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Vessels A and B are made of conducting material. Both contain water. Vessel A floats in B. Vessel B is now heated at a uniform rate, then a) Water in A boils first b) Water in A boils some time after water in B starts boiling c) Water in both A and B starts boiling simultaneously d) Water in A does not boil

Well logically I tried and got the answer as b) but apparently the correct option is a). I think that it may be possible that all the thermal energy being obtained by the water in B is conducted (whether by conduction or convection) to the water and A and hence the temperature remains more or less the same. But after some time when the water in A has reached a certain point after which it starts boiling, there is no other place for the thermal energy to go (it can't escape into the atmosphere since it is a comparatively worse conductor than water) and therefore the water in B starts boiling after A.

But I'm unable to put forward a concrete logic supported by scientific evidence. Any help would be appreciated.

(I apologise for the improper use of the tags as I'm unclear about the tags to be used.)

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I think you could argue the question is quite unclear. (from my perspective)

In a one-dimensional problem I will agree with your book that the answer is a). That is, assuming that the vessel A and B are only represented by height and vessel A is completely on top of vessel B. This is because the convection will always bring the warmest water upwards (due to the lowered density). Assuming the vessel A is sufficiently conductive the heat should keep rising through vessel A. Since vessel A is floating on B, in the one-dimensional vertical problem A will boil faster.

In the two or three-dimensional case I don't know if this question is clear.

In those situations it would depend a lot on the buoyant conditions, and as far as I could tell they would start at similar times. If the liquid level in vessel A was higher than B (it would have to be a vessel made of something lighter than water AFAIK) then liquid in A would start to boil first, due to convection upwards.

If the liquid level in B is higher than A, B should boil first, due to convection as well. If they were the same height, they should boil at the same time due to the convection.

See the bad paint diagram I included!

Vessel Heating Examples

This is all assuming the vessels are very conductive and thin; specifically vessel A, I don't know why vessel B is conductive. Maybe it's something I'm missing, but it seems like it would just slow the whole process by losing heat to the sides. This could hurt or hinder vessel A's heating, because if vessel A is in the very middle it may heat up first due to heat lost out the sides. If it's near the edge the middle will probably boil first, given sufficient total diameter; again depending on the problem specifics.

If anyone thinks of anything I've overlooked please let me know. I find heat transfer is easy to miss something that completely changes the situation.

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Since heat transfer occurs from water in $B$ to water in $A$, how can temperature in $A$ be ever higher than that in $B$? If water in $A$ is to reach 100 $^\circ$C, then it is not possible if temperature of water in $B$ is everywhere less than 100 $^\circ$C. Therefore for wall of finite conductivity, water in $B$ must reach boiling point first; if the wall is infinitely conducting, then assuming that convection is equally vigorous in both $A$ and $B$, both of them must reach the boiling point at the same time. In any case, water in $A$ reaching boiling point first seems impossible.

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