# Why is it cold on the sea floor if pressure heats things?

I was reading this and it says that Microsoft put a server farm at the bottom of the ocean because it's cooler there. Particularly it seems to imply that it get's colder as you go deeper, "Since ocean water gets pretty cold toward the sea floor..." But I know that pressure causes heat, for example it is responsible for igniting fusion at the center of the sun.. what gives?

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First, pressure doesn't cause higher temperature. This misconception is probably a result of a massive oversimplification with relation to the ideal gas equation. The actual relation is "increasing the pressure of an ideal gas while volume remains constant increases the temperature of the gas".

Two notable things here:

• Water and other liquids are barely compressible, so they behave nothing like an ideal gas (which is perfectly compressible). Ideal liquid doesn't compress at all.
• Temperature only increases as you put more stuff in the same volume. That is, it isn't pressure that increases temperature, it's compression. If you compress a volume of air, the temperature will rise, and if you release it again, the temperature will drop again.

Second, any closed system evolves toward thermal equillibrium. In simple terms, if you leave a hot coffee on your table, it will eventually cool down to room temperature. Even though compression increases temperature, this doesn't mean that constant pressure keeps producing more and more heat. When you compress a lot of air into a soccer ball, it will feel hot to the touch. But as it exchanges heat with the environment, it will cool down. This is very useful, of course, because it allows you to expend energy to cool things down, like in your A/C :)

What effect this has on pressure in turn again depends on the properties of the material you're working with. If you have a volume of air in a bottle, as you cool it down, the gas pressure decreases. If you heat it up, the pressure increases. This is the reason why you need to tweak the pressure in your car's tires even if they aren't leaking - you need to adjust for current temperature.

However, with a liquid, this isn't anywhere as simple. While there is a relation between temperature and density, it's nowhere near as big as in an ideal gas. The same goes with pressure and density - if it didn't, you wouldn't be able to walk (imagine that your legs would shorten by half every time you raised one leg - that just wouldn't work).

So, let's put this to use in our ocean example. Undisturbed, water will tend to be "vertically ordered" by density. Usually, this means that warmer water will tend to rise up, while colder water will tend to go down. So the weird thing is actually how relatively warm in the depths. The ocean floor tends to be around the same temperature, regardless of how warm or cold the upper layers are.

There's two main reasons for that, specific to water:

• The water anomaly - the peak of density occurs around 4 °C in water; both increasing and decreasing temperature from this point results in lower density. The effect is very important, because it means that even during winter, the bottom layers of lakes will have temperature around 4 °C even when the surface is frozen. And ice is actually a pretty good insulator too :) EDIT: As noted by David, this doesn't occur in ocean water, due to the high salinity which pushes the peak below freezing (around -4 °C). So in an ocean, the deepest layers are formed of water between about 0 °C to 3 °C.
• Ice - when water freezes, it forms ice, which has lower density than water. This is somewhat unusual (solids are usually higher-density than liquids), and it means that as water bodies start to freeze, it rises again.

With supercooled water, this effect is even more pronounced - a water at -30 °C has about the same density as water at 60 °C.

Oceans cool mostly by evaporation - the surface layers of water "spontaneously" changing state from liquid to gaseous. You get a balancing act between energy lost to evaporation, and incoming sunlight. However, there's a huge gap between the surface and the deeps, a lot of water mass - the incoming sunlight is nowhere near enough to warm ocean waters throughout. So you get warm surface waters, then a gradient of cooler and cooler water, and finally about 0-3 °C in the deep. To illustrate how big this gap is, about 90% of the worldwide ocean water is in the 0-3 °C range (hence the "nowhere near enough sunlight to heat the whole thing through").

Of course, a 4 °C body of water is great for cooling systems running at 40 °C and more. Air is actually a pretty good insulator, so air cooling gets tricky with large systems. Water, on the other hand, is pretty thermally conductive, and it easily convects, so cooling a huge data centre becomes almost trivial.

EDIT:

Let me address the Sun part, since there seems to be some confusion there as well.

Nuclear fusion is something that happens very infrequently. Two nuclei must come very close together to fuse, and they need enough kinetic energy to overcome the repulsion between each other (since both have the same electric charge).

