Answer :
Final Answer:
The estimated temperature in Kelvin at which the reading is one-fourth on the Fahrenheit scale is approximately 230 K.
Comparing this estimate with the given options, the closest one is: b) 225 K
Therefore, the final answer is: b) 225 K.
Explanation:
To estimate the temperature at which the reading in the Kelvin scale is one-fourth on the Fahrenheit scale, let's consider the relationship between these temperature scales.
The conversion formula from Fahrenheit (F) to Kelvin (K) is:
[tex]\[ K = \dfrac{5}{9} (F - 32) + 273.15 \][/tex]
Given that the reading in Kelvin (K) is one-fourth of the reading on the Fahrenheit (F) scale, we can set up the equation:
[tex]\[ \dfrac{1}{4} F = K \][/tex]
Now, we'll use the conversion formula to find the corresponding Kelvin temperature:
[tex]\[ K = \dfrac{5}{9} \left(\dfrac{1}{4} F - 32\right) + 273.15 \][/tex]
To simplify, let's find the temperature at which the Fahrenheit reading is 1:
[tex]\[ K = \dfrac{5}{9} \left(1 - 32\right) + 273.15 \][/tex]
[tex]\[ K = \dfrac{5}{9} \times (-31) + 273.15 \][/tex]
[tex]\[ K = \dfrac{5}{9} \times (-31) + 273.15 \][/tex]
[tex]\[ K \approx 229.817 \][/tex]
So, the estimated temperature in Kelvin at which the reading is one-fourth on the Fahrenheit scale is approximately 230 K.
Comparing this estimate with the given options, the closest one is:
b) 225 K
Therefore, the final answer is:
b) 225 K
Final Answer:
The temperature at which the reading in the Kelvin scale is one-fourth on the Fahrenheit scale is option d) 375 K.
Explanation:
To find the temperature in Kelvin when it's one-fourth on the Fahrenheit scale, we first convert one-fourth of the Fahrenheit scale to Kelvin. The Fahrenheit scale has 180 degrees between freezing and boiling points of water, while the Kelvin scale has 100 degrees between these points. Therefore, each degree Fahrenheit is equivalent to 5/9 degrees Kelvin. One-fourth of the Fahrenheit scale is 1/4 * 180°F = 45°F. Converting this to Kelvin, we get (45°F - 32) * (5/9) = 7.22 K. Finally, we add this value to absolute zero (0 K) to get the final temperature in Kelvin, which is 375 K.
In this problem, we first calculate the temperature difference between freezing and boiling points of water on the Fahrenheit scale, which is 180°F. Then, we find one-fourth of this value, which is 45°F. By converting this value to Kelvin using the conversion factor of 5/9, we obtain 7.22 K. Finally, adding this value to absolute zero, we arrive at the temperature of 375 K. Therefore, option d) 375 K is the correct answer.
The conversion between Fahrenheit and Kelvin scales involves adjusting for the different intervals between the freezing and boiling points of water. The Kelvin scale is based on absolute zero, while the Fahrenheit scale is based on the freezing and boiling points of water. Therefore, a conversion factor is applied to ensure accuracy when converting temperatures between these scales( option d).
