Question

C=

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:

$C=(F-32)\frac{5}{9}$    (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:

$F=(\frac{9}{5}C)+32$    (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 $1\ºF$:

$C=(1\ºF-32)\frac{5}{9}=-17.22\ºC$

This means: $1\ºF=-17.22\ºC$

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

$C=(2\ºF-32)\frac{5}{9}=-16.66\ºC$

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 $1\ºC$:

$F=(\frac{9}{5}1\ºC)+32$  

$F=33.8\ºF$  

This means: $1\ºC=33.8\ºF$  

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

$F=(\frac{9}{5}2\ºC)+32$  

$F=35.67\ºF$  

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 $1\ºC$:

$F=(\frac{9}{5}1\ºC)+32$  

$F=33.8\ºF$  

This means: $1\ºC=33.8\ºF$  

Now we are going to add $\frac{5}{9}\ºF$:

$33.8\ºF+\frac{5}{9}\ºF=34.35\ºF$

And use this value in the Celsius formula:

$C=(34.35\ºF-32)\frac{5}{9}=1.30\ºC$

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.