An Introduction to Transformational Geometry by F.M. Eccles

By F.M. Eccles

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P. Gin ßout o i l Q out Since then, = vy comp. P. P. 100 1 + 10 Wcomp. 09 B T U n *^ o ut Non-Mechanical Work 1-16 49 NON-MECHANICAL WORK In Section 1-6 mechanical work w a s mentioned and defined by Eq. 2). Actually, Eq. 2) is the definition of reversible mechanical work. H o w e v e r , as mentioned previously the w o r k term, W, Eq. 3) is an all inclusive o n e and all types of work, reversible or otherwise, are included. W e shall define all w o r k which c a n n o t be defined by a pistoncylinder system as non-mechanical even though, in a true sense, some of the non-mechanical work p r o c e s s e s are truly mechanical.

14) m a y be applied, with some c a r e , to the non-reactive gases. F o r a monatomic gas w e get good results as long as this equation is not used at extremely low t e m p e r a t u r e s . F o r a diatomic or e v e n a polyatomic permanent gas Eq. 14) will yield fair results if used in the neighborhood of room t e m p e r a t u r e , otherwise the results may h a v e a large error. W e may summarize, concerning a perfect gas, that a perfect gas possesses the following characteristics: ( 1 ) pv = RT ( 2 ) (i) = 0 as an equation of state, o r U = U ( T ) r - (3) cy = constant specific heat.

1-13 SPECIFIC HEAT AT CONSTANT PRESSURE Let us start the discussion of the cp for a simple closed system by repeating Eq. 1) V=V(T,p) By differentiating Eq. 1 ) w e get d V = { ^ ) d T + p {^)r dP · 2 ) U p o n substituting for dV into Eq. 4), we get F o r a constant p r e s s u r e p r o c e s s , the last term vanishes. 5) is a general statement for cp. U p to this point, w e h a v e not invoked the c o n c e p t of a perfect gas. 5), therefore, is valid for any simple system. F o r a perfect gas, by virtue of the relationship given by E q .

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