I'm referring to this brilliant post from Jedidia: "Spacecraft design for dummies" https://www.orbiter-forum.com/group.php?do=discuss&group=&discussionid=286
and particularly this part in the thermodynamics chapter:
Reading this made me wonder what would happen if a rude astronaut litters a closed bottle of water in deep space. In short, how long would it take for water to freeze? I found no explicit website yet about that and decided to try the calculation.
My hypothesis and rough calculation are as follows:
Calculation of the radiating power:
Calculation of the energy loss for a temperature change from 293°K to 273°K (20°C to 0°C):
Time to radiate 83720 J:
I know this is very basic math, but does that look roughly realistic?
To be honest, I was expecting a much longer time, at least longer than for convection/conduction cooling. I tried to freeze 1 liter of water in my freezer and it took way longer. This is possibly because the cooling process is not linear, and the temperature in the freezer is pretty high with respect to the absolute zero (minus 20°C is 253°K, after all).
and particularly this part in the thermodynamics chapter:
Many people think that space is awfully cold. Well, surprise: Space is not. [...] It is a Vacuum, and vacuum is a term we use to describe the absence (or mostly absence) of matter. Matter can be warm or cold. If there's no matter, there's nothing there to be warm, or cold, or whatever.
Reading this made me wonder what would happen if a rude astronaut litters a closed bottle of water in deep space. In short, how long would it take for water to freeze? I found no explicit website yet about that and decided to try the calculation.
My hypothesis and rough calculation are as follows:
- The sun radiation is ignored (too far from it, or in the shadow of a planet).
- The water container thermal properties are ignored, and the inner pressure is assumed standard.
- The water cooling is assumed linear.
Calculation of the radiating power:
Water volume: 1 liter.
Water is contained in a cylindrical container: radius 0.046m, height 0.15m, therefore a surface of 0.05675 m²
Water initial temperature is 293°K (20°C)
Water emissivity: 0.95
Radiating power of water at 293°K, according to Boltzman law (P = sk * T^4 * e): 397 W/m²
Radiating power of the water cylinder: 397*0.05675 = 22.53 W
Water is contained in a cylindrical container: radius 0.046m, height 0.15m, therefore a surface of 0.05675 m²
Water initial temperature is 293°K (20°C)
Water emissivity: 0.95
Radiating power of water at 293°K, according to Boltzman law (P = sk * T^4 * e): 397 W/m²
Radiating power of the water cylinder: 397*0.05675 = 22.53 W
Calculation of the energy loss for a temperature change from 293°K to 273°K (20°C to 0°C):
Water specific heat: 4186 J/kg
Water mass: 1 kg
Change in temperature: 20°K
Energy loss (specif heat * mass * temperature change): 83720 J
Water mass: 1 kg
Change in temperature: 20°K
Energy loss (specif heat * mass * temperature change): 83720 J
Time to radiate 83720 J:
83720 / 22.53 = 3716 s, or approximately 62 minutes.
I know this is very basic math, but does that look roughly realistic?
To be honest, I was expecting a much longer time, at least longer than for convection/conduction cooling. I tried to freeze 1 liter of water in my freezer and it took way longer. This is possibly because the cooling process is not linear, and the temperature in the freezer is pretty high with respect to the absolute zero (minus 20°C is 253°K, after all).