Question

On the Reaumur scale of temperature the melting point of ice and the boiling point of water are taken as 0 R and 80 R respectively. The freezing point and boiling point of mercury on Celsius scale are ${39}^o$C and ${367}^o$C respectively. Express these temperatures on Reaumur scale.
$\left(A\right)$ 12.2 R, 127 R
$\left(B\right)$ 41 R, 290 R
$\left(C\right)$ 31.2 R, 293.6 R
$\left(D\right)$ 71 R, 293.6 R

Answer 1

Hint: In this question apply the conversion of scale from Reaumur scale to Celsius scale as ${100}^{o}C=80R$ . The freezing point and boiling point of mercury on Celsius scale are given so we directly convert this into the Reaumur scale using the above formula, so use these concepts to reach the solution of the question.

Complete step-by-step solution -

Boiling point – The boiling point is a temperature at which the pressure outside the surroundings is equal to the vapor pressure of the liquid, the boiling point of different liquids are different.
Melting point – the melting point is a temperature at which the solid changes its state i.e. from solid to liquid, at the melting point solid phase and liquid phase remains in equilibrium.
Given data:
Freezing point of mercury = ${39}^{o}C$
And boiling point of mercury = ${367}^{o}C$
So we have to convert this degree Celsius scale into the Reaumur scale.
Now as we know that ${100}^{o}C=80R$, where R is the symbol of Reaumur scale.
Therefore $1^{o}C={\displaystyle \frac{80}{100}}R$
So, ${39}^{o}C={\displaystyle \frac{80\times 39}{100}}=31.2R$
And
${367}^{o}C={\displaystyle \frac{80\times 367}{100}}=293.6R$

Hence option (C) is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember is that always recall the scale conversion from degree Celsius scale to Reaumur Scale which is stated above, then convert the given degree Celsius into Reaumur scale as above which is the required answer.