Question

A faulty thermometer has its lower fixed point marked as $ - {10^o}C $ and upper fixed point marked as $ {110^o}C $ . If the temperature of a body in this scale is $ {62^o}C $ , what will be the temperature shown on the Celsius scale?

Answer 1

Hint: To solve this question, just recall the concept of lower fix point and upper fix point of temperatures on Celsius scale. Then use the conversion relation between the two temperature scales. Then we will substitute the given values of LFP and UFP of the both temperature scales and subsequently find the corresponding temperature on Celsius scale.

Complete Step By Step Answer:
In this question, we are given that the lower fixed point (LFP) is equal to $ - {10^o}C $ and the upper fixed point (UFP) is equal to $ {110^o}C $ for a faulty temperature scale. This faulty thermometer reads the temperature of the body as $ {62^o}C $ . Now we need to find the temperature of that body on a Celsius scale.
We know that the conversion relation between two temperature scales is,
 $ \dfrac{{{T_C} - LFP}}{{UFP - LFP}} = \dfrac{{{T_T} - LFP}}{{UFP - LFP}}.......(1) $
In the above expression,
 $ {T_C} $ is the temperature of the given body in the celsius scale
  $ {T_T} $ is the temperature of the given body which is measured by the faulty thermometer
 $ LFP $ is the lower fix point
 $ UFP $ is the upper fix point
We also know that for a celsius scale, $ LFP $ is $ {0^o}C $ and $ UFP $ is $ {100^o}C $
Also, in this question,
Temperature of the given body which is measured by the faulty thermometer $ {T_T} $ is $ {62^o}C $
Also, for the given the given fault thermometer,
 $ LFP $ is $ - {10^o}C $ and $ UFP $ is $ {110^o}C $
On putting these values in equation (1), we get,
 $ \dfrac{{{T_C} - 0}}{{100 - 0}} = \dfrac{{62 + 10}}{{110 + 10}} $
On simplifying the above expression, we get,
 $ \dfrac{{{T_C}}}{{100}} = \dfrac{{72}}{{120}} $
 $ {T_C} = \dfrac{{7200}}{{120}} $
On simplifying the above equation,
 $ {T_C} = {60^o}C $
Thus, the temperature shown on the Celsius scale is $ {T_C} = {60^o}C $ .

Note:
The above relation is used to determine the temperature on Celsius scale. If we ever want to measure the temperature of a particular body on the Fahrenheit scale, then we will simply use the LFP and UFP of the temperatures which are given in Fahrenheit scales. To solve such a category of questions, we should remember the LFP and UFP of Celsius scale as well as Fahrenheit scale.