My Math Forum temperature problem

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 March 1st, 2016, 07:32 PM #1 Senior Member     Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18 temperature problem Temperatures can vary widely in the American Midwest in spring. One day in Indianapolis, the temperature changes from 41 degrees Fahrenheit to 82 degrees Fahrenheit in 6 hours. Jeffrey said, "That means it's now twice as warm as it was this morning!" Is he correct? Explain. Would Jeffrey be able to say the same thing if the temperature were converted to Celsius? Explain. Thanks from Cheska Marie Letegio
 March 1st, 2016, 07:37 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 Have you made any progress on the problem? Usually you post your working.
March 1st, 2016, 08:11 PM   #3
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Quote:
 Originally Posted by Azzajazz Have you made any progress on the problem? Usually you post your working.
This is just a reasoning question. How can someone post his/her working in such a case? Maybe shunya can tell what he/she thinks.

 March 1st, 2016, 08:35 PM #4 Senior Member   Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230 Sure 82℉ is twice as far away from the arbitrary point 41℉, but what does that actually mean? Using absolute zero (total absence of energy in form of heat), your numbers actually mean something and doubling any temperature in Kelvin will be twice as warm. You can't say the same for any other (relative) scale like ℃ or ℉. Just as October 10th is not more "octobery" than October 5th.
 March 2nd, 2016, 01:42 AM #5 Senior Member     Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18 Azzajazz & Prakhar I actually don't know where to begin answering this question. Well, to draw an analogy... If a given line AB is 4 cm and another line CD is 8 cm, it is valid to say that CD is twice as long as AB. Then I think Jeffrey is right in claiming it has become twice as warm. Am I correct? Thanks from topsquark
 March 2nd, 2016, 02:59 AM #6 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,834 Thanks: 650 Math Focus: Yet to find out. Nice analogy! And it makes sense for the first part of the question. Have you tried converting the given temperatures to Celsius yet?
March 2nd, 2016, 04:43 AM   #7
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Quote:
 Originally Posted by shunya Temperatures can vary widely in the American Midwest in spring. One day in Indianapolis, the temperature changes from 41 degrees Fahrenheit to 82 degrees Fahrenheit in 6 hours. Jeffrey said, "That means it's now twice as warm as it was this morning!" Is he correct? Explain. Would Jeffrey be able to say the same thing if the temperature were converted to Celsius? Explain.
I think the question is testing you on the difference between interval and ratio variables. Fahrenheit and Celsius temperatures are both interval variables; it doesn't makes sense to say it's twice at hot. That only works for temperatures in Kevin, which is a ratio variable.

March 2nd, 2016, 06:41 AM   #8
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Quote:
 Originally Posted by 123qwerty I think the question is testing you on the difference between interval and ratio variables. Fahrenheit and Celsius temperatures are both interval variables; it doesn't makes sense to say it's twice at hot. That only works for temperatures in Kevin, which is a ratio variable.
Exactly. when measuring the temperature in Kelvin we have an absolute scale. At 0 degrees kelvin, no atoms are vibrating.

The centigrade scale measures from 0 - 100 (freezing - boiling point of water). The Celsius scale, is essentially the same as Centigrade, albeit can go below 0 and above 100.

Fahrenheit, the freezing point of water is 32 and boiling point is 212. This wiki article is quite good and shows the different conversions: https://en.wikipedia.org/wiki/Fahrenheit

 March 9th, 2016, 07:17 PM #9 Newbie   Joined: Mar 2016 From: Philippines Posts: 2 Thanks: 0 i still find it hard to understand temperature problem that's why i cannot answer it sometimes.

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