where Δ Δ U denotes the change in the internal energy of a closed system (for which heat or work through the system boundary are possible, but matter transfer is not possible), Q denotes the quantity of energy supplied to the system as heat, and W denotes the amount of thermodynamic work done by the system on its surroundings. An equivalent statement is that perpetual motion machines of the first kind are impossible; work W done by a system on its surrounding requires that the system's internal energy U decrease or be consumed, so that the amount of internal energy lost by that work must be resupplied as heat Q by an external energy source or as work by an external machine acting on the system (so that U is recovered) to make the system work continuously.