The two conditions under which heat becomes independent of path are (t) when volume remains constant.
(it) when pressure remains constant.
(a) At constant volume: By first law of thermodynamics, ∆U = q + W or q = ∆U-W. But W = -p∆V. Hence, q - ∆U + p∆V. But as volume remains constant, ∆V = 0.
.'. qv = ∆U. But ∆U is state function. Hence, qv is state function.
(b) At constant pressure: qp = ∆U + p∆V.
But ∆U + p∆V = ∆H.
qp = ∆H. As ∆H is a state function, therefore, qp is a state function.