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How much energy needed to heat ocean
How many BTUs to heat ocean
It takes 1 BTU to raise 1 pound of water by 1F at sea level

To heat the ocean by 1F...
... using 1 dimensional math and internet-derived numbers:

.... 332.5 million cubic kilometer of water in the ocean x 1.1 trillion gallons per cubic kilometer x 8.344 lbs per gallon = ?
332.5 million x 1.1 trillion x 8.3444 = 3051 million trillion lbs of water
... requiring 33.5 x 106 (million) x 1.1 x 1012 (trillion) x 8.344 BTUs 
How much is a million trillion? Add the exponents so 106 + 1012 = 1018 ... a quintillion. Eighteen zeros. Resource
-Result => 332.5 x 1.1 x 8.344 x 1018 (quintillion)
Answer = 3051 quintillion BTU to raise temperature of ocean 1F using 1-dimensional math without including variables.
-Compare 3051 quintillion BTU with standard 40 gallon gas water heater
3051 quintillion divided by 40,000 BTU water heater = 76 quadrillion water heaters, requiring a billion years of manufacturing at today's production rates, plus shipping.

-Compare 3051 quintillion BTU with total human BTU consumption:
A quintillion is 1000 times larger than a quadrillion: 1018 (quintillion with 18 zeros) compared with 1015 (quadrillion with 15 zeros).
It is estimated that humans in the world consume 500-900 quadrillion BTU per year.... for simplicity, let's round up and say that humans consume 1 quadrillion BTU ...  that's per year.

Human consumption per year = almost 1 quintillion BTU. But heating ocean by 1F takes 3051 quintillion BTU.
It would take more than 3051 years of world's BTU consumption, burning at 100% efficiency, to heat the ocean 1F, except efficiency of ordinary 40 gallon water heater is 61%, with the wasted 39% going up the flue pipe into the atmosphere, releasing NO SO CO CO2 and acidic water vapor ... all of which are harmful to the world as we have known it .... thus creating a new future.  Resource: How much does it cost to run gas water heater

However, the temperature of the ocean is not 1F. The average ocean temperature is 62.6F and rising, and the sun is sustaining this temperature year round, and keeping it at that temperature despite continual heat loss into the atmosphere ... requiring amounts of energy each day that far exceed the calculations shown here and outstrip Earth's total oil and gas resources.
Dying coral reefs.
The world's coral reefs are dying because of a 2F rise in ocean temperature.
This implies that at least 6100 quintillion more BTUs are being continually added to the ocean, just like a water heater burner raising temperature inside the tank.
A typical residential water heater burner is applying 40,000 BTU to the water, but it takes a while for 40 gallons of water to get hotter. This implis that the amount of BTUs being added to ocean warming is larger than the calculations shown on this page. So like a water heater, the burner is ON and the ocean is getting warmer.
A ≠ B The ocean-heating BTU calculations above do not factor two things:
1) Heat loss into the atmosphere: the sun does not heat the atmosphere, instead the atmosphere is heated by the surface of the earth. So, just like a cup of coffee gets cold, the ocean likewise loses heat very quickly into the air. Water heaters have standby loss as heat stored inside tank is lost to surrounding air. Heat loss into the atmosphere is a major factor not included into the numbers on this page.
2) Time: the energy must be applied continuously over time, like a kettle brewing on the stove. Thermodynamics is measured over time, so a correct calculation would have to factor in a period of time such as per day or per year. For example human consumption is estimated to be 1 quintillion BTU per year. But the calculation for raising ocean temperature by 1 does not include time period.
When the ocean is heated. the heating must be sustained over time to make up for heat loss into the atmosphere, especially on cloudy days and night time.
So how much energy is actually needed to sustain the temperature rise of the ocean?
That answer is beyond the simple 2-dimensional math in this analysis, and would have to consider complex variables such as seasonal change, effect of currents, cloud cover, latitude etc.

Large image
The atmosphere is an insulation blanket that keeps heat from escaping, and stops too much solar heat from entering.

