According to the first law of thermodynamics, the change in internal energy (∆U) of a system can be expressed as: ∆U=Q−W Where Q is the heat absorbed by the system and W is the work done by the system. For paths 1 and 2 from state A to state B, the change in internal energy is the same, regardless of the path taken: ∆U1=∆U2 Therefore, the heat absorbed and work done along the different paths follows the relationship: Q1−W1=Q2−W2 This equation signifies that the net change in energy (considering both heat and work) is equal for both paths due to the same change in internal energy from state A to state B.