# Temperature change in Celsius from Fahrenheit value

rubenhero

## Homework Statement

a) One day, the temperature outside changed by 13.7 degrees on a Fahrenheit thermometer. By how much did the temperature change on a Celsius thermometer?

F = (9/5)C + 32

## The Attempt at a Solution

F2 - F1 = 13.7
(9/5)C2 + 32 -(9/5)C1 + 32 = 13.7
(9/5)C2 - (9/5)C1 = -50.3
(9/5)(C2 - C1) = -50.3
(C2 - C1) = -27.94444444

I thought change in anything was the difference between the final and initial values. Here I needed Celsius change so I used the difference in Conversion formula to relate Fahrenheit to Celsius. Any help with figuring out what I did wrong is appreciated!

(a+b) - (c+d) = a + b - c - d, not a + b - c + d !

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## Homework Statement

a) One day, the temperature outside changed by 13.7 degrees on a Fahrenheit thermometer. By how much did the temperature change on a Celsius thermometer?

F = (9/5)C + 32

## The Attempt at a Solution

F2 - F1 = 13.7
(9/5)C2 + 32 -((9/5)C1 + 32) = 13.7
(9/5)C2 - (9/5)C1 = -50.3
(9/5)(C2 - C1) = -50.3
(C2 - C1) = -27.94444444

I thought change in anything was the difference between the final and initial values. Here I needed Celsius change so I used the difference in Conversion formula to relate Fahrenheit to Celsius. Any help with figuring out what I did wrong is appreciated!
There is a short cut to this. 9 Fahrenheit degrees cover the same temperature span as 5 Celsius degrees. So you could simply take 5/9 of 13.7. This shows that your answer must be wrong.

To see where you went wrong, see the parentheses in Red above.

Homework Helper

## Homework Statement

a) One day, the temperature outside changed by 13.7 degrees on a Fahrenheit thermometer. By how much did the temperature change on a Celsius thermometer?

F = (9/5)C + 32

## The Attempt at a Solution

F2 - F1 = 13.7
(9/5)C2 + 32 -(9/5)C1 + 32 = 13.7
(9/5)C2 - (9/5)C1 = -50.3
(9/5)(C2 - C1) = -50.3
(C2 - C1) = -27.94444444

I thought change in anything was the difference between the final and initial values. Here I needed Celsius change so I used the difference in Conversion formula to relate Fahrenheit to Celsius. Any help with figuring out what I did wrong is appreciated!

You left out some brackets - simplest arithmetic error!

F2 - F1 = 13.7
(9/5)C2 + 32 -{(9/5)C1 + 32} = 13.7
(9/5)C2 - (9/5)C1 = 13.7
(9/5)(C2 - C1) = 13.7
(C2 - C1) = you work out.

Note: - I used a higher level of parentheses {} since the lowest level () was already in use.

rubenhero
Thank you phyzguy and SammyS for responding. After taking into account about what you said, I realized that the 32s cancel themselves and ended up only needing to take 5/9 of 13.7. I got an answer of 7.61 Celsius degrees. Is this the correct?

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