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Quiz thread (don't be afraid of to be wrong)

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  • #32
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    Delphi91,
    I had not really thought of Newton's Law of Cooling and there's a big "IF" that goes along with this problem.

    I don't think Newton's Law of Cooling explains why the hotter one is able to reach and pass the temp of the cooler one and begin to freeze first.

    That's the weird part!


  • #33
    MoogPoo
    Registered Users, Registered Users 2 Posts: 156 ✭✭MoogPoo


    yeah newtons law wouldnt make it go cool faster but its rate would slow down as it gets closer to B's temp.

    Does bucket A have less water?


  • #34
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    MoogPoo wrote: »
    Does bucket A have less water?

    Initially, let's consider all things equal except for the temperatures of the water.

    So let's say they have the same volume of water which for all intensive purposes means they have the same mass. We can safely ignore the slight density difference.


  • #35
    ianobrien
    Registered Users, Registered Users 2 Posts: 2,751 ✭✭✭ianobrien


    I'm going to out on a limb here and say it's down to the dissolved gases....

    Upon heating the water, you're removing the dissolved gases, purifying the water. Also, if the water is boiled, some salts will fall out of suspension (hair in a kettle used to boil hard water). The cool water now is less pure than the hot water, depressing it's freezing point by just enough for this to be notable.

    Or am I talking through my posterior?


  • #36
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    ianobrien wrote: »
    I'm going to out on a limb here and say it's down to the dissolved gases....

    Upon heating the water, you're removing the dissolved gases, purifying the water. Also, if the water is boiled, some salts will fall out of suspension (hair in a kettle used to boil hard water). The cool water now is less pure than the hot water, depressing it's freezing point by just enough for this to be notable.

    Or am I talking through my posterior?

    I had not thought about the suppression of the freezing point - like why people put "salt" on snow in the winter.

    The difference is notable and I think a famous scientist first figured it out. Makes sense when it is explained.

    Again, there's one important question to be asked. If true, then it works, otherwise, bucket B freezes first.

    Probably not too late to mention that neither bucket has a lid.


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  • #37
    ianobrien
    Registered Users, Registered Users 2 Posts: 2,751 ✭✭✭ianobrien


    FISMA wrote: »
    .

    Probably not too late to mention that neither bucket has a lid.

    That has just triggered something....

    I was assuming that the same volume of water froze, like a dunderhead!

    Now, you put out the same weight of hot water & cold water. I forgot about the larger evaporation rate of the hot water compared to the cold. This means that there will be some evaporation of the hot water, reducing it's weight and volume.

    As the hot water cools faster than the cold water, it eventually reaches the same temperature as the cold water. At some point, both the hot and cold water reaches the same temperature. As there is now a smaller weight of "hot" water, it freezes before the "cold" water due to the latent heat of fusion being related to mass only.

    Or am I still a dunderhead?


  • #38
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    From what I remember, though I could be wrong, it is still an unsolved question in physics.


  • #39
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    ianobrien wrote: »
    As the hot water cools faster than the cold water, it eventually reaches the same temperature as the cold water. At some point, both the hot and cold water reaches the same temperature. As there is now a smaller weight of "hot" water, it freezes before the "cold" water due to the latent heat of fusion being related to mass only.
    Ian - you're close but missing one critical piece!;)

    You'll have to convince me (logic, math, bribery). How can you be sure that the mass lost during evaporation gets the hotter water to freeze before the cooler water when heat loss due to conduction through the bucket is considered?
    Morbert wrote: »
    From what I remember, though I could be wrong, it is still an unsolved question in physics.
    Unless I worded this one wrong, there's a good explanation. I think it was Bernouilli that figured it out. I look forward to your $0.02.


  • #40
    stevenmu
    Moderators, Society & Culture Moderators Posts: 9,688 Mod ✭✭✭✭stevenmu


    I'll guess that it's to do with the way water expands when it freezes. Of course like everything else water expands when heated, and contracts when cooled, but after a certain point it begins to expand again then freezes. So the arrangment of the water molecules in heated water is actually closer to the arrangement of molecules in ice than cold water would be.


    Btw, does it work for buckets left sitting in the cold? I did see on TV before that they threw some cold water out of a container into the cold and it hit the ground before freezing, and then threw boiling water out of a kettle and it froze before hitting the ground.


  • #41
    ianobrien
    Registered Users, Registered Users 2 Posts: 2,751 ✭✭✭ianobrien


    FISMA wrote: »
    Ian - you're close but missing one critical piece!;)

    You'll have to convince me (logic, math, bribery). How can you be sure that the mass lost during evaporation gets the hotter water to freeze before the cooler water when heat loss due to conduction through the bucket is considered?


    Unless I worded this one wrong, there's a good explanation. I think it was Bernouilli that figured it out. I look forward to your $0.02.

