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?

Homework Equations

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!

 

[phyzguy]

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

 

[SammyS]

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?

Homework Equations

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.

 

[PeterO]

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?

Homework Equations

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?

 

[SammyS]

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 !