. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. PRINCIPLES OF THE MECHANICAL THEORY OF HEAT 263 hence L'''=, or putting I'or jj and I tlieir numerical value, ly'= 10333 = 7419 metre-kili)granis. But tins value is evidently too great; the true value of the total work L is, at any rate, very nearly equal to the mean between Jy and L''; hence ^ L'+L'' 6902 + 7419 ^ 'r^an . Ti L=—^—= 3 7or Li=7160metre-kilograms; and the quantity of heat necessary for the performance of this wo
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. PRINCIPLES OF THE MECHANICAL THEORY OF HEAT 263 hence L'''=, or putting I'or jj and I tlieir numerical value, ly'= 10333 = 7419 metre-kili)granis. But tins value is evidently too great; the true value of the total work L is, at any rate, very nearly equal to the mean between Jy and L''; hence ^ L'+L'' 6902 + 7419 ^ 'r^an . Ti L=—^—= 3 7or Li=7160metre-kilograms; and the quantity of heat necessary for the performance of this work is, 424 424 The exact value of ic' is found by equation (1) in § 3, if we take _?/ = 10333, and a'=2 ; theresult is then L= • 10333 • log 2=7153 , a value from Avhich that obtained above in an approximative way differs but inconsiderably. When, now, the piston has become fixed, so that no further expansion of the air is possible, units of heat are necessary to raise the temperature of the included air from 0° to 273°, whereb}^ its elasticity also is enhanced from one- half to one *^tmosphere. Thus the final condition of the air is exactly the same as in the case above considered, in which the air expanded under a constant pressure. The <piantity of heat, however, requisite for the attainment of the final condition in ipiestion is, in the last case, only + , while in the first case it was equal to 83. Thus the quantity of heat which must be supplied to a body, in order that, starting from a given condition, it shall pass over into a determinate final con- dition, is by no means an invariable magintude, but on the magni- tude of the mechanical work which is done durina' that transition. -APPLICATION OF THE MECHAIflCAL THEORY OF HEAT TO AQUEOUS VAPOKS. . Suppose that at the bottom of a hollow cylinder, of which the transverse section is one square metre, there is a litre of water at 0°, and that directly upon this i
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