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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
Water boils at 100°C
God I'm stupid. I misread what you wrote as raising water to 70°, not raising water by 70°, without even thinking that that's not how you make tea. Fixed my math, and the numbers now check out.
Actshually, that is how you make green tea
In the ISA atmosphere model, the tropopause starts at an altitude of 11 km. So you might be able to say that 19 km counts as 'stratosphere'.
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