    The latent heat of vapourisation is mass dependent only. Thus, if there is less "hot" water there (post evaporation) it'll freeze before the larger weight of "cold" water as less energy input is needed.

    I imagine that given the large difference in weights between the bucket and water, the heat loss through the bucket (plastic or metal) compared to the mass of water is negligible when compared to the heat loss through evaporation.


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  • #42
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    FISMA wrote: »
    Unless I worded this one wrong, there's a good explanation. I think it was Bernouilli that figured it out. I look forward to your $0.02.

    Hmm I have not heard of an explanation by Bernoulli. Could you link me?


  • #43
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    Morbert wrote: »
    Hmm I have not heard of an explanation by Bernoulli. Could you link me?
    Morbert,
    I forget where I read the Bernoulli connection, but it does stand out in my head. Right now I am in the process of moving and the Physics books are in boxes. When I get them out, I'll post again.
    ianobrien wrote: »
    I imagine that given the large difference in weights between the bucket and water, the heat loss through the bucket (plastic or metal) compared to the mass of water is negligible when compared to the heat loss through evaporation.

    Ian,
    This is key to the puzzle and goes towards the question that needs to be settled to determine which freezes first. There's an initial condition that we have not addressed, without it, either could freeze first.

    Do you really believe that the heat lost through evaporation is greater than that conducted through a steel bucket?

    Anyhow, I'll give this thread until tomorrow and then post my understanding of the problem.


  • #44
    ianobrien
    Registered Users, Registered Users 2 Posts: 2,751 ✭✭✭ianobrien


    FISMA wrote: »
    a steel bucket?


    Ah, now you mention a steel bucket! I ignored the bucket as I assumed it was plastic (all mine are anyway.....). Plastic buckets are great insulators.

    There are questions like were the buckets allowed to reach steady state temp with the water contents before being exposed to the cold, or were they filled and immediatly placed outside. Also, metal vs plastic buckets and were the buckets placed together or far apart (if together, condensate forming on cold bucket from evaporated water from hot bucket)

    If the bucket is steel, as the specific heat capacity of steel is approx 10 times lower than that of water (going off memory), for a specific heat loss, the temp of the steel will be lower than that of the water and so on and so forth.....


  • #45
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    ianobrien wrote: »
    Ah, now you mention a steel bucket! I ignored the bucket as I assumed it was plastic (all mine are anyway.....). Plastic buckets are great insulators.

    Ian,
    Actually, I have been very careful to not mention the material the bucket is made out of.;) I only offered it in the last post to question your assertion.

    You're pretty much there. I was looking for someone to ask the important question - What's the bucket made out of: wood or metal?

    When you use wood buckets, the hot water freezes first. However, with a metal bucket, the cooler bucket should freeze first.

    Wood is a good insulator. Far better than metal. When the wooden bucket is used, heat is primarily lost through contact with the air.

    As you mentioned, the hotter water is evaporating at a greater rate than the cooler.

    Over time, the mass of the hotter water in the bucket decreases due to evaporation more so than the cooler water and we are no longer comparing apples to apples.

    Thus, you are trying to freeze less water which is why the bucket with the hotter water freezes first.

    Now if the buckets are metal, heat is lost through the walls of the container and, as expected, the cooler bucket should freeze first.

    Comments?

    Who wants to post the next quiz/brainteaser? Ian?


  • #46
    Professor_Fink
    Registered Users, Registered Users 2 Posts: 861 ✭✭✭Professor_Fink


    FISMA wrote: »
    As you mentioned, the hotter water is evaporating at a greater rate than the cooler.

    Over time, the mass of the hotter water in the bucket decreases due to evaporation more so than the cooler water and we are no longer comparing apples to apples.

    Actually the hot water already has less mass, since the heat has caused it to expand, so even if there was no evaporation, by the time it cools, it would still have less volume.


  • #47
    ianobrien
    Registered Users, Registered Users 2 Posts: 2,751 ✭✭✭ianobrien


    I was almost there with post #37!

    I'll have a good 'un in a day or so...


  • #48
    SOL
    Registered Users, Registered Users 2 Posts: 1,155 ✭✭✭SOL


    I have heard, and having not tested I don't know how true this is, but assuming the bucket is relatively insulating, the reason the hot water freezes faster is because large convection currents form in it compared to the cold water which doesn't cool very much and thus an insulating layer forms on the top.

    I assume such an effect however would be very scale dependent...



    Also, in terms of the loss of mass/ there being less of it anyway, surely such an effect would be insignificant given that you are talking about 5% difference maybe?


  • #49
    krd
    Banned (with Prison Access) Posts: 3,455 ✭✭✭krd


    If it was a solid block, the cooler one would reach 0C first.

    It's to do with conduction, convection, buoyancy and gravity. If you just consider the open end of the bucket to be where the heat is lost.

