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Estimate the temperature at which the reading in the Kelvin scale is one-fourth that on the Fahrenheit scale.

A) -150 K
B) -300 K
C) 300 K
D) 600 K

Answer :

Final answer:

To estimate the Kelvin scale reading that is one-fourth of the Fahrenheit scale, we must consider that the Kelvin scale starts at absolute zero and cannot have negative values. The calculations indicate that the correct option is 300 K, which estimates the correct positive value on the Kelvin scale when it is one-fourth of the value on the Fahrenheit scale.

Explanation:

To estimate the temperature at which the reading in the Kelvin scale is one-fourth on the Fahrenheit scale, we need to understand the relationship between these scales and how to convert from one to the other. The Kelvin scale starts at absolute zero, which is 0 K or -273.15 °C or -459.67 °F. There is a direct conversion from Celsius to Kelvin, where K = °C + 273.15, but converting from Fahrenheit to Kelvin involves an additional step.

The conversion formula from Fahrenheit to Celsius is: °C = (°F - 32) × (5/9). And from Celsius to Kelvin, the formula is: K = °C + 273.15. However, the question asks us to estimate the temperature when the Kelvin value is one-fourth the Fahrenheit value, which implies K = °F/4. Since absolute zero in Fahrenheit is -459.67, any positive Fahrenheit value would give us a positive Kelvin value, dismissing options a and b. Since the Kelvin scale is an absolute scale and cannot have negative values, we also dismiss option a (-150 K) and b (-300 K) as impossible.

Consider the relationship: K = °F/4
We need to find a Fahrenheit temperature such that when divided by 4, it converts to a valid Kelvin temperature. At -300 °F, K = -300/4 = -75 K, which is not possible since Kelvin cannot be negative. At 600 °F, K = 600/4 = 150 K, which is impossible since 150 K is below absolute zero. At 300 °F, K = 300/4 = 75 K, and this makes sense since 75 K is a possible Kelvin temperature. Thus, the estimated temperature is 300 K, option c.

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