Heat is Path Function

Lets us consider following two cycles: 1a2b1 and la2cl and apply the first law of thermodynamics Eq (6.2) to get

Figure 6.2

(6.3)

or,

(6.4)

Subtracting Eq. (6.4) from Eq. (6.3)

(6.5)

Since, work depends on the path

(6.6)

Therefore,

(6.7)

Energy transfer as heat is not a point function, neither is it a property of the system.

Heat interaction is a path function.