Question

When a thermometer is taken from the melting ice to a warm liquid, the mercury level rises to ${\left( {\dfrac{2}{5}} \right)^{th}}$ of the distance between the lower and the upper fixed points. The temperature of the liquid in $K$ is
(A) $217.15\;$
(B) $313.15\;$
(C) $220\;$
(D) $330\;$

Answer 1

We will first collect the values given in the question which are the lower and upper fixed points. Then we will find the difference between the upper and lower points of the thermometer on the Celsius scale then we will multiply it with the rise in the mercury level. After that, we will convert the temperature to $K$ scale.

Complete step-by-step solution:
We will first understand and discuss how the thermometer works. In the thermometer given in the question, it is mentioned that it is filled with mercury. When a thermometer is placed in any substance which is either hot or cold then its mercury level increases because of the very low melting point of mercury.
Now first we consider the lower fixed point that is given as ${T_L}$ which is the temperature when the thermometer was placed in ice which is equal to ${0^\circ }$ Celsius and we consider the upper limit as ${T_U}$ ${100^\circ }$ celsius. Now the difference between them is given as
${T_U} - {T_L} = {100^\circ } - 0^\circ$
$\Rightarrow {T_U} - {T_L} = {100^\circ }$
Now we will evaluate the temperature when the mercury level rises by some fraction which can be given by multiplying the fraction given in the question with the obtained that is ${100^\circ }$.
$T = {T_U} - {T_L} \times \dfrac{2}{5}$
$\Rightarrow T = {100^\circ } \times \dfrac{2}{5}$
$\therefore T = {40^\circ }C$
Now converting it in the kelvin scale as required, hence the temperature of the liquid can be given as
${T_K} = {40^\circ } + 273.15$
$\therefore {T_K} = 313.15K$

Hence option (B) is the correct answer.

Note: Here it is important to know the conversion of temperatures into different scales. The Kelvin scale always starts with the value of $273.15\;K$ for an equivalent temperature of ${0^\circ }$ Celsius. Therefore a celsius value can be converted by adding $273.15\;$ it to the celsius value.