. Applied thermodynamics for engineers. ACTUAL DIAGRAMIDEAL DIAGRAM Fig. 149. Art. 329. —Actual and Ideal Gas Engine Diagrams. Modified Analysis 329a. Specific Heats Variable. Suppose k=c-^bt, l — a-\-ht, R=k—l= c— a. For a differential adiabatic expansion Idt = —pdv,{a-\-bt)dt _ _ j^dv V dv ^^hdt=~-R-,t V Also, from pv = Bt, pdv + vdp = Bdt, ^ + ^ = ^; whence V p t (1) E dv V p V (a-\-E) — + a^-^ + bdt==0,V p MODIFIED ANALYSIS 203 (a -h R) logg V -\- a \og^j) -{-ht — constant,c logg V -\- a log^p -{-bt = constant, c bt - log, V + loggp + — = constant,a a e U j)}yi Qa — constant, where e is th
. Applied thermodynamics for engineers. ACTUAL DIAGRAMIDEAL DIAGRAM Fig. 149. Art. 329. —Actual and Ideal Gas Engine Diagrams. Modified Analysis 329a. Specific Heats Variable. Suppose k=c-^bt, l — a-\-ht, R=k—l= c— a. For a differential adiabatic expansion Idt = —pdv,{a-\-bt)dt _ _ j^dv V dv ^^hdt=~-R-,t V Also, from pv = Bt, pdv + vdp = Bdt, ^ + ^ = ^; whence V p t (1) E dv V p V (a-\-E) — + a^-^ + bdt==0,V p MODIFIED ANALYSIS 203 (a -h R) logg V -\- a \og^j) -{-ht — constant,c logg V -\- a log^p -{-bt = constant, c bt - log, V + loggp + — = constant,a a e U j)}yi Qa — constant, where e is the Napierian logarithmic base. Between given limits, the approximate value of n may be obtained asfollows : from Equation (1), alog,^-2-i-6(^2-^i) = -i^ a \^%p + a log, ^ -^hit,- t,) = -R log, ^, Pi ^1 ^L . alogJ^+(a + R)log/-^ = b(t,-t,). (2) Pi ^\ If we assume an equation in the form p^Vi —P2V2 to be possible, then l0g,^ = 7ll0g,^^.P2 Vi Substituting in Equation (2), (_ an + a + R) log, -^ ^ 6 (t^ - t,\ (- a?i
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