The first problem is solved by increasing density. The more nuclei you have in the same volume, the higher the likelihood of close contact. This is where pressure comes in - that's how you get a higher density. Stars are made of plasma, and plasma is easily compressible, similar to a gas, so as pressure increases, so does density. How compressed is it? Well, the Sun's core, where the fusion reactions are actually happening, contains 34% of the Sun's mass, in only 0.8% of the Sun's volume. In the centre, the density is around 150 times the density of liquid water. The pressure is about 100 000 times the pressure in the Earth's core, and about 100 000 000 times the pressure of the water on the bottom of the Mariana trench.

The second problem is solved by increasing the kinetic energy of the individual nuclei. In other words, increasing the temperature. Just like with compressing air, pressure is only a one-off deal in increasing temperature; the fusion reaction in the Sun was started using the residual heat of the collapse of matter forming the star (the gravitational potential energy) - I'm not sure how much of a factor was compression in particular. But again, this was only responsible for the initial ignition - today, the reaction is running entirely on the heat produced by fusion and the pressure supplied by gravity (which is actually lowered by the outward pressure of the energy released in the core - the two pressures form a stable equilibrium).

As a side note, despite the high temperatures and pressures, the fusion reaction powering the Sun is incredibly weak. If we could magically reproduce the same conditions on the Earth, it wouldn't really be usable for power generation at all - the energy produced is about 300 Watts per cubic metre at the very centre. To have a comparison, this is comparable to power density of a compost heap, and less than the power density of human metabolism. Yes, your own body is producing more power than the same volume of the centre of the Sun. I unsuccessfully tried to find data on power density of fission reactors, but a single CANDU reactor produces about 900 MW (that's "million watts"), and it sure isn't three million times as big.

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Off-topic, but could you also say, "any system evolves toward equillibrium." Not just specifically, "any closed system evolves toward thermal equillibrium." I understand that if you place two clocks next two each other which are slightly out of sync, they will auto-sync themselves. – user1477388 Feb 4 at 20:26
According to Wikipedia, the core size of the BN-600 fast reactor is 1 x 2 meters, and its electrical power is 600 MW, so the thermal power is probably around 1800 MW at 30 % efficiency. That's a fast reactor though – I didn't find exact core sizes for light water reactors. I estimate around 5 x 5 meters for the 880 MWe / 2500 MWth Olkiluoto 1/2. The CANDU is a pressure tube reactor so the core is larger. The core of a fission reactor is not homogeneous however, so a direct comparison with the sun is difficult. – ntoskrnl Feb 6 at 15:21
So I actually did find the exact dimensions of the Olkiluoto 1/2 core – 3.68 by 3.88 meters (height/diameter). That's a power density of 57 MW/m^3. The Loviisa 1/2 core is 2.42 by 2.73 meters at 1500 MWth for a power density of 106 MW/m^3. These are all light water reactors. The aforementioned BN-600 has a core power density of a whopping 573 MW/m^3! – ntoskrnl Feb 6 at 15:36
Excuse the spam, but I also found the height of the Olkiluoto 3 (EPR) core – 4.2 m. I don't know the diameter, but judging from the size of the pressure vessel, it's probably around 4.3 m. At 4500 MWth, the power density is 74 MW/m^3. So there you go, the power density of a typical light water reactor is around 50–100 MW/m^3. – ntoskrnl Feb 6 at 15:53
@Luaan your "side note" about the energy density of the fusion reaction at the core of the sun is fascinating - I had no idea - and I sort of hope someone asks a question for which you can put that as the answer. – davidbak Feb 7 at 17:16

It's not so much the pressure, but rather compression that creates heat. Heat is a measure of increased kinetic energy as molecules are forced into a smaller space. Water is not very compressible, and water at the bottom of the ocean is not confined to a significantly smaller space under pressure. The kinetic energy of water molecules at the bottom of the ocean does not increase significantly under pressure, as there is little compression of the liquid. A mole of water 4,000 meters beneath the ocean occupies only about 1.8% less volume than a mole of water at the surface. The bulk modulus of water indicates that water requires a great deal of pressure for a small change in volume.

