Question

A Fahrenheit thermometer registers ${110}^{\circ }F$ while a faulty Celsius thermometer registers ${44}^{\circ }C$. Find the error in the latter.
$$\begin{array}{rl}& A{.0.667}^{\circ }C\\ & B{.0.72}^{\circ }C\\ & C{.1.2}^{\circ }C\\ & D{.7.2}^{\circ }C\end{array}$$

Answer 1

Hint: We know that a thermometer is used to measure the temperature of any given body. Here the temperature is measured in Fahrenheit and Celsius. To find the error in the Celsius scale we must convert the measurements in Fahrenheit to Celsius and then find their difference.

Formula used:
${\displaystyle \frac{C}{5}}={\displaystyle \frac{F-32}{9}}$
Where, $C$ is the temperature in Celsius scale and $F$ is the temperature in Fahrenheit.

Complete step by step answer:
Temperature is a measure of how hot or cold an object is and it is generally measured using a thermometer in three different scales, namely the Kelvin, Fahrenheit and Celsius. The Celsius scale is commonly used to measure the temperature. Also we can convert one scale to another easily, using simple formulas.
Given that body when measured with a Fahrenheit scale measures ${110}^{\circ }F$. Let us assume this measurement to be correct. Then we know that ${\displaystyle \frac{C}{5}}={\displaystyle \frac{F-32}{9}}$.
Then we see that ${110}^{\circ }F$ can be converted to ${}^{\circ }C$. And the value is given by, $C_a=5\times {\displaystyle \frac{110-32}{9}}={\displaystyle \frac{5\times 78}{9}}={43.333}^{\circ }C$
Also, given that the temperature of the same body when measured with a faulty Celsius thermometer is $C_m={44}^{\circ }C$.
Clearly, the two values are not equal, then we can tell that there is some error in the measurements.
Then the error in the measurement of the Celsius thermometer is given by $\mathrm{\Delta }C=C_m-C_a=44-43.333={0.667}^{\circ }C$
Thus the error in the measurement is ${0.667}^{\circ }C$

So, the correct answer is “Option A”.

Note:
The Kelvin scale is called the absolute temperature. And it is predominately used in the scientific society. The absolute zero is the temperature $0K$, where the body has lost all the possible heat. Also, the Kelvin scale and the Celsius scale are linear.