Question

A Kelvin thermometer and a Fahrenheit thermometer used to record temperature of melting metal, read the same. What will a Celsius thermometer read at that temperature?
A. $301.25℃$
B. $273℃$
C. $457℃$
D. $760℃$

Answer 1

Hint:We can use the concept of thermometers, given as $\dfrac{t-l.p.}{n}=$ constant. Where t is the temperature reading in the thermometer, l.p. is the lower point of that thermometer and n is the number of divisions in that thermometer. One should know to relate temperature on the thermometer with different degree readings.

Formula used:
\[\dfrac{K-273}{100}=\dfrac{F-32}{180}=\dfrac{C-0}{100}\]

Complete step by step answer:
Let the temperature reading on the Kelvin thermometer and the Fahrenheit thermometer be $x$. (The question says both thermometers have the same reading) We know that for any thermometer$\dfrac{t-l.p.}{n}=$ constant. Where t is the temperature reading in the thermometer, l.p. is the lower point of that thermometer and n is the number of divisions in that thermometer.The relation between different thermometers is given by
\[\dfrac{K-273}{100}=\dfrac{F-32}{180}=\dfrac{C-0}{100}\].
Here K refers to the reading on the Kelvin scale, f refers to the reading on Fahrenheit scale and C refers to the reading on the Celsius scale.
From the first equality, by substituting the value of K and C$=x$, we get
$\dfrac{x-273}{100}=\dfrac{x-32}{180} \\
\Rightarrow 9\left( x-273 \right)=5\left( x-32 \right) \\
\Rightarrow 9x-5x=2457-160 \\
\Rightarrow 4x=2297 \\
\Rightarrow x=\dfrac{2297}{4}=574.25 \\$
Therefore, the temperature on Fahrenheit thermometer and kelvin thermometer is 574.25℉/K. From the second equality we have,
$\dfrac{F-32}{180}=\dfrac{C-0}{100} \\
\Rightarrow \dfrac{574.25-32}{180}=\dfrac{C-0}{100} \\
\therefore C=\dfrac{542.25\times 5}{9}=301.25 \\$
Therefore, the temperature on Celsius thermometer is 301.25 °C.Hence option A is correct.

Note:The most important point in this question is to remember the relation between thermometers with different scales \[\dfrac{K-273}{100}=\dfrac{F-32}{180}=\dfrac{C-0}{100}\]. One should also remember the lower point and number of divisions on the thermometer of different scales.

Scale	Lower point	Number of divisions
Kelvin	273	100
Fahrenheit	32	180
Celsius	0	100