On Aug 2, 7:32 pm, byblow wrote:
On Jul 30, 6:10 pm, Keith Henson wrote:



On Jul 27, 7:04 pm, byblow wrote:

A friend of mine who's a physicist says water in a container (a tank
or bladder) takes a long time to freeze in space because convection
and conduction of heat can't occur in a vacuum. But surely water in a
tank or bladder will eventually freeze in space if shaded from the
sun, right?

Can anyone tell me how long it would take? The water is distilled, so
no worries about impurities. I'm interested in how long it would take
for large amounts to freeze, like 1,000 tonnes or more. Does the
amount of water affect how long it takes to freeze?

The question is how long does it take radiation to take away the neat
of water freezing?

Starting with 1000 tons, water is a ton per cubic meter so this would
be 1000 cubic meters, or ten by ten by ten meters as a cube.

The cube surface area would be be 600 square meters. At the freezing
point of water, the black body radiation is ~300 W/m^2 or J/s/m^2, so
the radiation from the whole thing would be around 180,000 J/s

It takes 3.34 x 10^5 J/kg to freeze water. At 1 M kg that's 3.34 x
10^11 J. Divided by the radiation rate of 1.8 x 10^5J/s, 1.86 x 10^6
seconds, 515 hours or 21.5 days.

A cubic meter of water would freeze faster. It would lose heat at 6
x
300 or 1800 j/s and, to freeze need to lose (3.34 10^5 j/kg x 1000 kg)/
(1.8 x 10^3)/s or 1.86 x 10^5 s or 2.1 days.

This doesn't take into account water cooling to freezing or the
conduction of heat out through the ice, but I expect them to be minor
corrections especially for the 1000 ton case.

Keith

Wow! I had no idea it was so complicated. Could I impose upon you to
calculate the time it would take for 50,000 tonnes of water in a
spherical bladder -- like a water balloon -- to freeze in space
(assuming it's shaded)?

Sheesh. I am sure you took geometry long after I did.

V =(4/3)*pi*r^3

50,000 /(4/3)*pi = r^3

r = 22.85 m

A = 4 * pi * r^2

A = 6563 m^2

heat loss A * 300 j-s/m^2

q = 1.969 M J-s for the whole thing.

From above, you need 3.34 * 10^11 * 50 / q

T = 8481392 s

2356 hr

98 days

Again, no correction for the conductivity of ice and the water is at
freezing to start. And I have made no effort to check the results.

Keith