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Converting between a known and unknown temperature scale

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data

    On a Temperature scale, the ice point is 25.6°I and the steam point is 155°I. If the temperature reads 66.6°I what is the equivalent in °C?


    3. The attempt at a solution

    25.6°I = 0°C

    155°I = 100°C

    1°I = 5/647 of the interval between boiling and freezing.

    1C° = 647/500 I°

    1I° = 500/647C°

    66.6°I = 51.5°C

    I arrive at this answer but i'm not convinced i've done this correctly. When changing from faranheit to celsius for example, I have to subtract the offset from zero...

    So should my answer actually be 51.5 - 25.6 °C?

    I'd really appreciate some help,

    thanks!
     
  2. jcsd
  3. Oct 15, 2013 #2

    DrClaude

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    Staff: Mentor

    That's not correct. And I don't understand where you get fractions like 5/647.

    I think that an easier way to do the problem is to try to solve for the formula
    $$
    a T_I + b = T_C,
    $$
    where ##T_I## is the temperature in °I and ##T_C## is the temperature in °C. Using the data you have, that gives you two equations for two unknowns (##a## and ##b##).
     
  4. Oct 15, 2013 #3

    DrClaude

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    Staff: Mentor

    After recalculating a few things, I find that
    is correct. The problem is the shifting of the scale. Neither
    nor
    are correct.
     
  5. Oct 15, 2013 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Note that Dr. Claude is using the fact that the relation between the two temperature scales is linear- one degree Celcius converts to the same number of degrees Farenheit, and vice-versa, at any temperature.
     
  6. Oct 15, 2013 #5
    When converting between faranheit and celsius, we say that 1°F = 1/180 of the interval between the boiling and freezing point.

    Compared to the 1/100 of the interval that 1°C expresses.

    9/5 of a degree faranheit is equivalent to 1 degrees celsius.

    It was this method I was trying to use that gave me those strange fractions...

    I haven't seen the method you are talking about before, please could you apply it to something so I can see what you mean?
     
  7. Oct 15, 2013 #6

    DrClaude

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    Staff: Mentor

    Right. It is implicit in the problem. Good of you for pointing this out.
     
  8. Oct 15, 2013 #7
    Ok,

    I think this makes sense to me, I hope it does to you.

    °C = ([°I] - 25.6) x 500/647

    giving me the answer that 66.6°I = 31.7°C
     
  9. Oct 15, 2013 #8

    DrClaude

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    Staff: Mentor

    Edit: You got the correct answer in the previous post while I was typing the following. I'll leave it in case someone else has a similar problem.

    Lets say we want to rederive the conversion from Fahrenheit to Celcius. Take

    freezing point: 32 °F = 0 °C
    boiling point: 212 °F = 100 °C

    We look for an equation of the type
    $$
    a T_F + b = T_C
    $$
    For the values above
    $$
    a \times 32 + b = 0 \\
    a \times 212 + b = 100
    $$
    From the first equation, we have ##b = -32 a##. Using that in the second equation, we get
    $$
    212 a - 32 a = 100 \Rightarrow a = \frac{100}{180} = \frac{5}{9}
    $$
    and ##b = -160 / 9##. So
    $$
    \frac{5}{9} T_F - \frac{160}{9} = T_C
    $$

    I realize now that this is not the usual formula. You should therefore try it yourself using
    $$
    \left( T_F + a \right) \times b = T_C
    $$
    to get the factors you know. You can then do the same for your problem.
     
  10. Oct 15, 2013 #9

    DrClaude

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    Staff: Mentor

    Correct!
     
  11. Oct 15, 2013 #10
    Thank you for the help
     
  12. Apr 23, 2017 #11
    IMG_2247.JPG This is a detailed explanation on how to solve this problem and solve any problem based on temperature scale conversion. It's very easy. Hope it helps. I AM THE ONE WHO KNOCKS.
     
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