If you don't get it:
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:
0.24 kg × 75 °C × 4182 J/kg°C ~ 75kJ
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.
The general formula:
MCT=MGH
So height=(heat capacity of liquid*change in temp)/9.81
In our case (4184*70)/9.81 ~ 30,000 meters
We could be running several space habitats by now if people just weren't drinking so much tea.
Bertrand Russell looking at his teapot
Is there a site that does a variety of energy comparisons
