Question

A faulty thermometer has its fixed points marked as $3^\circ$ and $120^\circ$. The temperature of the body measured by the faulty thermometer is $80^\circ$. Find the correct temperature of the body on Celsius scale.
A. $36.5^\circ \,{\text{C}}$
B. $77.8^\circ \,{\text{C}}$
C. $25.8^\circ \,{\text{C}}$
D. $65.8^\circ \,{\text{C}}$

Answer 1

Recall the lower fix point and upper fix point of temperatures on Celsius scale. Use the conversion relation between two temperature scales. Substitute the given values of LFP and UFP of the both temperature scales and solve for corresponding temperature on Celsius scale.

Formula used:
$\dfrac{{{T_C} - LFP}}{{UFP - LFP}} = \dfrac{{{T_T} - LFP}}{{UFP - LFP}}$
Here, ${T_C}$ is the temperature of that body on Celsius scale, ${T_T}$ is the temperature of the given body measured by the faulty thermometer. $LFP$ and $UFP$ are the lower fix point and upper fix point of the temperatures in their respective scales.

Complete step by step solution:
We have given the lower fixed point (LFP) is equal to $3^\circ$ and upper fixed point (UFP) is equal to $120^\circ$ for a faulty temperature scale which reads temperature of the body as $80^\circ$. Now we want to measure the temperature of that body on a Celsius scale.
We know the conversion relation between two temperature scales,
$\dfrac{{{T_C} - LFP}}{{UFP - LFP}} = \dfrac{{{T_T} - LFP}}{{UFP - LFP}}$
Here, ${T_C}$ is the temperature of that body on Celsius scale, ${T_T}$ is the temperature of the given body measured by a faulty thermometer. $LFP$ and $UFP$ are the lower fix point and upper fix point of the temperatures in their respective scales.
We know the LFP of Celsius scale is $0^\circ C$ and UFP is $100^\circ C$.
We substitute $0^\circ C$ for LFP, $100^\circ C$ for UFP for Celsius scale and $80^\circ$ for ${T_T}$, $3^\circ$ for LFP and $120^\circ$ for UFP for the given temperature scale of the faulty thermometer in the above equation.
$\dfrac{{{T_C} - 0}}{{100 - 0}} = \dfrac{{80 - 3}}{{120 - 3}}$
$\Rightarrow \dfrac{{{T_C}}}{{100}} = \dfrac{{77}}{{117}}$
$\Rightarrow {T_C} = 65.8^\circ C$
Therefore, the corresponding temperature of the body's Celsius scale is $65.8^\circ C$.

So, the correct answer is “Option D”.

Note:
The above relation determines the temperature on Celsius scale. If you want to measure the temperature of the body on Fahrenheit scale, you can simply use the LFP and UFP of the temperatures in Fahrenheit scales. To solve this type of questions, students must remember the LFP and UFP of both Celsius scale and Fahrenheit scale.