270 PEINCIPLES OF THE MECHANICAL THEORY OF HEAT. 



Let the steam be now supposed slowly to expand, and the pressure on the piston 

 to be, at each moment, equal to the corresponding tension of the steam. During 

 this expansion both the temperature and elasticity of the steam is lowered. 



Suppose the steam to expand till its temperature has fallen 5°, and hence in 

 the case under consideration from 160° to 155°. "We will inquire now how much 

 heat must be supplied to this expanding steam, if, during the expansion in ques- 

 tion, no C(jndensation take place and the quantity of steam is to remain unaltered. 

 Bj om* table we have for 155°, 



-y/^z 0.3387 cubic metre. 



j>/=5558S.l kilograms. 



J'= 609.35 units of heat. 



The volume of the steam has therefore increased by ^^=^'—^=0. 0385 of a 

 cubic metre. The work done during this, expansion we know at least approxi- 

 mately, L=V • — — ~ whence, in our special case, we put 



L= 0.0385 • 59415.7 = 2287.5 metre-kilograms; 

 the quantity of heat requisite for this work is, 



AL^ =~ 1_ = 5.39 units of heat. 



424 424 



At the beginning of the expansion the total heat contained in the steam, 

 J^610.53, at the termination of the expansion, J' = 609.35; thus we see that 

 during the expansion, J— J', equal in units of heat to 1.18, has disappeared from 

 the steam. But this quantity of heat is not sufficient to execute the work 

 amounting to 2287.5 metre-kilograms; so that 5.39 — 1.18 = 4.21 units of heat 

 must be added from without, if the steam is to expand in the manner above 

 stated, without diminution of the quantity of steam. 



If we repeat the same process for the temperature standing in the beginning 

 at 120°, (instead of 160°, as in the preceding case,) we find, 



V=?/'-v = 0.1433. 

 ^j+p'=18767.2. 

 L=2689.3. 



A L= 6.34 units of heat. 

 ■ J — J^=1.12 units of heat. 



In this last case, therefore, an addition of 6.34 — 1.12=5.22 units of heat is 

 needed. Now, if the numerical values just calculated, make no pretension to 

 exactness, theystill serve to show that a considerable addition of heat is necessary 

 if the steam is to expand in the way specified, ivithout the occurrence of XMrtial 

 condensation. 



But since, in our expansion steam-engines, no further addition of heat ensues 

 after the shutting off of the supply of steam, it is clear that in consequence of the 

 expansion a partial condensation of steam must follow. The last part, therefore, 

 of the proposition announced by Pambour, " Steam, while expanding without 

 heat being supplied, remains saturated, and no vapor is thereby precipitated," 

 is inadmissible ; much rather would it be proper thus to modify the proposition, 

 " While steam is expanding without a supply of heat, it remains, indeed, saturated, 

 hut thcrchy is a proportional quantity of vapor precipitated." Hence, at the end 

 of the expansion the quantity of steam is less than at its commencement. 



It is through the condensation of steam that the heat must be furnished, 

 which is in deficiency, for the performance of the work of expansion. 



This important discovery, respecting the action of steam during its expansion, 

 was made almost simultaneously by Clausius and Rankine. It is clear that the 

 theory of steam-engines must, from this fact, undergo an essential modification. 



That the expansion of steam is attended by partial condensation, admits of 

 being likewise experimentally demonstrated. Into a glass balloon, (Fig. 12,) 



