Question

The temperature T(d) in degrees Fahrenheit in terms of the Celsius temperature d is given by T(d) = 9/5 * d + 32

The temperature C(v) degrees Celsius in terms of the Kelvin temperature by C(v) = v - 273
Write a formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature
It is not necessary to simplify

Answer 1

`\displaystyle F(v) = (9)/(5)(v-273)+32`

Explanation:

The temperature T(d) in degrees Fahrenheit in terms of Celsius d is given by:

`\displaystyle T(d)=(9)/(5)d+32`

And the temperature C(v) in degrees Celsius in terms of Kelvin v is given by:

`C(v)=v-273`

We want the formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature.

So, we can use a composition of functions. Since T(d) outputs the temperature in Fahrenheit and C(v) inputs the temperature in Kelvin, T(C(v)) will be the temperature in Fahrenheit given the temperature in Kelvin. So:

`\displaystyle T(C(v))=(9)/(5)(C(v)))+32`

Substitute:

`\displaystyle T(C(v)) = F(v) = (9)/(5)(v-273)+32`

Therefore:

`\displaystyle F(v) = (9)/(5)(v-273)+32`