It takes the same amount of energy to increase the temperature of water by ~70°C (room temp=30°C and boiling point = 100°C) as it takes to send that cup of water 30 000 meters into the air. (If I did the math right)
My math:
Boiling a cup (0.24 kg) of water from 25°C to 70°C ~45kJ (0.24kg×45°C×4182J/kg°C)
Raising 0.24 kg of water up a height 30,000 m ~ 71kJ (0.24kg × 9.8m/s^2 × 30,000 m)
So my math says raising the temp of a cup of water from room temp would be equivalent to raising it about 19 km high.
Edit: I'm a moron who can't read, boiling water from 25 to 100 °C takes:
Now if only we could figure out a way to actually do that without burning a bunch of fuel for the purpose of lifting fuel! Something something tyranny of rockets.
As with so many problems, this one can be solved with a suitably large cannon. Why you'd want to fire cups of water into the stratosphere is left as an exercise for the interested reader.
It takes the same amount of energy to increase the temperature by ~70°C as it takes to send that cup of water 30 000 meters into the air. (If I did the math right)