Algebra

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A temperature of 30 degrees F is equivalent to 271.89 degrees K, while a temperature of 94 degrees F is equivalent to 307.44 degrees K. Find the equation converting Kelvin temperature to Fahrenheit. What is the Fahrenheit temperature when it is 212 degrees K?

  • Algebra -

    Assume a linear relationship of:
    F=mK+b ....(1)
    where m=slope, and b=intercept.

    We have two given points, (271.89,30) and (307.44,94)

    The standard formula for m (slope) is:
    m=(y2-y1)/(x2-x1)=(94-30)/(307.44-271.89)=1.8
    With m=1.8, substitute one of the points into equation (1) to find b:
    30=1.8(271.89)+b
    b=30-1.8(271.89)=-459.4

    So the conversion equation is:
    F=1.8K-459.4

    I leave it to you to substitute K=212 in order to find the fahrenheit degrees.

  • Algebra -

    Let F = aK + b , (treating it like the linear equation y = mx + b)

    we have two points (271.89, 30) and (307.44, 94)
    a = slope = (94-30)/(307.44 - 271.89) = 64/35.55
    = 1.80028
    let's go with 1.8

    so F = 1.8K + b
    sub in (271.89,30) to find b
    30 = 1.8(271.89) + b
    b = -459.48

    F = 1.8K - 459.48
    so when K = 212
    F = 1.8(212) - 459.48 = -77.9° Fahrenheit

  • To MathMate - Algebra -

    What's that saying again, some kind of minds thinking alike ?? lol

  • Algebra -

    Great minds think alike! haha!

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