Question

C=

5
9
(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only

Answer 1

Right answer: I and II only

If we already have the formula to find how temperature measured in degrees Fahrenheit, relates to a temperature in degres Celsius:

`C=(F-32)(5)/(9)` (1)

We can know the formula to find how temperature measured in degrees Celsius, relates to a temperature in degres Fahrenheit, only by isolating F:

`F=((9)/(5)C)+32` (2)

Having both formulas, let’s begin:

I) If we want to prove that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius:

Beginning with
`1\ºF`:

`C=(1\ºF-32)(5)/(9)=-17.22\ºC`

This means:
`1\ºF=-17.22\ºC`

Now we are going to increase 1 degree Farenheit. In other words, we are going to use
`2\ºF`:

`C=(2\ºF-32)(5)/(9)=-16.66\ºC`

This means:
`2\ºF=-16.66\ºC`

Calculating the difference between
`-16.66\ºC` and
`-17.22\ºC`:

`-16.66\ºC-(-17.22\ºC)=0,55\ºC`>>>>This is equal to 5/9 degree Celsius, hence is correct

II) If we want to prove that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit:

Beginning with
`1\ºC`:

`F=((9)/(5)1\ºC)+32`

`F=33.8\ºF`

This means:
`1\ºC=33.8\ºF`

Now we are going to increase 1 degree Celsius. In other words, we are going to use
`2\ºC`:

`F=((9)/(5)2\ºC)+32`

`F=35.67\ºF`

This means:
`2\ºC=35.67\ºF`

Calculating the difference between
`35.67\ºF` and
`33.8\ºF`:

`35.67\ºF-33.8\ºF=1.8\ºF`>>>>This is a proof of the statement, hence is also correct.

III) If we want to prove that a temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius:

Beginning with
`1\ºC`:

`F=((9)/(5)1\ºC)+32`

`F=33.8\ºF`

This means:
`1\ºC=33.8\ºF`

Now we are going to add
`(5)/(9)\ºF`:

`33.8\ºF+(5)/(9)\ºF=34.35\ºF`

And use this value in the Celsius formula:

`C=(34.35\ºF-32)(5)/(9)=1.30\ºC`

This means:
`1.30\ºC=34.35\ºF`

In other words: An increase in 5/9 degree Fahrenheit is equivalent to a temperature increase of 1.30 degree Celsius, not 1 degree Celsius.

Therefore this statement is incorrect.