Hydrogen is the lightest element, so it's cable of lifting the most weight in out atmosphere (probably not the best terminology there, but you get the picture)
Would hot hydrogen (in the same sense as hot air) be able to lift even more mass? Would a higher or lower density of hydrogen in a ballon lift more? If you could have a balloon which had nothing in it (it was a vacuum inside) would that lift more than a hydrogen balloon?
Basically what are the physics to balloons and lifting?
(really not sure what to tag this, so if someone else could that'd be great)
Answer
Would hot hydrogen (in the same sense as hot air) be able to lift even more mass?
Yes. Though I suppose the fire danger goes up, and you certainly can't use a propane burner to warm it...
Would a higher or lower density of hydrogen in a ballon lift more?
Lower density always means higher buoyancy.
If you could have a balloon which had nothing in it (it was a vacuum inside) would that lift more than a hydrogen balloon?
Yes, and this has been proposed in various ways in science fiction literature. The engineering challenge is finding a away to confine the vacuum that is as light as a gas bag so that you don't loose the advantage to extra weight.
In general a volume $V$ of material of density $\rho$ immersed in a fluid of density $\rho_f$ experiences a buoyant force of
$$ F_b = gV\rho_f $$
and a weight of
$$W = -gV\rho $$
so the available lifting force is
$$ F_l = gV(\rho_f - \rho) .$$
Where the object is floating at the surface of a liquid the buoyant force is modified to reflect the volume of liquid displaced $F_b = g V_d \rho_f$ where $V_d$ is enough to cover the weight of the floating object.
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