THERMODYNAMICS OF THE ENGINE 49



change of internal energy



A= heat supplied = H
Then | change of internal energy | B

= \T.d
}bcp

= Area AB6a

= Area AOa — area B06

The internal energy at A, reckoned from absolute zero tempera-
ture, is represented by the area AOa, and the internal energy at B,
reckoned from absolute zero temperature, is represented by the
area B06.
Thus the area subtended by the constant volume curve through
a given point on the Ty curve represents the internal energy of a
gas defined by the co-ordinates of that point.
Change of Entropy for Expansion Law PV = constant.
Let P.V" = constant.
It has already been shown that from the above equation the
new relation is obtained : —



/V \"~i T



V T

We can substitute the value for — in terms of =- in the Entropy



Equation cp ^ <p„ = G, log/-) + R log/-) . . . (32)

rp T> rn

or 9? - 95„ = C„ log,— + J--— ^ log; —

And since C„.(y — 1) = R this becomes

• ?'-^o-C„log(l)(^) . . .(34)

Entropy Temperature Diagrams for Standard Cycles.
(1) The Carnot Cycle.
This cycle, as previously pointed out, consists of two adiabatic
and two isothermal changes, as represented on the PV diagram
by the area ABCD.
50



HIGH SPEED INTERNAL COMBUSTION ENGINES




■'\ Entropy. <l>z
Fig. 26. — Entropy Tesipekattjke
DiAGKAM rOK Caknot Cyole.
Now if these changes
are considered upon the
entropy - temperature
diagram (Fig. 26), the
adiabatic lines AB and
DC will be straight lines
of constant entropy par-
allel to the temperature
axis ; the isothermal lines
BC and AD will be
straight lines of constant
temperature parallel to
the entropy axis.
