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Temperature change in Celsius from Fahrenheit value

  1. Dec 3, 2011 #1
    1. The problem statement, all variables and given/known data
    a) One day, the temperature outside changed by 13.7 degrees on a Fahrenheit thermometer. By how much did the temperature change on a Celsius thermometer?


    2. Relevant equations
    F = (9/5)C + 32

    3. The attempt at a solution
    F2 - F1 = 13.7
    (9/5)C2 + 32 -(9/5)C1 + 32 = 13.7
    (9/5)C2 - (9/5)C1 = -50.3
    (9/5)(C2 - C1) = -50.3
    (C2 - C1) = -27.94444444

    I thought change in anything was the difference between the final and initial values. Here I needed Celsius change so I used the difference in Conversion formula to relate Fahrenheit to Celsius. Any help with figuring out what I did wrong is appreciated!
     
  2. jcsd
  3. Dec 3, 2011 #2

    phyzguy

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    (a+b) - (c+d) = a + b - c - d, not a + b - c + d !!!
     
  4. Dec 3, 2011 #3

    SammyS

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    There is a short cut to this. 9 Fahrenheit degrees cover the same temperature span as 5 Celsius degrees. So you could simply take 5/9 of 13.7. This shows that your answer must be wrong.

    To see where you went wrong, see the parentheses in Red above.
     
  5. Dec 3, 2011 #4

    PeterO

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    You left out some brackets - simplest arithmetic error!!!

    F2 - F1 = 13.7
    (9/5)C2 + 32 -{(9/5)C1 + 32} = 13.7
    (9/5)C2 - (9/5)C1 = 13.7
    (9/5)(C2 - C1) = 13.7
    (C2 - C1) = you work out.

    Note: - I used a higher level of parentheses {} since the lowest level () was already in use.
     
  6. Dec 3, 2011 #5
    Thank you phyzguy and SammyS for responding. After taking into account about what you said, I realized that the 32s cancel themselves and ended up only needing to take 5/9 of 13.7. I got an answer of 7.61 Celsius degrees. Is this the correct?
     
  7. Dec 3, 2011 #6

    SammyS

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    That looks much better !
     
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