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# Thermodynamics/warmth mixing water and air

Question
Hi,

Maybe an odd question:
How much can 1 liter ice of -20°, cool a room of 250m2/ 30° Celsius down?
Without calculating that that room has any losses trough the walls and window.

I see a lot of selfmade buckets with bottles of ice and a fan. In my own knowledge I think that water has more density then the air and thereby accumulates more warmth/energy. But I don't even know if 1 part air of -20°C mixed with 1 part air of 30°C would become 10°C ? :§

thank you.
Michel
From Belgium ;-)

Hi Michel,

Each g of ice that melts removes 333J of heat from the surrounding air.
Thus 1 kg (1l) of ice when it melts will remove 333 kJ of heat. Air has a heat capacity of 1000 J/kg/K so 1l of ice will cool 1 kg of air by 3k. 1 kg of air = 0.833 m^3 air.
In addition the ice once melted to water will extract more heat on warming to 30 from 0 c.
Also on warming the ice from -20 to 0 c will extract heat from the air

So as an approximation each litre of ice at -20 c will cool 1 m^3 of air by 4 c.

All can be calculated accurately if required. Its a bit tedious at a weekend!

Best wishes
Kevin
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Thermodynamics

Volunteer

#### Kevin

##### Expertise

Thermodynamics, chemistry, chemical reactions, kinetics, chemical reaction safety, dust explosion technology, static electricity. General science.

##### Experience

Over 40 years experience as a practicing thermochemist in industry. Head of the fire and explosion laboratory of a major European chemical company (Ciba-Geigy). Now retired.

Organizations
Institute of Chemical Engineers. Royal Society of Chemistry.

Education/Credentials
Chartered Chemist, Member of the Royal Society of Chemistry (C.Chem MRSC). Msc Sheffield.