Final Answer:
The temperature at which the Kelvin scale reading doubles that of the Fahrenheit scale is approximately -40 degrees.
Step-by-step explanation:
To understand at what temperature the Kelvin scale reading would double that of the Fahrenheit scale, we need to equate the two scales using their respective formulas and find the temperature where this equivalence occurs.
The formula to convert Celsius to Kelvin is K = C + 273.15, and to convert Celsius to Fahrenheit is F = (C × 9/5) + 32. Setting the Kelvin temperature equal to twice the Fahrenheit temperature, we can represent this mathematically as 2F = K.
Now, let's use these conversion formulas to equate the temperatures:
Let the Fahrenheit temperature be F and the corresponding Kelvin temperature be K. Therefore, K = 2F.
By the conversion formulas, we can equate the two scales: K = C + 273.15 and F = (C × 9/5) + 32.
Substituting F = (C × 9/5) + 32 into K = C + 273.15, we get: 2[(C × 9/5) + 32] = C + 273.15.
Solving this equation for C gives us C ≈ -40. This means that at approximately -40 degrees Celsius, the Kelvin scale reading will be double that of the Fahrenheit scale.
Therefore, by substitution and solving the equations derived from the conversion formulas for the two temperature scales, we find that the temperature at which the Kelvin scale reading doubles that of the Fahrenheit scale is approximately -40 degrees.