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Name: Greg
Status: other
Grade: other
Location: NY
Country: USA
Date: March 2009

Question:
Hi; I understand that water boils at different temperatures at different air pressures. Does the boiling point also change with water depth? For example, if the air pressure is 746 mm Hg, it looks like boiling point would be about 99.47 degrees C. If I have a container with 8 inches or so of water in it, as far as I can tell the water would add about 15 mm Hg pressure at the bottom. So, does the water at the bottom boil at something like 100.04 C while the water at the top boils at 99.47 C? Or is there just one "boiling point"? If I have a quick responding (and precise) thermometer would I expect to see one temperature (in a container of boiling water)? Or a fluctuating temperature (because of the water circulation between a gradient of temperatures between the top and bottom)?

Perhaps a bit more detail will help.

I am probably getting a little too far ahead of myself, but I was basically trying to understand what really is happening in an open container of water being boiled. (As I have discovered, when looking closely/precisely at how things work, things are usually much more complicated they I would have thought.) For example, if I stick a fast reacting precision digital thermometer in an open container of boiling water, is all the water going to be one temperature (the 'boiling point'), or is there going to be some small temperature variation (say 0.2 C) above and below an average boiling temperature? Or, small variations with the boiling point being the absolute upper limit, etc?

The water is losing heat from the exposed top, and through the sides of a container (being heated from the bottom) and convecting. So, it seemed to me that some small variability of temperature (in all that turbulence) might be observed if water from these areas was being cooled and then churned back into the main body of water.

Thinking about this, I began to wonder if all the water in a given container actually has one single boiling point to begin with. As I understand it (perhaps incorrectly), the boiling point of water is affected by the atmospheric pressure, and this is related to the vapor pressure of the water at a given temperature working against the atmospheric pressure. When the vapor pressure exceeds the atmospheric pressure, the water will boil.

There are formula that I found for predicting the boiling point based on the current atmospheric pressure.

But, since the water exerts a pressure of its own (increasing with depth), my question was what, if any, effect does this have on 'the boiling point'. Does the pressure of the water at a given depth add to the atmospheric pressure (working against the vapor pressure) to increase the boiling point?

Does water at the bottom of a 1 inch deep container boil at a different temperature than water at the bottom of a 3 foot deep vat (at the same atmospheric conditions)? (If so, I thought perhaps I could look up the predicted boiling point by adding the atmospheric pressure to the additional water pressure at a given depth).

And, if the pressure of the water is relevant, and the water pressure increases with the depth, then does this create different 'boiling points' at different depths in an open container?

And if that was the case, what is the practical result of having these different boiling points at different depths (with the water being churned by the boiling action and presumably changing depth between the different pressure areas)?

As I said, I am probably getting a bit too far ahead of myself, since the later questions arise from assumptions I do not know the answer to. Sorry to be confusing.



Replies:
Greg,

This is very astute reasoning.

One of the definitions of boiling point is - the temperature at which the pressure of the particles entering the gas phase from the liquid phase is equal to the pressure exerted by the fluid on the liquid phase. Since it is not relevant what is exerting a pressure on the liquid phase (it could be the atmosphere, a different liquid, the liquid itself) then the temperature needed for the liquid to form an equilibrium between the gas and liquid phase should be higher at the bottom of a liquid column.

As far as measuring this temperature difference and accounting for convections and variations in temperature and so forth - remember that another definition of boiling point is - the temperature at which the gas phase is in equilibrium with the liquid phase. This is a steady state condition, there is no net change, the amount of particles entering the gas phase is the same as the amount entering the liquid phase, and should not involve kinetic effects or factors that vary over time.

To prove that the column of liquid has an effect on the boiling point of the liquid, we need only to look at deep sea steam vents, measure the temperature of the gaseous and liquid water to realize that indeed the water here boils at a much higher temperature.

We can then interpolate to smaller column heights.

Greg (Roberto Gregorius)


Let us go to nature, in fact to Yellowstone N. P. and Old Faithful geyser, for what I hope will be an answer to all your questions.

