The first law of thermodynamics, better known as Conservation of Energy, says
that you can't create energy from nothing: it prohibits perpetual motion
machines of the first type, which run and run indefinitely without consuming
fuel or any other resource. According to our modern view of physics, energy is
conserved in each individual interaction of particles. By mathematical
induction, we see that no matter how large an assemblage of particles may be, it
cannot produce energy from nothing - not without violating what we presently
believe to be the laws of physics.
This is why the US Patent Office will summarily reject your amazingly clever
proposal for an assemblage of wheels and gears that cause one spring to wind up
another as the first runs down, and so continue to do work forever, according to
your calculations. There's a fully general proof that at least one wheel must
violate (our standard model of) the laws of physics for this to happen. So
unless you can explain how one wheel violates the laws of physics, the assembly
of wheels can't do it either.
A similar argument applies to a "reactionless drive", a propulsion system that
violates Conservation of Momentum. In standard physics, momentum is conserved
for all individual particles and their interactions; by mathematical induction,
momentum is conserved for physical systems whatever their size. If you can
visualize two particles knocking into each other and always coming out with the
same total momentum that they started with, then you can see how scaling it up
from particles to a gigantic complicated collection of gears won't change
anything. Even if there's a trillion quadrillion atoms involved, 0 + 0 + ... + 0
= 0.
But Conservation of Energy, as such, cannot prohibit converting heat into work.
You can, in fact, build a sealed box that converts ice cubes and stored
electricity into warm water. It isn't even difficult. Energy cannot be created
or destroyed: The net change in energy, from transforming (ice