Boiling a glass of water in a bowl of water - tricky question?

[Physics Slayer]

Homework Statement

A glass of water is placed in a bowl of water, each are filled till the brim, the glass of water floats in the bowl. The bowl is heated, when will the water in the glass boil? before/after/same time as the water in the the bowl.

Relevant Equations

no equations

I think the water in the bowl of water will boil first because the glass won't conduct the heat instantaneously, and hence the water in the glass will boil after the water in the bowl. Is this correct?

I am guessing this is a trick question and the water in both boil at the same time, but I don't see how that would be possible.
(I don't know the correct answer)

 

[Physics Slayer]

or is it that both will boil at the same time because change of state happens at a constant temp. and as long as the water in the glass is not at 100deg C, the water in the bowl will keep cooling down by loosing heat to the water in the glass and hence only when they are both at the same temp. the water will be able to boil from the bowl and along with that from the glass as well. does this reasoning make sense?

 

[phinds]

A glass of water is placed in a bowl of water, each are filled till the brim, the glass of water floats in the bowl.

That's a good trick right there considering that the density of glass is higher than that of water.

 

[haruspex]

That's a good trick right there considering that the density of glass is higher than that of water.

So clearly the glass is one of those insulating glasses with a double shell and an air space in between. (I have two.) That should settle the question.

 

[phinds]

So clearly the glass is one of those insulating glasses with a double shell and an air space in between. (I have two.) That should settle the question.

Uh huh. You really think that's what the OP had in mind?

 

[Steve4Physics]

I think the water in the bowl of water will boil first because the glass won't conduct the heat instantaneously, and hence the water in the glass will boil after the water in the bowl. Is this correct?

@haruspex’s (amusing) reply in Post #4 highlights a useful general 'trick' for some problems.

Imagine what would happen in an extreme case. So here, imagine the ‘glass’ is not simply a poor thermal conductor, but is an extremely poor conductor.

 

[hutchphd]

Like a vacuum. And then we could put areflective coating on the glass!

The point here is (I think) that temperature is really only well defined for a system at equilibrium. The system defined is being heated and might be in steady state but it is not in equilibrium. Perhaps subsections of it can rou8ghly equilibrate

 

[Physics Slayer]

A pal of mine went ahead and actually did the experiment and found out that they infact do not boil at the same time. He actually put a small bowl(made of steel) in a larger bowl(again made of steel)

Whenever I face questions like this where you can't really apply equations(can you?) I don't see a straightforward method of solving the problem do I just rely on Intuition?(which really just feels like guess work with extra steps)

 

[Frabjous]

Fluids heat by convection and conduction. An internal boundary will interfere with convection. The internal boundary will take a finite amount of time to reach the bath temperature, so the fluid inside of it will also see a time lag. So the fluid in the inner area will boil later.

I am guessing that convection is the larger effect, so it would be an interesting experiment if the small steel bowl was replaced by foil.

 

[jbriggs444]

If one cleans the inner surface of the outer bowl and the outer surface of the inner glass well and uses distilled water in the outer bowl but ordinary tap water in the inner bowl then it ought to be possible to get the inner glass to boil first. That would be a mildly amusing parlor trick.

But back to the situation at hand.

How does the rate of heat transfer change as the inner reservoir heats up toward the boiling point? Can two reservoirs in thermal contact ever equilibriate in finite time?

 

[pbuk]

distilled water in the outer bowl but ordinary tap water in the inner bowl

or maybe the other way round? In any case the difference in boiling points is so small it would be very difficult to achieve in practice.

But back to the situation at hand.

Where we must assume that the boiling point of the water inside the glass is identical to that of the water outside the glass.

In this case you only need to consider this:

How does the rate of heat transfer change as the inner reservoir heats up toward the boiling point? Can two reservoirs in thermal contact ever equilibriate in finite time?

to know the answer, although there is another reason that is more important in practice.

 

[Frabjous]

In any case the difference in boiling points is so small it would be very difficult to achieve in practice.

Impurities raise the temp a couple of degrees. You could cheat and dissolve salt/sugar. I do not know which is better.

 

[Lawi Theofans]

Homework Statement:: A glass of water is placed in a bowl of water, each are filled till the brim, the glass of water floats in the bowl. The bowl is heated, when will the water in the glass boil? before/after/same time as the water in the the bowl.
Relevant Equations:: no equations

I think the water in the bowl of water will boil first because the glass won't conduct the heat instantaneously, and hence the water in the glass will boil after the water in the bowl. Is this correct?

