# Temperature change in Celsius from Fahrenheit value

• rubenhero
In summary, on a Fahrenheit thermometer, the temperature changed by 13.7 degrees. On a Celsius thermometer, the temperature changed by -50.3 degrees.
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 !

rubenhero said:

## 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.

rubenhero said:

## 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.

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?

rubenhero said:
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?

That looks much better !

## What is the formula for converting from Fahrenheit to Celsius?

The formula for converting from Fahrenheit to Celsius is: (°F - 32) * 5/9 = °C

## How do I convert a Fahrenheit temperature to Celsius?

To convert a Fahrenheit temperature to Celsius, you can either use the formula (°F - 32) * 5/9 = °C or use an online temperature conversion tool.

## What is the freezing point of water in Celsius?

The freezing point of water in Celsius is 0°C.

## What is the boiling point of water in Celsius?

The boiling point of water in Celsius is 100°C.

## Why do different countries use different temperature scales?

Different countries use different temperature scales because they were developed at different times and in different regions of the world. Fahrenheit was developed in Germany in the early 18th century, while Celsius was developed in Sweden in the mid 18th century. The United States, which uses Fahrenheit, has not officially adopted the metric system like many other countries, which use Celsius.

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