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You might want to stress out that even the volume change results in a one off change in temperature, not a continuous increase. When you compress air in a balloon, sure, it's going to get hot. But the heat is going to be exchanged with the environment as usual, until it forms an equillibrium, dropping to ambient temperature. In the depths of the ocean, where convection readily moves warm water to the top, which in turn cools very easily due to evaporation... that means cold water. – Luaan Feb 3 at 8:48
That is the same principle that a refrigerator works on. Gas is compressed to a liquid, and the extra heat is released behind the fridge in a radiator until the liquid is about room temperature. Then, the liquid is decompressed from a gas which gets really cold. This works off the "one off" temperature change. – wedstrom Feb 3 at 21:47
This tells us why it's not hot, but doesn't exactly answer why it is cold (as in colder than atmosphere above or molten rocks far below). – Mołot Feb 4 at 0:56
@Molot: See JDlugosz answer for some great links that explain the ocean circulatory system, and how the earth's heat at the ocean floor rises away from the bottom. Radiant energy from the Sun doesn't reach the ocean floor in any significant amount. And, as Luaan points out in his comment, convection moves any heat from the lower to the upper layers of ocean water. Cold is the absence of heat. – Ernie Feb 4 at 7:33
@Luaan Consider making an answer out of your comment. – CJ Dennis Feb 4 at 9:27

Colder water is denser until it reaches a temperature a couple degrees above freezing, then it gets lighter again. So the water at the bottom is at the specific temperature where it is densest: any heating makes it rise. Any further cooling makes it rise.

This further points out that without ocean circulation it would take a year for the Earth's heat at the ocean floor to heat up the water at the bottom by one degree C.

See also Global Ocean Circulation and Deep Sea Temperatures for more depth. It states that the deepest water settled at the bottom of the basins is about 2°–3°C, and that the cold water comes from melting glaciers at the poles.

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If I recall correctly that temperature is 4⁰C, though I am not sure if that changes with pressure. – kasperd Feb 3 at 13:58
Likewise; that's why I left it vague for a quick answer without looking up details. – JDługosz Feb 3 at 21:04
The first paragraph is incorrect with regard to sea water. While fresh water does indeed undergo a density change at about 4C, salty water does not. At the typical density of 34 ppm salt, salt water just keeps getting denser and denser with decreasing temperature until the temperature becomes very, very close to freezing (which is below zero for salt water). The thermocline in the oceans is typically much deeper than is the thermocline in a freshwater lake. The thermocline in a freshwater lake is very much dictated by that density inversion at ~4C, the thermocline in the oceans is not. – David Hammen Feb 4 at 5:40
Nonetheless, this is a better answer than is the other even more highly voted answer. I've done my best, @JDlugosz: I've upvoted your answer. – David Hammen Feb 4 at 5:42
Interesting: even the legitimate science outreach sites keep repeating the max density at a couple degrees above freezing, albeit withnthe observation that it's 2 or 3, not 4. – JDługosz Feb 4 at 6:42

It has been covered above that there is little scope for water to be heated by compression to begin with. Another aspect is that the water at the bottom of the ocean has been there for a considerable length of time. Hence, if it had heated up to any large extent when the oceans were formed, there has been ample time for the heat of compression to have dispersed, even if it were several degrees Centigrade.

Btw, the notion of a gas being heated by compression, and the heat being lost easily, is crucial to refrigeration, as if one pressurises a gas, then allows it to cool before depressurising it again, the final temperature will be lower than ambient (reverse Carnot cycle).

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There is another factor that I feel the other answers have overlooked, because there is a similar analogy with air, and air is compressible. Specifically, why is air in valleys often colder than at the top of the hill when pressure heats things?

In reality, there are two different dynamics at work. One is adiabatic compression, which as has been mentioned isn't significant for water, because water isn't very compressible. The other dynamic is convection, or in water, currents, which redistribute bulk matter. Cold water (or air) is heavier than warm water (or air) and thus will sink to the bottom. In the atmosphere this is at odds with adiabatic compression, as well as wind cycles generated by the sun. In water those effects are less, and thus cold water sinking becomes a more dominant factor.

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