To determine the equivalent temperature in Kelvin for water boiling at [tex]\( 212^{\circ} \text{F} \)[/tex], we need to use the conversion formula between Fahrenheit and Kelvin. The formula is:
[tex]\[ K = (F - 32) \times \frac{5}{9} + 273.15 \][/tex]
Let's break this down step-by-step:
1. Subtract 32 from the Fahrenheit temperature:
[tex]\[ 212 - 32 = 180 \][/tex]
2. Multiply the result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ 180 \times \frac{5}{9} = 100 \][/tex]
3. Add 273.15 to the result:
[tex]\[ 100 + 273.15 = 373.15 \][/tex]
Thus, the equivalent temperature of [tex]\( 212^{\circ} \text{F} \)[/tex] is [tex]\( 373.15 \, K \)[/tex]. When we look at the given choices:
A. [tex]\( 0 \, K \)[/tex]
B. [tex]\( 100 \, K \)[/tex]
C. [tex]\( 244 \, K \)[/tex]
D. [tex]\( 373 \, K \)[/tex]
E. [tex]\( 485 \, K \)[/tex]
The closest and correct equivalent temperature is [tex]\( 373 \, K \)[/tex], aligning with the result [tex]\( 373.15 \, K \)[/tex] we found in our step-by-step calculation. Therefore, the correct answer is:
D. [tex]\( 373 \, K \)[/tex]
