A Kelvin thermometer and a Fahrenheit thermometer both give the same reading for a certain sample. The corresponding Celsius temperature is about
So, the temperature in Kelvin (K) is x, and the temperature in Fahrenheit (F) is x.
We need to find the corresponding temperature in Celsius (C).
The conversion formulas between these scales are:
1. Fahrenheit to Celsius: C = (F – 32) * 5/9
2. Kelvin to Celsius: C = K – 273.15 (or often approximated as C = K – 273)
Let’s use the exact conversion K = C + 273.15 and F = (9/5)C + 32.
Since K = x and F = x, we have:
x = C + 273.15 (Equation 1)
x = (9/5)C + 32 (Equation 2)
Equating the right sides of Equation 1 and Equation 2:
C + 273.15 = (9/5)C + 32
Rearrange the terms to solve for C:
273.15 – 32 = (9/5)C – C
241.15 = (9/5 – 5/5)C
241.15 = (4/5)C
C = (241.15 * 5) / 4
C = 1205.75 / 4
C = 301.4375
Rounding to the nearest whole number or considering the options, the corresponding Celsius temperature is about 301 °C.