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Temperature Conversions

  1. Nov 17, 2013 #1

    Qube

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    On a new Jekyll temperature scale, water freezes at 17 degree(s) J and boils at 97 degree(s) J. On another new temperature scale, the Hyde scale, water freezes at 0 degree(s) oH and boils at 120 degree(s) oH. If methyl alcohol boils at 84 oH, what is its boiling point on the Jekyll scale?

    2. Relevant equations

    Jekyll has a FP 17 degrees higher than the Hyde scale.

    3. The attempt at a solution

    Alright. Freezing point on Jekyll is 17 degrees higher than it is on Hyde.

    Therefore, any formula relating J and H must have the general form of:

    J(H) = H + 17, where H = 0.

    The general formula is:

    J(H) = H[(97-17)/120] + 17

    Checking my work:

    H = 0, J = 17. Correct.

    H = 120. J = 97. Correct.

    What are some good ways of tackling this problem? Why does subtracting two points on the Jekyll scale divided by subtracting the two points on the Hyde scale multiplied by H work?
     
  2. jcsd
  3. Nov 19, 2013 #2

    DrClaude

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    Staff: Mentor

    The best way is to tackle this mathematically.

    You are looking for a formula of the form
    $$
    J(H) = a H + b
    $$
    (i.e., assuming that the two scales are linear).

    You then have
    $$
    J(0) = 17 = a \times 0 +b
    $$
    and
    $$
    J(120) = 97 = a \times 120 + b
    $$
    or, in other words, two equations with two unknowns. The first is easily solved for ##b = 17##, which allows you to solve the second for ##a##.
     
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