We have already Pv n=C

V n d P + P n v n 1 dv = 0

dp / du = – n p / u

slope = – n p / u

From there we get that slope depends on P and v for a particular n, in negative sense.

ProcessValue of nEquation of process
Isobaric Process

Isothermal Process

Isentropic Process

Isometric or isochoric Process

n = 0

n = 1

n = y

·

P = Const.

T = Const.

S = Const.

v = Const.

 

P – v and T – s Diagrams for Pv” = C

 

Similarly u1 = u2

u2 = u3 and so on

u = constant for n=∞

 

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