#1. Suppose you were dissatisfied with both Celsius and Fahrenheit units and wan

Question

#1. Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of -117.3?C and a boiling point of 78.5 ?C, but on your new scale calibrated in units of degrees ethanol, ?E , you define ethanol to melt at 0 ?E and boil at 100?E. How does your ethanol degree compare in size with a Celsius degree? How does an ethanol degree compare in size with a Fahrenheit degree? What are the melting and boiling points of water on the ethanol scale? What is normal human body temperature (98.6 ?F) on the ethanol scale?

Explanation / Answer

1) size E = (300 - 0)/[78.5 - (-117.3)] *size of C

size E = 1.53* size of C

E degree is about 1.5 times the size of C

2) F = (9/5)*C + 32

So F is 9/5 the size of C.

size E = 1.53*(5/9)*size F = 0.846 size of F

3)

E - 300 = 1.53*(C -78.5)          (pointslope form from your algebra class)
E = 1.53*C + 180

water boils at 100C. It melts at 0 C

E_water melt = 180 E
E_water boil = 1.53*100 + 180 = 333

4)

E = 1.53*C + 180
F = (9/5)*C + 32 => C = [5/9]*(F-32)

E = 1.53*(5/9)*[F-32] + 180
F = 98.6

E = 1.53*(5/9)*[98.6-32] + 180 = 236.61

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