What is the temperature at which Fahrenheit and Celsius are equal?

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Discussion Overview

The discussion revolves around the question of at what temperature the Fahrenheit and Celsius scales have the same numerical value. Participants explore the mathematical relationship between the two temperature scales, focusing on the conversion formula and the algebraic steps to find the solution.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how the answer of -40 was established after working on physics problems.
  • Another participant suggests that the solution involves equating the temperature in one scale to the conversion formula of the other scale.
  • A third participant emphasizes that the problem is straightforward algebra, requiring minimal physics knowledge, and mentions key reference points for the temperature scales.
  • A later reply provides the conversion formula and demonstrates the algebraic steps leading to the conclusion that -40 degrees is the temperature where both scales are equal.

Areas of Agreement / Disagreement

Participants generally agree on the method to find the temperature where Fahrenheit and Celsius are equal, but there is no explicit consensus on the clarity of the initial question or the ease of the solution.

Contextual Notes

Some participants assume familiarity with algebra and the temperature conversion formula, which may not be universally understood. The discussion does not resolve any potential confusion regarding the initial question posed.

Dan Monaghan
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I'm doing some problems for physics at the end of one the chapters and I get to a question that asks
"At what temperature does Fahrenheit and Celsius have the same numerical value?"

Now the answer is -40, but I'm not sure how this answer was established. Between class, lab and study time, I've been pouring over physics for the last 7 hours and I'm toasted. I have a feeling that the answer is pretty simple, but I can't seem to get it. Does anybody have any answers?
 
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Well you just have to equate the temperature in one scale to the formula for conversion in the other scale and solve the unknown, right?
 
from Dan Monaghan:
I get to a question that asks
"At what temperature does Fahrenheit and Celsius have the same numerical value?"

That is simple first-year high school Algebra. You barely need any physics knowledge at all. F: fahrenheit, water boils at ~212, freezes at ~32. C: Celsius, water boils at 100, freezes at 0. Find the linear equation.
 
F = (9/5)C + 32
We're looking for an F where F = C, so

F = (9/5)F + 32

-(4/5)F = 32

F = -32 * 5/4

F = -40

So at -40 degrees the Celsius value is the same as the Fahrenheit value.
 

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