How much would the earth heat up if all water turned to vapour?

[Synetos]

We have 1.400.000.000 km³ water which would become 2.24E12 km³ of water vapour.
Does anyone know how much the Earth would heat up due to the greenhouse effect of all this vapour?

 

[klimatos]

We have 1.400.000.000 km³ water which would become 2.24E12 km³ of water vapour.
Does anyone know how much the Earth would heat up due to the greenhouse effect of all this vapour?

I would guess that your question cannot be answered in the form stated. First of all, the surface temperature of the Earth would have to be raised above the critical point of water (647.10K) before all liquid water could be vaporized. Secondly, your volume change assumes normal atmospheric pressure, and the addition of all that water vapor would raise the pressure immensely.

At present, the water content of the atmosphere is generally regarded as equivalent to 2.5 cm of liquid water if condensed and evenly distributed over the face of the Earth. Scholars differ on the precise absorption of water vapor, but a shortwave absorption of 64 watts per square meter and a longwave absorption of 128 watts per square meter is in the ballpark. Add another 19 shortwave and 59 longwave for clouds (liquid and solid water).

Increasing the number of vapor molecules in the atmosphere will not result in a linear increase in absorption, since little increase results once the optical depth is attained. That is, once the number is such that no significant solar radiation in the absorption spectra of vapor reaches the Earth and once the number is such that no significant terrestrial radiation in that spectra reaches the outside of the atmosphere then further increases in the amount of water vapor in the atmosphere will have little effect on atmospheric temperature.

I'll let you take it from there.