For example, the Moon has no atmosphere.
Day temperatures are estimated at 212 F
Night temperatures are -343F
Yielding 555 degree temperature differential each day
Estimated average temperature on the moon -65F, while Earth has average temperature 60+F
A difference of 115F in average temperature between Earth and Moon despite both being same distance from sun.
Earth without atmosphere would presumably have same temperatures as moon.
Except earth has average temperature of 61F
Indicating that the atmosphere (air) is an effective insulator...

The Earth's atmosphere is 60-300 miles thick, but the majority of the insulating atmosphere is 10 miles thick ... a distance you can drive in a few minutes...
The atmosphere is a thin haze of air that surrounds the 7917.5 mile diameter of our tiny mud and nickel ball that is spinning and spiraling along with the sun as it races though the universe.
How lucky we are to have an atmosphere to moderate temperatures of the sun.
Without the atmosphere, the ocean temperatures would drop to average temperature of moon, -65F, and become a disappearing block of ice burned away in the day and refroze at night until the molecules are blown away into space by the solar wind.
R =
Insulatiing value of atmosphere:
The construction industry uses an R rating based on the science of thermodynamics, or the loss of thermal energy over time.
To the construction industry, air is the enemy from which you protect yourself to stay comfortable year round.
The R rating applies to different materials, with air ranked lowest with R value of 1 or 1.44 for small dead air spaces between walls.
The story of air is more complicated since many insulating materials require cellular structures that contain vast numbers of small air spaces to achieve their full insulating potential, such as fiberglass insulation. If the air spaces in fiberglass insulation collapse, the insulation value drops.

In the phsyical world of Earth, air is the insulator that makes the construction industry possible, suggesting that self-regulating industry and expert applications should be viewed as an evolving target requiring periodic renewal.
For example, the water heating industry added more insulation to their tank heaters to meet DOE energy standards in April 2015. This followed decades of industry claims that water heaters had enough insulation despite simple thermometer test that proved otherwise. Tape thermometer covered with insulation to side of water heater and check before and after temperatures reveals heat loss. There's even a name for it: standy loss.

No matter the fine points of economic promotion, thicker insulation means less loss of energy. So 10 miles of atmosphere is better than 5 miles, explaining why there is snow on the mountain while it's warm in the valley.
So what is R value of 10 miles of air?
According to one source, air has R value of 1.00 per 1/2" to 4" of dead air space inside a wall.
10 miles of air is 600,000+ inches, so does the atmosphere have R value of 150,000 ?
Again there are too many variables for the simple one-dimensional math presented here, but to reach some level of understanding, look at the numbers: average temperature of Earth is 115 higher than average temperature of the Moon, and the Moon has no atmosphere while the Earth does, so the insulating value of the air in the atmosphere must be significant.

Here is a link if you want to start the calculation and consider the variables:
http://legacy.jefferson.kctcs.edu/kteam/ph171/chapter5/ch5f.htm
? Questions to ask:
If more CO2 and CH4 are being added to the atmosphere, are these molecules displacing other molecules, or is the atmosphere going to get higher than 10 miles?
If warm air expands, and the atmosphere extends higher than 10-300 miles, will the expanded atmosphere hold in more heat, or will the very top be blown away as molecules extend beyond the protective magnetic field?
Would some molecules be more likely to be blown away than others?
If so, what will be depleted? O2 or N or what?
What affect will breathing a higher percentage of CO2 and CH4 have on living things?
Will new lung diseases arise, or will it affect our cognition? How will our species adapt of evolve to meet the changes?

Accepted science shows that there were previous periods of warming and cooling on Earth.
Was the atmosphere thinner or thicker? Was the magnetic field protecting the earth stronger or weaker? Was intensity of the sun different? Was the atmosphere different? Were the causes different for each event?
Folks who deny that todays warmer temperatures are caused by increased carbon in the atmosphere often rely on previously accepted science of warming and cooling periods on Earth to discredit the more recent science that shows carbon dioxide increases insulation factor of atmosphere. Is the tactic of using older science to discredit newer science an acceptable practice when those who use this tactic are not scientists?
Is discrediting science a useful strategy when every technology from electricity to chemical refining to automobile tires is based on science?
Should only a few people be aware of science, and the rest be made ignorant as a means of human control? Or is this a natural evolution of human society when under stress about possible future outcomes. Should humans come together to meet the challenge, or continue forward with a splintering of groups? Which is the best route for survival?