<Dl> <Dd> Δ U = Q − W . (\ displaystyle \ Delta U = Q-W .) </Dd> </Dl> <Dd> Δ U = Q − W . (\ displaystyle \ Delta U = Q-W .) </Dd> <P> It states that the change in the internal energy ΔU of a closed system is equal to the amount of heat Q supplied to the system, minus the amount of work W done by the system on its surroundings . An equivalent statement is that perpetual motion machines of the first kind are impossible . </P> <P> Investigations into the nature of heat and work and their relationship began with the invention of the first engines used to extract water from mines . Improvements to such engines so as to increase their efficiency and power output came first from mechanics that worked with such machines but only slowly advanced the art . Deeper investigations that placed those on a mathematical and physics basis came later . </P>

1st law of thermodynamics for a closed system undergoing a change of state
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