PRINCIPLES OF THE MECHANICAL THEORY OF HEAT 263 



hence L'''=0.718jj/, or putting I'or jj and I tlieir numerical value, ly'=0.71S. 

 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 7 or Li=7160 metre-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=2.302G • 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, 58.63 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 58.63 + 16.88=75.51, 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 is. dependent on the magni- 

 tude of the mechanical work which is done durina' that transition. 



VII.- 



-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 is placed a piston on which a 

 pressure JJ is exerted, (Fig, 10.) This pressure J9 is that 

 which is equal to the elasticity of the saturated vapor of 

 t°C The table on a following page, contains, accord- 

 ing to Regnault's experiments, the values of j) for the 

 tenqjeratures given in the first column, jj being the pres- 

 sure which the saturated vapor of the corresi)onding 

 temperature exerts on one square metre. 



Let the water under the piston be lunv heated from 

 0° to t° ; it will thus exjiand to a magnitude which, for 

 our })resent i)ur})Ose, may remain unknown. There 

 needs for this elevation of temperature.a ((uantity of heat 

 expressed by W=^+O.OOU02//'-f0.0000003/^, if we take 

 into consideration the variableness of the specific heat 

 of water; while Vl=t would be the expi-ession, were the specific heat of water 

 taken as constant and equal to one. Hence the quantity of heat to be taken as 

 a unit is that which is rcfjuired to raise the temperatm'e of one kilogram (one 

 litre) of Avater from 0° to 1° C. During this exaltation of temperatiu-e from 0° 

 to t° no steam can be formed. 



But if we continue the sapi)ly of heat, the formation of steam commences, 

 and the steam has forthwith the elasticity of p ; it jiushes l)ack the ])iston, and 

 the space made free is continually filled with fresh vapor, until finally all the 

 water is converted into va})or. At this moment the end is attained ; the heat 

 which must l)e sup})lied to the water of t° during the formation of steam with 



