Suppose you were dissatisfied with both Celsius andfarenheit units and wanted to

Question

Suppose you were dissatisfied with both Celsius andfarenheit units and wanted to design your own temperaturescale based on ethyl alcohol (ethanol). On the Celsius scale,ethanol has a melting point of -117.3 Celsius and the boiling pointof 78.5 Celcius, but on your new scale calibrated in units degreesethanol, E, you define ethanol to and melt at 0 E and boil at300 E. Question: 1. What does your ethanol degrees compare in size with aCelsius degrees? 2. What does an ethanol degrees compare in size with aFarenheit degress? 3. What are the melting and boiling points of water onthe ethanol scale? 4. What is the normal human body temperature (98.6 F) on theethanol scale? Suppose you were dissatisfied with both Celsius andfarenheit units and wanted to design your own temperaturescale based on ethyl alcohol (ethanol). On the Celsius scale,ethanol has a melting point of -117.3 Celsius and the boiling pointof 78.5 Celcius, but on your new scale calibrated in units degreesethanol, E, you define ethanol to and melt at 0 E and boil at300 E. Question: 1. What does your ethanol degrees compare in size with aCelsius degrees? 2. What does an ethanol degrees compare in size with aFarenheit degress? 3. What are the melting and boiling points of water onthe ethanol scale? 4. What is the normal human body temperature (98.6 F) on theethanol 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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