Although heat is a path function but heats

Heat is independent of the path under 2 conditions:

1. When the volume of the system is kept constant-

By 1st law of thermodynamics:

q = ΔU + (-w)

and -w = pΔV

Therefore , q = ΔU + pΔV

ΔV = 0 (at constant volume)

Hence, qv = ΔU + 0 = ΔU= change in internal energy

2. When the pressure of the system is kept constant –

At constant pressure, qp= ΔU + pΔV

But , ΔU + pΔV = ∆H

Therefore , qp = ∆H = change in enthalpy.