To find a formula for the temperature [tex]\( F(v) \)[/tex] in degrees Fahrenheit given the temperature [tex]\( v \)[/tex] in Kelvin, we will combine the two given formulas.
1. Temperature Conversion from Celsius to Fahrenheit:
The formula given is:
[tex]\[ T(d) = \frac{9}{5} d + 32 \][/tex]
This states that the temperature [tex]\( T(d) \)[/tex] in Fahrenheit can be found from the Celsius temperature [tex]\( d \)[/tex] by the above relation.
2. Temperature Conversion from Kelvin to Celsius:
The formula given is:
[tex]\[ C(v) = v - 273 \][/tex]
This tells us that to convert a temperature [tex]\( v \)[/tex] in Kelvin into Celsius, you subtract 273.
3. Combining the Formulas:
To express Fahrenheit directly in terms of Kelvin, we need to substitute the Celsius formula into the Fahrenheit formula.
Start with:
[tex]\[ d = C(v) \][/tex]
Substitute [tex]\( d \)[/tex] with [tex]\( v - 273 \)[/tex] (from the Kelvin to Celsius conversion):
[tex]\[ d = v - 273 \][/tex]
Now place this into the Celsius to Fahrenheit formula [tex]\( T(d) \)[/tex]:
[tex]\[ T(d) = \frac{9}{5} d + 32 \][/tex]
Since [tex]\( d = v - 273 \)[/tex], substitute [tex]\( d \)[/tex]:
[tex]\[ T(v-273) = \frac{9}{5} (v - 273) + 32 \][/tex]
Therefore, the formula for the temperature [tex]\( F(v) \)[/tex] in degrees Fahrenheit in terms of Kelvin temperature [tex]\( v \)[/tex] is:
[tex]\[ F(v) = \frac{9}{5} (v - 273) + 32 \][/tex]
