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?
574
301
273
232
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC NDA-1 – 2017
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:
$T_C + 273.15 = \frac{9}{5} T_C + 32$
$273.15 – 32 = \frac{9}{5} T_C – T_C$
$241.15 = (\frac{9}{5} – 1) T_C$
$241.15 = (\frac{9-5}{5}) T_C$
$241.15 = \frac{4}{5} T_C$
$T_C = \frac{241.15 \times 5}{4} = \frac{1205.75}{4} = 301.4375$
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.
$T_C + 273 = \frac{9}{5} T_C + 32$
$273 – 32 = \frac{4}{5} T_C$
$241 = \frac{4}{5} T_C$
$T_C = \frac{241 \times 5}{4} = \frac{1205}{4} = 301.25$
This value is also very close to 301. This confirms that 301 is the most likely intended answer, allowing for slight rounding or the use of an approximation in the original question setting.