Temperature DifferenceDate: 05/20/99 at 07:54:52 From: Tim Davis Subject: Temperature Is it possible for 44 degrees centigrade to equal 80 degrees fahrenheit when you are talking temperature difference? I have a friend who says they are the same, but I say 44 C is equal to 111.2 F at any time. Could you help on this one? Date: 05/21/99 at 14:07:27 From: Doctor Fwg Subject: Re: Temperature Dear Tim, Thank you for sending this interesting question. It is true that one may use the formula: F = (9/5)C + 32 to convert temperatures is degrees C to equivalent temperatures in degrees F, and vice versa. However, to calculate temperature differences, you might write the following equations: Fo = (9/5)Co + 32 and F = (9/5)C + 32, where the Fo and F are two Fahrenheit temperatures and Co and C are the two equivalent Celsius temperatures. So, to find the temperature differences you might write: (F - Fo) = [(9/5)C + 32] - [(9/5)Co + 32] = (9/5)(C - Co) = (9/5)(C - Co) Do you see that the constant term "32" subtracts out? From this you can see that when converting temperature differences from one of these systems to the other, you only need to divide or multiply by (9/5) or 1.8. However, if you are interested in calculating a specific temperature the "32" must be used. In other words, your initial guess was wrong because you applied the equation: F = (9/5)C + 32 to convert a temperature difference in degrees C to a specific temperature in degrees F. You can only use this equation to convert from one specific temperature to another specific temperature. For example, using this formula you can show that the specific temperature of 0.0 C equals 32 F, or that the specific temperature of 100 C equals 212 F. However, a temperature difference of 100 degrees on the Celsius scale is the same as a temperature difference of 180 F on the Fahrenheit scale. So, your friend was right, a temperature difference of 44 C is nearly equal to a Fahrenheit temperature difference of 80 F (more precisely, a temperature difference of exactly 44.0 C is equivalent to a Fahrenheit temperature difference of exactly 79.2 F). I hope this has been helpful to you and now that you understand it I hope you will explain this to at least one other interested person. With best wishes, - Doctor Fwg, The Math Forum http://mathforum.org/dr.math/ |
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