Question

A correct thermometer in Fahrenheit is introduced in a water bath along with a Celsius thermometer. The readings observed are 86 \[{}^\circ F\] and 32 \[{}^\circ C\]. The correction to be made to the Celsius reading will be:
A. 2.5 \[{}^\circ C\]
B. 2 \[{}^\circ C\]
C. 1.5 \[{}^\circ C\]
D. 3 \[{}^\circ C\]

Answer 1

Hint: It is given that the correct temperature of the water bath is 86 \[{}^\circ F\]. And we also know that interconversion between different temperature scales is possible and the relation used is given below. Converting the correct Fahrenheit scale reading to Celsius would give us the correct Celsius scale reading and the difference between the incorrect and correct one would be the correction to be made to the Celsius reading.

Formula Used:
\[{}^\circ C=({}^\circ F-32)\times \dfrac{5}{9}\]

Complete step-by-step solution:
Temperature can be measured on many different scales, there is a Kelvin scale, Celsius scale, etc. But since all these scales represent the same quantity interconversion between this is possible. For instance, the relationship between Fahrenheit and Celsius scale is given as:
\[{}^\circ C=({}^\circ F-32)\times \dfrac{5}{9}\]
Now coming to the question, the temperature of the water bath is given in two different scales. And it is provided that the Fahrenheit thermometer is correct while nothing has been said about the Celsius thermometer. So we know that the correct temperature of the bath is 86 \[{}^\circ F\], to know the correct reading in the Celsius scale we simply convert the Fahrenheit scale reading to the Celsius scale. We already the relation that is,
\[{}^\circ C=({}^\circ F-32)\times \dfrac{5}{9}\]
Plugging in the reading of Fahrenheit scale we get,
\[\begin{align}
  & {}^\circ C=(86-32)\times \dfrac{5}{9} \\
 & {}^\circ C=30 \\
\end{align}\]
So, the correct temperature of the water bath in Celsius is 30\[{}^\circ C\]
Now coming to the correction part. The incorrect reading of the Celsius thermometer is given to be 32 \[{}^\circ C\]and from our calculation, we know that the correct value is 30\[{}^\circ C\]. So,
Correction = $32 -30$
Correction = 2 \[{}^\circ C\]
The correction to be made to the Celsius reading will be 2 \[{}^\circ C\]
So, Option B is the correct one.

Note: The scales of temperature are often used to confuse the students. To avoid such confusion, it is important to remember the interconversion of temperature on different scales. Some of the important relations used for conversion are
\[{}^\circ C=({}^\circ F-32)\times \dfrac{5}{9}\]
\[{}^\circ F=\left( {}^\circ C\times \dfrac{9}{5} \right)+32\]
\[{}^\circ C\] + 273.15 = K