How quickly does water lose heat by thermal radiation? Let's say I hold in space room-temperature water, shadowed so no radiation is emitted onto it and surrounded by vacuum (let's assume it won't boil even with the low pressure). I assume the surface area matters, so let's say the shape of water is of a thin layer.
How quickly would heat escape the water? How example going from 20° Celsius to 0° Celsius?
 A: Your question is not simple. Thus, I do not have an answer, but I’ll point you in the right direction. Here are the steps to get an estimate; hopefully I haven’t forgotten anything. Let’s be real, I probably forgot something. In any case, pay attention to your units so you don’t screw something up. 


*

*Look up the water absorptivity spectrum (=emissivity spectrum).

*Assume you have enough water the it is optically “thick” for all the emission wavelengths and multiply by the black body emission spectrum at 20 $^\circ$C.

*Assume that the black body emission spectrum is constant over your temperature range of interest, integrate over wavelength, surface area, and 4$\pi$ steradians, and obtain the total power emission rate.

*Look up the heat capacity of water and assume it is constant over your temperature range of interest (definitely not true when crossing a phase transition). So redefine your problem so you’re asking only about a 1 $^\circ$C change.

*Multiply your energy rate of change by heat capacity to solve for temperature rate of change, per volume. 

*Plug in the size of your water blob and desired temperature difference to solve for time.

*Crack open a beer and celebrate: You’ve estimated something rather silly and unphysical, but interesting nonetheless?

