometer-readings taken during a gas-analysis with a Fortin barometer, of which the maker's correction was+o'19 mm., were 754.83 mm., 756°21 mm., 757 39 mm., and 758 27 mm. The temperature of the instrument was throughout 18° C., what were the barometer-heights reduced to o°C.? = = 35. Supposing the barometer to stand at 753·82 mm. at London (Lat. 51° 30' N. T: 8°C)., Liverpool (Lat. 53° 25′ N. T 14°C.), Madeira I. (Lat. 32° 45' N. T = 20 ̊C.), and Bombay (Lat. 19° 8' N.T 19°C.); what is the true pressure of the atmosphere at each of these places? = 36. Fill in the reduced barometric heights, in column. VI. of the annexed table. All the barometers have brass scales. I. Temperature of barometer at the time of observation. II. Height of place of observation above the sea-level. III. Latitude of,, IV. Maker's correction. |