Evaporative Cooler and Tonnage

Evaporative coolers are very useful in dry and hot climate. Pour a lot of water and run the fan, and get the cool moist breeze. It is a simple device and it is good for what it provides – fresh cool air. For a long time I have been thinking how to compare the evaporative cooler with a standard air conditioner.

Tonnage is one of the most commonly used words used in Air Conditioning and Refrigeration industry. It is typically used for all vapor compression refrigeration systems and for the bigger chiller based systems. For evaporative coolers, people use the amount of area that could be cooled (sqft or sq metre), amount of air pushed (CFM or CMM) or even simply the water capacity of the tank. Tonnage is typically never used for evaporative cooling systems. Even though both systems are used for cooling purpose, their performance metrics are different. Is there anyway to relate the two?

Before finding any relation, let us find what is the meaning of a tonnage. In simple words that is the latent heat of fusion of one short ton of ice. One short ton is 2000 lbs or 907kg. That means the amount of heat energy absorbed when one short ton of ice at 0 °​C becomes water at 0 °​C. The catch is that it is time bound, and the time frame given to melt this ice is 24 hours. So the unit of tonnage transforms into a unit of power.

To give some calculations, the latent heat of fusion for water is 334 KJ/kg. In English units it is 144 BTU/lb. So for 2000 lbs that would become 288000 BTUs in a time limit of 24 hours. Then the effective rate is 12000 BTU per hour. And this 12000 BTU per hour is taken as the definition of one ton of cooling.

In terms of SI units that would be 303 MJ or 84.4 KWh of heat absorbed in a day. That effectively becomes 3517W. To understand that, suppose this short ton of ice is in a thermally sealed room and we keep an electric heater of 3517W, then at 24 hours the ice would have just melted. Both BTU and MJ are the units of energy, but when the time limit of 24 hour is applied then it would become the unit of power consumed or transferred. In olden times, there used be ice houses, special buildings to store tons of ice. People used to move the ice accumulated during winter and store it inside these ice houses to use for cooling purpose in the summer. That is the real history of tonnage.

Until now, we have seen the story of fusion. But evaporative coolers use vaporization instead. The latent heat of vaporization of water is even more. It is 970.4 BTU/lb or 2260 KJ/kg. So when 1 Litre that is roughly 1 kg of water got evaporated from a wet cloth, it would have cooled the surroundings by absorbing 2260 KJ of heat from the atmosphere. Just doing some calculations we can see that 134 Litres of water could absorb the same 303 MJ of energy. As latent heat of vaporization is 6.76 times that of latent heat of fusion, then the requirement of water also gets reduced. That way 134 kg of water could provide the same cooling power as 907 kg of ice.

Now coming back to the original question. If our Evaporative Cooler consumes 134 Litres of water, then it has provided us with one ton of cooling.

Published by Anand Sivaram (आनन्दः )

twitter.com/anand_sivaram https://www.linkedin.com/in/anandsivaram/

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