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2 way equation? (which is right?)

  1. Apr 17, 2003 #1
    2 way equation??!! (which is right?)

    I'm used to the formula(for converting celcius in to farenhiet):
    c=f+ 30 x 2. BUT, in some book (call it book B), its different. You just use F= 9/5 (C-32) and replace C with the given celcius temprature and multiply every thing by 9/5. Anyhow, I used both formulas, and got 2 different answers (and checked my work). Personally, I think the way book B put it doesn't make sense. If it makes sense to you, please explain.
     
  2. jcsd
  3. Apr 17, 2003 #2

    HallsofIvy

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    Either you have a whole stack of books that should be thrown out or you are not reading them very closely. Both formulas are wrong!

    For one thing you must surely know that 0 degrees Celcius is 32 degrees Fahrenheit so you can use that as a check:
    Using your formula: c=f+ 30 x 2 (as you wrote it) f= 32 would give c= 32+ 60= 96! Of course, you really meant c= (f+32)*2 but that would be 64*2= 128 which is even worse! c= (f-32)*2 would give c=0 for f= 32 but gives c= (212-32)*2= 180*2= 360 degrees for the boiling point of water when it should be 100 degrees.

    The formula you give for "book B":F= 9/5 (C-32) is almost exactly backwards: it should be C= (5/9)(F-32) (or F= (5/9)C + 32) so that when F= 32, C= 0 and when F= 212, C= (5/9)(180)= 5(20)= 100 degrees.
     
  4. Apr 17, 2003 #3
    These formulas are incompatible. Surely you mean F = (9/5)C +32???
     
  5. Apr 17, 2003 #4
    what i learn also F=(9/5)C + 32 F
    when C = -40....F= -40 also...
    and use calculator can get the same answer
     
  6. Apr 17, 2003 #5
    Let me (try to) make everything clear.
    Take two test points :
    0 C 32 F
    100 C 212 F
    X C Y F
    (Tell me if my test points are wrong, i am not familiar with the fahrenhite system)
    Now, try to solve the problem

    Now, we know that the relation between X and Y is linear, so :
    Y=aX+b
    Apply this to the two test points
    32=a*0+b
    so ... b=32
    Apply this to the second test point
    212=a*100+32
    (212-32)/100=a
    a=1.8
    So:
    Y=1.8*X+32
    or (the way people understand it more)
    F = 1.8C + 32

    And this is the right equation (isn't it ?)
     
  7. Apr 17, 2003 #6
    ^Yes.
     
  8. Apr 17, 2003 #7

    Integral

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    I frequently use an approximation which resembles VMs first equation

    C= (F-32)/1.8 ~ (F-30)/2

    or
    F= (1.8C)+32 ~ (2C)+30

    The last of those relationships is much easier to do in your head and for normal temps is pretty close.

    edit: opps! I fixed a sign error in the last line
     
    Last edited: Apr 18, 2003
  9. Apr 18, 2003 #8
    Here's what book A says:
    "We frequently want to convert from one scale to another, so we need a convenient formula to help us with the conversion. The formula C= 5/9 (F-32) shows us the relationship between Celsius and Fahrenheit and allows us to change form one scale or another.
    Example one:
    Change 77 degrees Fahrenheit to Celsius.

    Analysis:
    Let F= the Fahrenheit temprature
    Let C= the Celsius temprature

    We'll use our formula and then simply substitute 77 for F.

    Work:
    C=5/9(F-32) F=77:
    C=5/9(77-32)
    C=5/9(45)
    C=25
    answer: 25 degrees Celsius"

    "Example 2:
    Find the Fahrenheit equivalent of 55 degrees Celsius.

    Analysis:"
    F= Fahrenheit
    C= Celsius
    "Use the same formula and then just substitue 55 for Celsius.

    Work:
    C= 5/9(F-32) C=55:
    55=5/9(F-32)

    Multiply by 9/5: 9/5(55=5/9(F-32)
    99=F-32
    Add 32: 131=F"



    And Book B:

    "F= 9/5C+ 32" (the book basically tells you to solve for C)."

    "You can estimate temprature in degrees Fahrenheit by the formula
    F=2 x C+30"
     
  10. Apr 18, 2003 #9

    HallsofIvy

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    And neither of those is what you gave in your original post!

    (And, yes, I mistyped "9/5" for "5/9" myself earlier.")
     
  11. Apr 20, 2003 #10
    *Slaps head* Ahh!! Stupidity Strikes Again!! tsk, tsk, tsk...
    Forgive my folly.
     
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