Water in O. F. is heated from the rocks around and below it, yet it erupts only occasionally. This is because, at depth, the water pressure prevents water from turning to a gas at its normal boiling temperature. The waters at depth continue to heat up to temperatures past their normal boiling temperature.

These superheated waters heat water nearer the surface until some of the near surface water boils. (This surface boiling is seen as a small overflow of water from the basin just before the big eruption.) The hydrostatic pressure below this boiling water (which has a lot of gas [steam] mixed in) drops allowing that deeper water to boil which in turn reduces the pressure on even deeper waters.

This pressure reduction cascades down the water column as more and more of the water column goes gaseous. (Note that the eruption takes time to build up to maximum?). At the height of the eruption pretty much the entire water column is taking part and

shoots out the top of the geyser.

So . . . water pressure does affect boiling point and there can be a temperature gradient in a fluid that is boiling.

Hope this helps.

Bob Avakian
OSU Institute of Technology
Okmulgee, OK


Hi Greg,

These are great questions. There are a few things I suggest for you to keep in mind in answering this question.

First is convection, which is movement of mass (in this case) water. When you have different temperatures of water in the same vessel, the water will begin to mix (by itself). The hotter water will tend to rise to the top, while the colder water will sink. This is known as autoconvection ('auto' because it does it itself -- you can cause 'regular' convection with a spoon too). So when you apply heat to the surface of a container (such as a flame to a pot), you will get some areas of the water that are warmer than others, and thus you will get autoconvection. There are many factors that affect how much autoconvection you get, such as viscosity and thermal conductivity. If you have a very viscous (or, say, a solid) material and very good thermal conductivity, the heat would conduct faster than the material would move -- and thus you would have very little autoconvection. Conversely, if you have low viscosity and low thermal conductivity, you would get lots of autoconvection because it's easier for the material to move around rather than for heat to be conducted.

Next is nucleation. If you look at boiling at the molecular level, you would see atoms (or molecules) constantly changing configurations relative to each other. In the case of a phase change, such as boiling or freezing, you get little clusters of molecules forming one phase or the other -- in the case of boiling, you get a small 'bubble' of water vapor forming. This pre-bubble is known as a 'nucleus' -- not to be confused with the nucleus of an atom. Once a nucleus forms, because the water is hot, it prefers to be a vapor, and a liquid water molecule next to the bubble might 'join' the bubble. So you have nucleii forming and then growing. There are thermodynamic explanations for how and why this happens -- let me know if you want more detail on nucleation. In any event, after a bubble nucleates, it grows, and then gets big enough to float to the surface. There are lots of factors that influence nucleation, but perhaps the most important one is that the bubbles need a 'home' to begin. These are known as nucleation points. Usually, a 'home' that a bubble likes is a small scratch a little bigger than the nucleus size. In a vessel with lots of nucleation points, bubbles will form and grow quickly. If there are few nucleation points (a very smooth container), then bubbles won't form as quickly. In fact, there are special drinking glasses with laser-etched bottoms to enhance bubble formation for carbonated beverages. In the case of boiling, a smooth surface can be very dangerous. If you heat water (say, in a glass inside a microwave), but the glass is smooth, it may become super-heated, which means it's above it's boiling point, but hasn't boiled. Think of a stretched-rubber-band that's ready to snap. If you then provide a nucleation point (by adding a tea bag, for example), the water can explosively and instantaneously come to a boil -- and possibly hurt the tea-maker.

Last, 'boiling point' is not a very exact term. It reflects an average temperature at which phase changes occur, but does not represent any immutable constant or property of matter. Lots of factors affect boiling point, including pressure and nucleation.

Put these together, and you create a complex situation where boiling may or may not occur at exactly the "boiling point", as affected by many parameters. To address your specific question, yes, if you had a 'super-thermometer' that could instantly divine the water temperature at different locations (without transferring heat and without mixing and without providing a nucleation point), then yes, it would measure a range of temperatures throughout the 'boiling' (or near-boiling) water. The water might be a little colder here and a little warmer there based on the parameters above (and there are more if you are interested). I say 'super-thermometer' because the act of measuring the temperature may also impact the water, especially if it is superheated.

Hope this helps,

Burr Zimmerman



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