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experimentX

  • 2 years ago

You have 25 liters of water in bucket A and 25 in bucket B. The difference in temperature difference is 40K between them. Now if you take one liter from A to B and then from B to A (after mixing properly). What would be the temperature difference between A and B. If you do this activity 5 times what would be the final temperature difference. What would be temperature difference in 10 th time?

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  1. sauravshakya
    • 2 years ago
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    AFTER FIRST TIME THE DIFFERENCE WILL BE 36.92307692 K

  2. sauravshakya
    • 2 years ago
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    ACTUALLY I THINK I FOUND THE SERIES: t_0=40 t_1=40*(24/26)=40*(12/13) t_2=t_1*(12/13)=40*(12/13)^2 . . . t_n=40*(12/13)^n

  3. sauravshakya
    • 2 years ago
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    So, after five times, t_5=26.807 K AND AFTER 10 times, t_10=17.965 K

  4. Mikael
    • 2 years ago
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    I think both @demitris and @sauravshakya are almost excatly there. However neither of you guys has clearly A) stated B) Reasoned in explaining you respective \[ \Large\color{Magenta}{\text{Recursion Equation }} \\ \\ \\ Concentration(n+1) = \\\ =\Large{F}{(Concnetrat._{\,\,hotb}(n)\,\, , Concentrat. _{\,\,coldb}(n) )} \] Of course we mean concentration of heat. now \[ Heat.Concentrat. \,\,\sim\, Temperature \]

  5. Mikael
    • 2 years ago
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    We all understand that this is a kind of geometric decrease , yet you have endeavored to SOLVE it exactly.... Did you not ?

  6. Mikael
    • 2 years ago
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    @demitris and @sauravshakya

  7. Mikael
    • 2 years ago
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    The night was silent in fron of him ... \[ \Huge\color{green} {\underbrace{\ddot{}}} \]

  8. sauravshakya
    • 2 years ago
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    WASNT THE ANSWER GIVEN BY ME CORRECT

  9. sauravshakya
    • 2 years ago
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    @mikael

  10. experimentX
    • 2 years ago
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    not sure if that was correct ... I didn't have answer and don't remember my answer either. I had got the recursion relation. pretty close \[ t_n = {25 \over 26}t_{n-1}\]

  11. experimentX
    • 2 years ago
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    while demetris had got \[ t_n = {24 \over 25}t_{n-1}\] which is pretty close. probably weather you take from hot cold or cold to hot might make difference. Not sure though. If you are interested you can check.

  12. sauravshakya
    • 2 years ago
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    I solved it assuming the water is transferred from cold to hot and back from hot to cold.

  13. experimentX
    • 2 years ago
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    try assuming water is transferred from cold to hot and from hot to cold. also use 1 liter.

  14. sauravshakya
    • 2 years ago
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    U MEAN HOT TO COLD NOW?

  15. experimentX
    • 2 years ago
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    yep ... if results are symmetric then you must be correct.

  16. sauravshakya
    • 2 years ago
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    YEP GOT THE SAME SERIES.

  17. sauravshakya
    • 2 years ago
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    OK HERE IS MY METHOD. LET THE DIFFERENCE IN TEMPERATURE OF 25 liters of water in bucket A and 25 in bucket B be x KELVIN (ALSO LET A IS HOTTER THAN B).......ALSO LET TEMPERATURE OF BUCKET B BE y KELVIN THEN the temperature of bucket A is (y+x) kelvin NOW, FROM B TO A: WHEN 1 liter of water is transferred from B to A then, THE temperature of bucket B does not change but the temperature of bucket A changes. The temperature of bucket A will be (1*y+25*(y+x))/26 = y+25/26 x Now again 1 litre of water is transferred from bucket B to A.... THIS TIME the temperature of bucket A will remain constant but the temperature of bucket B will change: TEMPERATURE OF BUCKET B = {1*(y+25/26 x) + 24*y}/25 =y+(1/26)x NOW, DIFFERENCE IN TEMPERATURE=y+25/26 x -y-1/26x = 12/13 x

  18. sauravshakya
    • 2 years ago
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    WHICH CLEARLY SHOWS THAT temperature difference is in geometric series with common ratio 12/13

  19. sauravshakya
    • 2 years ago
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    GOT SAME RESULT WHEN ASSUMED WATER IS TRANSFERRED FROM A to B.

  20. experimentX
    • 2 years ago
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    worked out again and ... looks like both of you are right!! Help each other with medals.

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