Question

A Fahrenheit thermometer reads ${{113}^{\text{o}}}F$ while a faulty Celsius thermometer reads ${{44}^{\text{o}}}C$. The correction to be applied to the Celsius thermometer is:
$\left( a \right)-{{1}^{\text{o}}}C$
$\left( b \right)+{{1}^{\text{o}}}C$
$\left( c \right)+{{2}^{\text{o}}}C$
$\left( d \right)-{{2}^{\text{o}}}F$

Answer 1

Since, the thermometer gives wrong reading of the temperature so we will use the formula which explains the relation between Fahrenheit and Celsius. After getting the correct value of Celsius we will subtract it with the error value to get the required correction.

Formula used:
$F=\dfrac{9}{5}C+32$ where F is Fahrenheit and C is Celsius, error will be = correct value – incorrect value.

Complete answer:
Thermometer: A thermometer is a familiar word as it is seen in our daily lives. We use it to check a body’s temperature to note. So, we will define Fahrenheit as a measuring instrument whose job is to measure the temperature of a human being. For this reason it consists of a structure of glass tube markings on it.
Celsius thermometer: If a thermometer is observing water’s freezing point as ${{0}^{\text{o}}}C$ and boiling point as ${{100}^{\text{o}}}C$ so, we say that the thermometer is a Celsius based thermometer.
Fahrenheit thermometer: If a thermometer is giving reading of water’s freezing point as ${{32}^{\text{o}}}F$ and water’s boiling point as ${{212}^{\text{o}}}F$ then, we say that the thermometer is a Fahrenheit based thermometer.
We will use the formula expressing the relation between Celsius and Fahrenheit as $F=\dfrac{9}{5}C+32$. As according to the question we are having a condition in which the reading of Fahrenheit thermometer reads ${{113}^{\text{o}}}F$ with the equal reading in Celsius thermometer as ${{44}^{\text{o}}}C$ which is wrong so, we will use the formula $F=\dfrac{9}{5}C+32$ to calculate the correct reading. As we are already given that the reading by Fahrenheit thermometer is ${{113}^{\text{o}}}F$ thus, by the formula we get,
$\dfrac{9}{5}C=F-32$
$\Rightarrow C=\dfrac{5}{9}\left( F-32 \right)$
$\Rightarrow C=\dfrac{5}{9}\left( 113-32 \right)$
$\Rightarrow C=\dfrac{5}{9}\left( 81 \right)$
$\Rightarrow C=5\times 9$
$\Rightarrow C=45$
Therefore, the error will be = correct value – incorrect value. Thus, we get an error of ${{1}^{\text{o}}}C$. So, the correction should be $-\,{{1}^{\text{o}}}C$.
Hence, the correct option is $\left( a \right)-{{1}^{\text{o}}}C$.

Note: It is important to remember the following points to get the right way for solution.
(1) The formula to find Fahrenheit: $F=\dfrac{9}{5}C+32$.
(2) To find the error: find correct value – incorrect value.
(3) The presence of Kelvin instead of Celsius will hardly create problems.
(4) Thermometer is of three types: Fahrenheit, Celsius and Kelvin.