Let the reading on both the Kelvin and Fahrenheit scales be $x$. The conversion formula from Celsius ($T_C$) to Kelvin ($T_K$) is $T_K = T_C + 273.15$. For many problems, 273 is used as an approximation, but using 273.15 gives a more precise answer. The conversion formula from Celsius ($T_C$) to Fahrenheit ($T_F$) is $T_F = \frac{9}{5} T_C + 32$. We are given $T_K = T_F = x$. So, we have two equations: 1) $x = T_C + 273.15$ 2) $x = \frac{9}{5} T_C + 32$ Set the two expressions for $x$ equal to each other: $T_C + 273.15 = \frac{9}{5} T_C + 32$ (\frac{9}{5} - 1) T_C$ $241.15 = (\frac{9-5}{5}) T_C$ $241.15 = \frac{4}{5} T_C$ $T_C = 301.4375$ The question asks for the reading in a Celsius thermometer. The calculated value is approximately 301.44. Among the given options, 301 is the closest value.
A Kelvin thermometer and a Fahrenheit thermometer both give the same reading for a certain sample. What would be the corresponding reading in a Celsius thermometer?
Asked in UPSC NDA 1 2017 · Topic: Heat and Thermodynamics (Zeroth and First Laws of Thermodynamics (Internal Energy, Work, Heat, Enthalpy))
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