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Finally, using the definition of t and Form D of the First Law [I.C.12], we can construct a Conservative Form of the First Law of Thermodynamics, tt + (tv) = 0, [Equation I.C.14] which may replace the adiabatic form of the First Law in our set of principal governing equations.
The first law is often formulated by stating that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, minus the amount of work done by the system on its surroundings. Equivalently, perpetual motion machines of the first kind are impossible.