    Since the cooling is happening at the top of the bucket, in each bucket, warm water will be carried from the bottom of the bucket upwards by convection. Heat is also being transferred through conduction - this changes the buoyancy of water.

    An effect that will happen in both buckets - but for the sake of argument I'm going to say it only happens in one bucket and not the other. As I imagine in the cooler bucket it will have a greater effect in slowing its' cooling.

    In the cooler bucket the convection currents of warm water moving upwards have less energy than the currents in the hotter bucket. As the cool water falls, it's warmed through conduction (and expands becoming more buoyant). In the cooler bucket a layer of buoyant water is formed (let's just say in the middle of the bucket). The downward convection currents do not have enough energy to break through the layer, but their weight/gravity helps hold the layer in place - conduction also changes the buoyancy of the falling water. the convection current beneath the layer can't break through either.

    So in the cooler bucket, warm water is trapped in the bottom of the bucket.

    In the hotter bucket, the warm convection currents have more energy, so they take the warm water to the top of the bucket. No trap layer is formed and the water cools much faster than the cooler bucket.


    So what I am saying, is there is a trap layer in the cooler bucket.

    If you poured the contents of each bucket into large trays the cooler one would freeze first.


  • #50
    ianobrien
    Registered Users, Registered Users 2 Posts: 2,751 ✭✭✭ianobrien


    While I think of a proper chemistry one (mass spec based maybe?), try this logic one.

    Using the following pieces of information
    1. New York & LA are 3000 miles apart
    2. The day contains 24 hours
    3. New York & LA are separated by three time zones.

    Deduce the circumference of the Earth.

    I want an explanation based on the above facts only. Fermi used the above facts to deduce a figure to within 1% of the correct figure!


  • #51
    krd
    Banned (with Prison Access) Posts: 3,455 ✭✭✭krd


    ianobrien wrote: »
    While I think of a proper chemistry one (mass spec based maybe?), try this logic one.

    Using the following pieces of information
    1. New York & LA are 3000 miles apart
    2. The day contains 24 hours
    3. New York & LA are separated by three time zones.

    Deduce the circumference of the Earth.

    I want an explanation based on the above facts only. Fermi used the above facts to deduce a figure to within 1% of the correct figure!

    NY is on Eastern Time and LA is on pacific time. There is a three hour difference. The world is divided up into 24 time zones - as it takes the earth 24hours to rotate.

    So, that would mean, each time zone is 1,000 miles and the circumference of the earth is 24,000 miles. Which I know is not correct - but as an approximation, it's approximately correct - but nowhere near an error of 1%.


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  • #52
    ianobrien
    Registered Users, Registered Users 2 Posts: 2,751 ✭✭✭ianobrien


    krd wrote: »
    NY is on Eastern Time and LA is on pacific time. There is a three hour difference. The world is divided up into 24 time zones - as it takes the earth 24hours to rotate.

    So, that would mean, each time zone is 1,000 miles and the circumference of the earth is 24,000 miles. Which I know is not correct - but as an approximation, it's approximately correct - but nowhere near an error of 1%.

    Yep, that's the way Fermi did it, and the circumference of the earth is 24,901 miles at the equator, or 24,860 from pole to pole.

    When I did the maths on the error, I used a figure of 24,091 to determine the error so Oops!, wrong error figure given (the error is 3.75%).


  • #53
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    Thought I would post another here... Things are a bit quiet.

    ******************************************************
    Quiz #6
    ******************************************************
    You are given a scale, a block of wood, and wedge that have masses of 1.00kg each.

    You place the wedge on the scale and of course, the scale reads 1.00kg.

    Next, you place the 1.00kg block on the wedge. What does the scale read now?

    Let's be even more specific. Let's say there are three cases: (a) the block sticks to the wedge, (b) the block slides down the wedge with a constant velocity, and (c) the block accelerates down the wedge.

    For those cases, would the scale read: (a) 2.00kg, (b) less than 2.00kg, or (c) more than 2.00kg?

    As always, explanations are more appreciated than answers.

    Enjoy!
    :-)


  • #54
    krd
    Banned (with Prison Access) Posts: 3,455 ✭✭✭krd


    Quiz #6

    In a way it is troubling.


    If the block and the wedge are at rest (a). Then the net weight will be 2kg.

    (b). In the real world the block can't slide down with a constant velocity. If it did have a constant velocity. The weight would be greater than 2kg.


    (c) As the block accelerates down the wedge, due to gravity, before it comes to rest the weight will be greater than 2kg.

    Sorry I haven't done any equations.

    Another way of looking at this - put a unicyclist on a weighing scale - and watch how the needle won't settle on a net weight as the unicyclist maintains their balance. In the real world it's impossible for them to get a perfect balance, where all forces are static.


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