I am guessing this is a trick question and the water in both boil at the same time, but I don't see how that would be possible.
(I don't know the correct answer)

Both they will boil in the same Temperature but different Time.

 

[Steve4Physics]

Whenever I face questions like this where you can't really apply equations(can you?)

There is an equation (related to thermal conductivity) that can be used. But using it would be an unnecessarily complicated way to solve a simple problem like this
.

I don't see a straightforward method of solving the problem do I just rely on Intuition?(which really just feels like guess work with extra steps)

One of my first physics lessons at school (aged 11, many years ago) involved a demo’ showing us that conduction of heat takes time. Something like this (turn the sound down and skip through it).:


Knowing this, and that water must be heated to 100ºC to boil (at atmospheric pressure), you can answer the question with only simple logic.

 

[pbuk]

You will get the right answer by looking at conduction, but for the wrong reason. Convection is much more significant than conduction when boiling a liquid in an open pan.

 

[Steve4Physics]

You will get the right answer by looking at conduction, but for the wrong reason. Convection is much more significant than conduction when boiling a liquid in an open pan.

Good point. So the glass acts as a barrier to limit convection (as well as its less significant conduction effect).

Would that mean even some sort of 'ideal' perfectly conducting glass will reduce the overall rate of heat transfer to the water in the glass? I guess so.

 

[hmmm27]

No matter what, it's the same answer whether the section you're studying concerns heat transfer, specific/latent heats, or sous vide cooking.

 

[Physics Slayer]

There is an equation (related to thermal conductivity) that can be used. But using it would be an unnecessarily complicated way to solve a simple problem like this

Could you link the wiki page for the equation you talk about, even though I might not have the math background yet, I would absolutely love to have a curious glance at it!

 

[jbriggs444]

Impurities raise the temp a couple of degrees. You could cheat and dissolve salt/sugar. I do not know which is better.

Lack of nucleation points raises the temperature a fair bit more.

 

[TonyStewartEE75]

Homework Statement:: A glass of water is placed in a bowl of water, each are filled till the brim, the glass of water floats in the bowl. The bowl is heated, when will the water in the glass boil? before/after/same time as the water in the the bowl.
Relevant Equations:: no equations

I think the water in the bowl of water will boil first because the glass won't conduct the heat instantaneously, and hence the water in the glass will boil after the water in the bowl. Is this correct?

I am guessing this is a trick question and the water in both boil at the same time, but I don't see how that would be possible.
(I don't know the correct answer)

The fluid furthest away from the heat source is coolest, boils last.

 

[Frabjous]

Lack of nucleation points raises the temperature a fair bit more.

Do you have a number? I cannot seem to find one.

I would think the boundary would put an upper limit to the value. I believe that superheating occurs in a microwave because the container acts as a heat sink while the bulk is heated. For the geometry of this thread, the hottest part is the bottom of the bowl (which is why you suggested cleaning it).

 

[Steve4Physics]

Could you link the wiki page for the equation you talk about, even though I might not have the math background yet, I would absolutely love to have a curious glance at it!

I’m no expert so I can only give a few pointers on the maths (and only considering conduction, not convection).

Heat transfer by conduction is governed by Fourier’s Law (also referred to by other names such as Fourier’s Heat Equation). E,g, see: https://en.wikipedia.org/wiki/Thermal_conduction#Fourier's_law

This is simply a starting point. In your problem, the temperatures are changing; we say we are not in a ‘steady state’. The process of heat-transfer while temperatures change is called ‘transient heat transfer’ and makes applying Fourier’s law much harder.

For a general (non-mathematical) description of transient heat conduction try this: https://en.wikipedia.org/wiki/Thermal_conduction#Transient_conduction

For some mathematics (with one of the temperatures kept constant - a much simpler situation than your glass problem) try this (a pdf file):
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj6t7nCj9_1AhWPY8AKHbeeBjMQFnoECDEQAQ&url=https://www.sfu.ca/~mbahrami/ENSC%20388/Notes/Transient%20Heat%20Conduction.pdf&usg=AOvVaw3_Zc-t9iwQqQM8ZaUdWSBE