Derive temp conversion formula

[briteliner]

Homework Statement

the fahrenheit temp scale is defined to that ice melts at 32 F and water boils at 212 F. Derive formulas for converting fahrenheit to celsius and back.

Homework Equations

c=5/9(f-32)

The Attempt at a Solution

ok so i figured that 212-32= 180
and
100-0=100
so the ratio of c/f= 5/9
i don't know how to get the 32 part into the equation

 

[Dick]

0C=32F. So a fahrenheit temperature f is (f-32) fahrenheit degrees above 0C. Now just convert the (f-32) fahrenheit degrees to celsius degrees.

 

[thomate1]

Great job on recognizing the ratio of 5/9 for converting between Fahrenheit and Celsius! To incorporate the 32 part into the equation, we can use the fact that 32 degrees Fahrenheit is equivalent to 0 degrees Celsius. So, if we subtract 32 from both sides of the equation, we get:

c-32=5/9(f-32)

This gives us the formula for converting Fahrenheit to Celsius. To derive the formula for converting Celsius to Fahrenheit, we can rearrange the equation to solve for f:

f=(9/5)c+32

This formula can be used to convert Celsius to Fahrenheit. Keep in mind that when using these formulas, it is important to keep track of which unit you are starting with and which unit you want to end with. For example, if you are starting with a temperature in Fahrenheit and want to convert it to Celsius, you would use the first formula. But if you are starting with a temperature in Celsius and want to convert it to Fahrenheit, you would use the second formula.