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Question: Accurate Celsius thermometer and a Fahrenheit thermometer register \(60^{\circ}\) and \(141^{\circ}\...

Accurate Celsius thermometer and a Fahrenheit thermometer register 60∘60^{\circ} and 141∘141^{\circ} respectively when placed in the same constant temperature enclosure. What is the error in the Fahrenheit thermometer?

  1. 1∘F1^{\circ} \mathrm{F}
  2. 3∘F3^{\circ} \mathrm{F}
  3. −5∘F-5^{\circ} \mathrm{F}
  4. 2∘F2^{\circ} \mathrm{F}
Explanation

Solution

Here, for conversion from Celsius to Fahrenheit or from Fahrenheit, we shall use the formula. This formula is going to help us turn 60 degrees Celsius into Fahrenheit. If the value obtained in Fahrenheit is the same as the value of the question given, then there is no error. And if the value is greater than or less than the value given, then there is an error.

Complete solution:
Given , the temperature in degree Celsius is C=60∘CC=60^{\circ} \mathrm{C} and the temperature in Fahrenheit shown by the thermometer is F=141∘FF=141^{\circ} \mathrm{F}.
We write the formula for conversion from Celsius to degree Fahrenheit. It will give us the accurate conversion of degree Celsius to Fahrenheit.
C5=F−329\dfrac{C}{5}=\dfrac{F-32}{9}
Substitute the value of temperature in degree Celsius in the above relation. 605=F−329\dfrac{60}{5}=\dfrac{F-32}{9}
12=F−32912=\dfrac{F-32}{9}
Now, we perform cross multiplication in the above equation.
F−32=108F-32=108
⇒F=140∘F\Rightarrow F=140^{\circ} \mathrm{F}
The conversion of 60 degree Celsius into Fahrenheit gives the value of 140∘F140^{\circ} \mathrm{F}.
Now, we compare this value with the given value of temperature in Fahrenheit which is more by 1 degree Fahrenheit.
Then, the error in the thermometer is given as,
e=141∘F−140∘Fe={{141}^{{}^\circ }}\text{F}-{{140}^{{}^\circ }}\text{F}
e=1∘Fe={{1}^{{}^\circ }}\text{F}
The thermometer shows the error in the reading as 1∘F1^{\circ} \mathrm{F}.

So, the correct answer is "Option B".

Note:
We understand that the three temperature scales are used for temperature measurement purposes. In the question of Celsius and Fahrenheit, two of the temperature scales are given and the third one is Kelvin. Zero degree Celsius is equal to 273 Kelvin, and we have to add 273 to the degree Celsius if we want to convert the degree Celsius into Kelvin units.