You're talking about refrigeration here. It is a unit of power generally referred to as the latent heat of fusion (look that up for more info on the subject)
The amount of heat absorbed by one (short*) ton of pure ice melting at 0°C** in twenty four hours at 14.7psi*** is 288,000 BTUs, which equates to 12000 BTUs per hour.
One BTU equals 0.293 watts.
12000 X 0.293 = 3516 w
So one ton of refrigeration is 3.516 kW/hr or 12000 BTU/hr required to make 1 ton of ice at 0°C** in 24 hours.
* A short ton is 2000 pound, a long (imperial) ton is 2240 pound, a metric ton (tonne 1000 kg) is 2240.62262 pound. So 1 long ton or metric tonne of refrigeration is almost 10% larger than 1 short ton of refrigeration.
** The importance of the 0°C is that the water/ice combination will remain at 0°C until all of the ice has melted. Immediately that has occurred, any further input of energy will raise the temperature of the water and is no longer valid in the calculation. Conversely, when undergoing cooling, the combination will also remain at 0°C until all of the water has crystallised, whereupon any further input of cooling energy will lower the temperature and is no longer valid.
*** The importance of the 14.7 psi (one atmosphere of pressure) is that when exposed to greater pressure, less heat energy is required to melt the ice.
It's not unusual to rate residential airconditioners in tonnage, and a 12000 BTU (1 ton) room airconditioner is a common size for cooling around 3000 cu/ft
Assuming a non inverter type unit, then provided the ambient is sufficient to engage the compressor (it doesn't have to be really high), a 1 Ton A/C would draw around 1.2kW.
This is lower than the 3.516 kW being discussed because we are comparing electrical energy in (1200w) to refrigeration energy out (3516w).
An 1 ton inverter AC could well be running at just 0.6kW, but it would not be delivering the full ton of cooling capacity.
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