To solve the temperature conversion problem presented, which starts with a temperature in Fahrenheit (87.1°F) and aims to convert it to Kelvin (K), follow these detailed steps:
1. Convert Fahrenheit (°F) to Celsius (°C):
The formula to convert Fahrenheit to Celsius is:
[tex]\[
\text{Temp}_\text{Celsius} = (\text{Temp}_\text{Fahrenheit} - 32) \times \frac{5}{9}
\][/tex]
Substituting 87.1°F into the formula:
[tex]\[
\text{Temp}_\text{Celsius} = (87.1 - 32) \times \frac{5}{9}
\][/tex]
Calculate the value inside the parentheses first:
[tex]\[
87.1 - 32 = 55.1
\][/tex]
Then multiply by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
55.1 \times \frac{5}{9} \approx 30.61111111111111
\][/tex]
Therefore, 87.1°F is approximately 30.61°C.
2. Convert Celsius (°C) to Kelvin (K):
The formula to convert Celsius to Kelvin is:
[tex]\[
\text{Temp}_\text{Kelvin} = \text{Temp}_\text{Celsius} + 273.15
\][/tex]
Using the previously calculated value of 30.61°C:
[tex]\[
\text{Temp}_\text{Kelvin} = 30.61 + 273.15
\][/tex]
Perform the addition:
[tex]\[
30.61111111111111 + 273.15 \approx 303.76111111111106
\][/tex]
Therefore, 87.1°F is approximately 303.76K.
By following these two conversion steps, you can accurately convert a temperature from Fahrenheit to Kelvin.
