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### Temperature Difference

```
Date: 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/
```
Associated Topics:
Middle School Temperature

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