Every day across the Unites States, an army of compressors work tirelessly to keep our food cold and our living spaces comfortable. On their best days, cooling technologies fade into the background, unobtrusively making life better, it is high time we thought a bit more about the energy used to keep our nation cooled.
Before the invention of modern refrigeration technologies humans would sometimes use giant blocks of ice that had been harvested in the winter to make life more bearable. What would it look like if we had to keep our civilization cold with one giant block of ice, and how big would that block of ice end up being?
Every year the United States consumes about 3.7 trillion kilowatt hours of electricity. Of those 3.7 trillion kilowatt hours 697 billion kilowatt hours are used for some kind of cooling or refrigeration (about 19% of the national total (1)). Right now we have a nicely estimated number based on some federal data from the Energy Information Administration what we need now is a way to turn kilowatt hours into a block of ice.
Making ice is a cool process (bad pun intended) where you remove enough heat from water to cause the water to go from a liquid to a solid, this is called the heat of solidification. Water has a relatively high heat of solidification, which is helpful as our iceberg would be really massive otherwise. The size of the iceberg will depend on several assumptions, for this post we are going to do the a rather basic calculation where all of the cooling will come from melting ice into water*.
And now the math.... (feel free to skip to the BIG NUMBER section to see the size of the iceberg)
First we need to make our units as easy as possible to handle, converting kilowatt hours into joules
kWh*J/kWh =
0.697 trillion kilowatt hours * (3.6*10^18 J/trillion kilowatt hours) = 2.51*10^18 J
now to calculate the mass of the ice that would need to be melted to meet our needs
Cooling requirement/Heat of fusion of ice
2.51*10^18 Joules/(333.55 J/1 gram of water) =7.52*10^15 grams
Finally the total volume of the ice
Ice has a density of 0.92 grams/ cm^3
Mass of ice/density = Volume
7.52*10^15 grams/density of ice at 0 degrees C
7.52*10^15 grams/0.92 grams/cm^3 = 8.17*10^15 cubic centimeters
8.17*10^9 cubic meters
Volume of the empire state building =37 million cubic feet
35.3147 cubic feet/cubic meter
Empire State building =1.048 million cubic meters
8.17*10^9 cubic meters* 1 Empire State Building/1.048*10^6 cubic meters = 7800 Empire State Buildings
BIG NUMBER
8.17 billion cubic meters or the equivalent of about 7800 Empire State buildings of Ice
Hope this was interesting, if you have any questions please feel free to ask, I am attaching a screen grab of the excel file I used to do my calculations, if you would like a copy please let me know.
Sources for information are provided below.
Sources
Wikipedia "Ice storage air conditioning" big stat: 1 cubic meter of water can store 334 MJ the equivalent of 93 kWh Fun fact: the origianl definition of 1 ton of cooling, meant the total heat energy you would need to cool a 3000 square foot home in Boston (this is fun as I am Boston based)
Wikipedia "Enthalpy of fusion" 1 gram of water requires 333.55 joules to go from liquid to solid or vice versa
EIA (US Energy Information Administration) The United States uses a mix of energy sources
EIA Use of Electricity
Main stats (from 2017) Residantial energy consumption was 1.38 trillion kWh (about 37.4 % of all energy demand) for domestic consumption cooling/airconditioining composed 15.4% of energy use Refrigeration is 7.2% and freezing was 1.6%
Commercial was 1.35 trillion kWh (36.6% of all electricity demand) Refrigeration was 14% Space cooling was 10.6%
Industrial was 0.95 trillion kWh (25.7% of all American electricity demand) Facility heating, ventilation, air conditioning, and cooling is 9.5% (this is where math would get rather fuzzy) Process cooling and refrigeration 7.3%
(1) see attached excel screen grab (core data taken from EIA page Use of Electricity)
* Assumptions include but are not limited to, assuming that the energy needed to melt the ice is only coming from cooling things, and that there is no solar gain
Before the invention of modern refrigeration technologies humans would sometimes use giant blocks of ice that had been harvested in the winter to make life more bearable. What would it look like if we had to keep our civilization cold with one giant block of ice, and how big would that block of ice end up being?
Every year the United States consumes about 3.7 trillion kilowatt hours of electricity. Of those 3.7 trillion kilowatt hours 697 billion kilowatt hours are used for some kind of cooling or refrigeration (about 19% of the national total (1)). Right now we have a nicely estimated number based on some federal data from the Energy Information Administration what we need now is a way to turn kilowatt hours into a block of ice.
Making ice is a cool process (bad pun intended) where you remove enough heat from water to cause the water to go from a liquid to a solid, this is called the heat of solidification. Water has a relatively high heat of solidification, which is helpful as our iceberg would be really massive otherwise. The size of the iceberg will depend on several assumptions, for this post we are going to do the a rather basic calculation where all of the cooling will come from melting ice into water*.
And now the math.... (feel free to skip to the BIG NUMBER section to see the size of the iceberg)
First we need to make our units as easy as possible to handle, converting kilowatt hours into joules
kWh*J/kWh =
0.697 trillion kilowatt hours * (3.6*10^18 J/trillion kilowatt hours) = 2.51*10^18 J
now to calculate the mass of the ice that would need to be melted to meet our needs
Cooling requirement/Heat of fusion of ice
2.51*10^18 Joules/(333.55 J/1 gram of water) =7.52*10^15 grams
Finally the total volume of the ice
Ice has a density of 0.92 grams/ cm^3
Mass of ice/density = Volume
7.52*10^15 grams/density of ice at 0 degrees C
7.52*10^15 grams/0.92 grams/cm^3 = 8.17*10^15 cubic centimeters
8.17*10^9 cubic meters
Volume of the empire state building =37 million cubic feet
35.3147 cubic feet/cubic meter
Empire State building =1.048 million cubic meters
8.17*10^9 cubic meters* 1 Empire State Building/1.048*10^6 cubic meters = 7800 Empire State Buildings
BIG NUMBER
8.17 billion cubic meters or the equivalent of about 7800 Empire State buildings of Ice
Hope this was interesting, if you have any questions please feel free to ask, I am attaching a screen grab of the excel file I used to do my calculations, if you would like a copy please let me know.
Sources for information are provided below.
Sources
Wikipedia "Ice storage air conditioning" big stat: 1 cubic meter of water can store 334 MJ the equivalent of 93 kWh Fun fact: the origianl definition of 1 ton of cooling, meant the total heat energy you would need to cool a 3000 square foot home in Boston (this is fun as I am Boston based)
Wikipedia "Enthalpy of fusion" 1 gram of water requires 333.55 joules to go from liquid to solid or vice versa
EIA (US Energy Information Administration) The United States uses a mix of energy sources
EIA Use of Electricity
Main stats (from 2017) Residantial energy consumption was 1.38 trillion kWh (about 37.4 % of all energy demand) for domestic consumption cooling/airconditioining composed 15.4% of energy use Refrigeration is 7.2% and freezing was 1.6%
Commercial was 1.35 trillion kWh (36.6% of all electricity demand) Refrigeration was 14% Space cooling was 10.6%
Industrial was 0.95 trillion kWh (25.7% of all American electricity demand) Facility heating, ventilation, air conditioning, and cooling is 9.5% (this is where math would get rather fuzzy) Process cooling and refrigeration 7.3%
(1) see attached excel screen grab (core data taken from EIA page Use of Electricity)
* Assumptions include but are not limited to, assuming that the energy needed to melt the ice is only coming from cooling things, and that there is no solar gain
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