hmm.A Theory of Heat to the Steam-engineP '^'■"- 345 



the sum of all the quantities of heat received by the mass during 

 a circular process must be equivalent to the whole amount of 

 external work thereby performed. 



The following quantities of heat have been successively con- 

 sumed: — '^* 



(1) To raise the temperature of the mass M in the boiler from 

 Tg to Ti, and at the latter temperature to evaporate the part m^j 



?'>(2) To condense the part m^ at the temperature TJ^' 3'>i7fi*/Jii9 



!-:•;> '^in .mi iiiiii e5iJO-iuqii£^6! .; ic y-s ^t'^^^l ^^^ J:i4ff»«0qqu** Sff 



.(f^X TP cool the part f* from T^ to To,'oa *in bnc liroqs/ ^idi V 

 ..; > . a — /ic(T2--To). ' - ' ^^-^^'^ :?2mvlqn« ^m 



^'<4) To evaporate the part fir. at the temperature Tii''"^^^^ ?f^-4] 



Hence me total quantity of heat, .rf aw ^jA :i\ji\d 311 

 , Q=m,^.-mjr-, + Mc(T,-T,)-|^/2^Jv,-2';;tc(t-tyi • (36)^,, 



The quantities of work may be found as follows : — -f ^ 



(1) In order to find the space described by the surface of the 

 piston during the entrance of the vapour, we know that at the 

 end of that time the whole mass M + /-t occupies the space ^ fS\ "t'>^ 



J<rom this we must deduct the vicious space. As at the com- 

 mencement, this was filled by the mass //,, of which fiQ was vapo- 

 rovi§^,,ajt the temperature Tq, its volume is ta^ui viyj mJaaotib^i 



Deducting this from the foregoing magnitude, and multiplying 

 the difference by the mean pressure p'l, we have for the first 

 amount of work. . 



(2) The work expended in condensing the mass m^ is :m 



(d) 1x1 torcmg back the mass M intoihe,boiler-i ...- f.. t . 



And (4). In evaporating the part /Hq, f^ -M ^'^^H. ^lUiii^iai >i nh 



By adding these four magnitu^^^, 7\^^ql^,^f^ij\ fei;.tli^ ^.Me jYPrls; W. 

 the foUowing expression :-r-^^x^ ^^^ ^4^ x.,ifu/i«i niiUr ul ,1 S 



W=m2«2(yi.-;?2)-Ma-(;?i-yi)->oWo(;'i'-;'o)- • (37) 

 PhiL Mag. S. 4. Vol. 12. No. 80. Nov, 1856. 2 A 



