At what temperature are the Celsius and Fahrenheit readings equal? QUESTION: At what temperature are the Celsius and Fahrenheit readings equal? A. –40o, B. 32o, C. 100o, D. 212o Freezing point of water: 0oC or 32oF Boiling point of water: 100oC or 212oF Celsius-to-Fahrenheit: F = 1.8C + 32 Let x=F=C x = 1.8x + 32 -0.8x = 32 x = 32/(-0.8) = -40 At what temperature are the Celsius and Fahrenheit readings equal? A. –40o, B. 32o, C. 100o, D. 212o PAUSE We eliminate choices B, C, and D immediately. CLICK We know that freezing point of water is at 0 degrees Celsius, which is equivalent to 32 degrees fahrenheit. Therefore 32 degrees celsius and 32 degrees fahrenheit do not refer to the same temperature. CROSS OUT CHOICE B CLICK We also know that water boils at 100 degrees Celsius, which is equivalent to 212 degrees fahrenheit. Therefore 100 degrees correspond to different temperatures on the two scales. CROSS OUT CHOICE C Similarly, 212 degrees also correspond to different temperatures on the two scales. Therefore, the correct answer is A.... a reading of –40 degrees means the same temperature on either scale. Let’s verify that this is, indeed, the case. CLICK Here’s the formula relating celsius and fahrenheit readings. Let x be the reading on both scales that correspond to the same temperature. This means that x is equal to both F and C in the formula Plugging in x for F and C, we get CLICK x equals 1.8 times x plus 32 ...Subtracting 1.8x from both sides, we get CLICK -0.8x equals 32 Solving for x, we get CLICK x equals 32 divided –0.8, which is equal to –40. Note that since 1.8 and 32 are exact numbers, our answer here is also an exact number. CLICK PAUSE END RECORDING

Video ID: 1A-6-3 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08