Question

The upper and lower fixed points of a faulty mercury thermometer are ${210}^{{}^{\circ }}F$and ${34}^{{}^{\circ }}F$ respectively. The correct temperature read by this thermometer is:
(A) ${22}^{{}^{\circ }}F$
(B) ${80}^{{}^{\circ }}F$
(C) ${100}^{{}^{\circ }}F$
(D) ${122}^{{}^{\circ }}F$

Answer 1

Hint: To answer this question we have to first know the formula which develops the relationship between the correct temperature and the upper and the lower limits of the mercury thermometer. Then we have to put the values that are mentioned in the question in the formula. Once the values are put all we left to do is evaluate and ultimately obtain the required answer.

Complete step by step solution
We know that:
${\displaystyle \frac{F-32}{180}}={\displaystyle \frac{F-L}{U-L}}$
Here L is the lower fixed point of the faulty mercury thermometer and U is the upper fixed point of a faulty mercury thermometer.
So now put the values in the formula to get:
${\displaystyle \frac{F-32}{180}}={\displaystyle \frac{F-34}{210-34}}$
$\Rightarrow {\displaystyle \frac{F-32}{180}}={\displaystyle \frac{F-34}{176}}$
$\Rightarrow {\displaystyle \frac{F-32}{45}}={\displaystyle \frac{F-34}{44}}$
Hence now on we have to further solve the equation, to get:
$45F-45\times 34=44F-44\times 32$
$\Rightarrow 45F-44F=1530-1408$
$\Rightarrow F={122}^{{}^{\circ }}F$
Hence we can say that the correct temperature that is measured by this thermometer is ${122}^{{}^{\circ }}F$.

So the correct option is D.

Note We should all know that the mercury thermometer is defined as a glass tube which is filled with mercury and consists of a temperature scale which is marked on the scale. Whenever there are changes in the temperature the mercury present in the glass tube contracts and expands. The temperature that is obtained after the final contraction and extraction can be read from the scale.
It should be known to us that the upper limit is defined as the largest data value and the lower limit is defined as the smallest data value.