Sure, let's go through the steps to convert 298 Kelvin to degrees Fahrenheit.
1. Understand the given equations:
- [tex]\( T_F = 1.8 T_C + 32 \)[/tex]
- [tex]\( K = T_C + 273 \)[/tex]
2. Begin with the given temperature in Kelvin:
- [tex]\( K = 298 \)[/tex]
3. Convert Kelvin to Celsius:
- Using the equation [tex]\( K = T_C + 273 \)[/tex], we solve for [tex]\( T_C \)[/tex]:
[tex]\[
T_C = K - 273
\][/tex]
Substituting the given Kelvin value:
[tex]\[
T_C = 298 - 273 = 25
\][/tex]
So, the temperature in Celsius is 25 degrees.
4. Convert Celsius to Fahrenheit:
- Using the equation [tex]\( T_F = 1.8 T_C + 32 \)[/tex], we substitute the Celsius value:
[tex]\[
T_F = 1.8 \times 25 + 32
\][/tex]
[tex]\[
T_F = 45 + 32 = 77.0
\][/tex]
So, the temperature in Fahrenheit is 77.0 degrees.
5. Round the result to the nearest whole number:
- The decimal value 77.0 is already a whole number.
Therefore, the temperature converted from 298 Kelvin to Fahrenheit, rounded to the nearest whole number, is [tex]\( \boxed{77} \)[/tex].
