The Principles of Thermodynamics

244 The Principles of Thermodynamics

n are the same, and equal to -P. Let us concentrate only at the end points l and n.

Therefore, there are three possibilities: i) the points l and n have a common tangent,

ii) the one at n lies above that at l, or iii) the tangent at n lies below that at l. Let us

consider possibility ii) first. Let ( f



,v

n

) be a point on the tangent at l. In other words,

the tangent at l intersects the vertical line v = v

n

at f



. Clearly, f

n

> f



. Since the

slope of the tangent at l is -P it follows that

f



− f

l

v

n

−v

l

= −P →−P(v

n

−v

l

)= f



− f

l

< f

n

− f

l

→ g

l

< g

n

(12.44)

This means that ii) represents the case when the liquid phase is more