Question

The distance between the LFP and UFP of a thermometer is $18cm$. The reading on the thermometer in Fahrenheit scale when the length of the mercury thread is $8cm$ is __________.

• A. ${212}^{0}F$
• B. ${112}^{0}F$
• C. ${80}^{0}F$
• D. ${180}^{0}F$

Answer 1

The correct option is B

${112}^{0}F$

Step 1: Given data:

The distance between the LFP and UFP of a thermometer is $18cm$

Length of the mercury thread is $8cm$

Step 2: Finding the reading on the thermometer in Fahrenheit scale:

We know that in Celsius scale, $100-0=18cm$,

Where $100$ is the UFP and $0$is the LFP.

Thus, $1cm={\left(\frac{100}{18}\right)}^{0}C$

For $8cm$ the temperature

$\Rightarrow 8\times {\left(\frac{100}{18}\right)}^{0}C$

We know that,

${}^{0}F=\left(\frac{9}{5}{\times }^{0}C\right)+32$

Hence, ${}^{0}F=\left(\frac{9}{5}\times 8\times \frac{100}{18}\right)+32$

$\Rightarrow {}^{0}F={112}^{0}F$

Hence, the length of the mercury thread is $8cm$, then the reading on the thermometer in Fahrenheit scale is ${112}^{0}F$.