Application of First Law of Thermodynamics

Consider a system that consists of a gas enclosed by a piston in a cylinder. Suppose the system is taken quasistatically from an initial state Pi, Vi, Ti to a final state Pf, Vf, Tf. At each step the work done and heat exchanged are measured. We know that both the total work done W and the total heat transfer Q to or from the system depend on the thermodynamic path. However, the difference Q – W, is the same for all paths between the given initial and final equilibrium states, and it is equal to the change in internal energy DELTA U of the system.

U = Q – W

In  the above statement, Q is positive when heat enters the system and W is positive when work is done by the system on its surroundings.