(technical) How much energy would it take to warm the oceans by 1 degree Fahrenheit?

[Edena_of_Neith]

How much heat energy would it take to warm the surface of Earth's oceans by 1 degree Fahrenheit?
Surface, in this case, includes the water down to 100 feet deep. This is still above the beginning of the thermocline, where the water temperature starts dropping rapidly with depth.

Do not include the melting of any ice in this equation.

What would be the required energy be in joules?
What would be the required energy be in calories?
How would this compare with the energy generated by mankind?
How would this compare with the energy generated by a nuclear explosion?

 

[Lurks-no-More]

Quick calculation gives .2521882708*10^16 joules, or 2.52 petajoules.

You can get that amount of energy from 28.06 g of total conversion, roughly an ounce.

Incidentally, one megaton is about one petajoule, so theoretically -- very theoretically -- you could do it with a 2.5 megaton bomb.

Hope this helps.

 

[Agback]

How much heat energy would it take to warm the surface of Earth's oceans by 1 degree Fahrenheit?
Surface, in this case, includes the water down to 100 feet deep.

What would be the required energy be in joules?
What would be the required energy be in calories?
How would this compare with the energy generated by mankind?
How would this compare with the energy generated by a nuclear explosion?

The world is approximately a sphere with a radius of 6*10^6 metres. The area of a sphere is 4*pi*r^2, so the surface area of the Earth is about 4.5*10^14 square metres. The oceans cover about 70% of this, or roughly 3.2*10^14 square metres. 100 feet is approximately 30 metres, so you are talking about a total of about 9.5*10^15 cubic metres. The density of water is roughly 1000 kg/m^3 (salt water is actually somewhat more, but we're only aiming at a ballpark). That means that the mass involved is 9.5*10^18 kg. One degree Fahrenheit is 5/9 of a Kelvin, so we are talking about 5.3*10^18 times the amount of energy required to warm one kilogramme of water by 1 kelvin.

The thermal capacity of water is 417 Joules per kilogramme per Kelvin, so the total is 2.2*10^21 J. So my quick calculation suggests that the figure is about one million times what Lurks-no-more said.

You have to be careful with calories, since the food calorie is one thousand times the physicists calorie. Using physicists' calories the figure is 5.3*10^21.

A 1 kilotonne explosion releases approximately 4.2*10^12 J, so you would need all the energy released by 520,000 1-megatonne bombs.

I'm not sure what total annual energy production is, but I would guess that you were talking about centuries worth. Time to hit the Web.

Regards,


Agback

 

[Lurks-no-More]

Re: Re: (technical) How much energy would it take to warm the oceans by 1 degree Fahrenheit?

The thermal capacity of water is 417 Joules per kilogramme per Kelvin, so the total is 2.2*10^21 J. So my quick calculation suggests that the figure is about one million times what Lurks-no-more said.

Dang!
Can't figure out where I made the error... something to do with the powers of ten, probably.

Double dang goes for me for not noticing the magnitude problem and blithely saying 2.5 megatons would suffice nicely...

 

[Umbran]

Sorry, Agback, but you might want to double check your specific heats. The specific heat of water is 4186 Joules per kg per Kelvin.

Let's try this again, shall we?

Water area of the Earth = 3.61x10^8 sq km (Webster's New World Encyclopedia) = 3.61x10^14 sq m.

If we go down 30m, that's a volume of 1.08x10^16 cubic meters of water.

It's seawater, which is a bit heavier than normal water (1030 kg/cubic meter). Total seawater mass = 1.11x10^19 kg.

If we assume this seawater has the same speciifc heat as pure water, raising it one degree Farenheight (5/9 of one degree Celcius), we get Total Heat = 2.58x10^22 Joules.

The USGS says that total world energy production in 1998 was 379.7 quad Btu. That translates into about 4x10^18 joules. That means, it'd take all the energy the human race produced, pumped into the ocean for 6,450 years to produce that change.

By my quick calculation, if every single scrap of solar energy that fell on the Earth went into heating the water (and absolutely nothing else - nothing relfected or re-radiated, nothing absorbed by land, etc), it'd take a bit over 40 hours.

And, let's be careful - we can say that "this is equivalent to the energy in X bombs". That's a far, far cry from saying "you can do it with X bombs", even very, very theoretically. Explosive release of energy is a lousy way to heat water, folks

 

[reapersaurus]

And, let's be careful - we can say that "this is equivalent to the energy in X bombs". That's a far, far cry from saying "you can do it with X bombs", even very, very theoretically. Explosive release of energy is a lousy way to heat water, folks

Thanks for saying that, Umbie.

It was starting to sound childish.

Very impressive calculations, guys.

(Umbran - is that Webster's counting fresh water in their estimation of water area?
And not all that water area is even 100 feet deep...)

 

[Umbran]

(Umbran - is that Webster's counting fresh water in their estimation of water area? And not all that water area is even 100 feet deep...)

I'm not sure it matters. The area of fresh water is small. For example, the Great Lakes of North America take a whole whopping 245,000 sq km. That's 0.06% of the water area. Even if you add in every lake and river, you're not going to be changing the value much.

More important, perhaps, is the fact that at shorelines oceans are less than 100 feet deep. I expect, though, that the shore dropoffs are fast enough that the difference is probably still pretty small. Close enough for our consideration here, at least.

 

[Edena_of_Neith]

All of the energy produced by our race (at current production levels) for 6,500 years.
Or, half a million hydrogen bombs, if somehow they could all directly tranfer all of their energy into heat which was stored in the water.
Just to raise the temperature of the top 100 feet of Earth's oceans by 1 degree Fahrenheit.

Obviously then, the amount of heat in Earth's oceans is staggering.
For the oceans certainly average more than 100 feet deep.

I actually read that, if Earth was thrown out of orbit and went sailing into deep space, it would take a million years for the oceans to freeze clear to the bottom.

 

[Edena_of_Neith]

Thank you

Thank you for the replies.
Thanks for the help here. You guys know your math. I couldn't figure it out!

 

[Crothian]

Out of curiousity (And good job on the math and science guys!! ) why do you want to know this?