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Question: An accurate Celsius thermometer and a faulty Fahrenheit thermometer read \(60^\circ {\rm{C}}\) and \...

An accurate Celsius thermometer and a faulty Fahrenheit thermometer read 60∘C60^\circ {\rm{C}} and 141∘F141^\circ {\rm{F}} respectively when placed in the same bath. Find the error in the Fahrenheit thermometer.
(A) 11∘F11^\circ {\rm{F}}
(B) 1∘F1^\circ {\rm{F}}
(C) 13∘F13^\circ {\rm{F}}
(D) 0.5∘F0.5^\circ {\rm{F}}

Explanation

Solution

Here, we will use the formula for conversion from Celsius to Fahrenheit or from Fahrenheit. This formula will help us to convert 60 degree Celsius into Fahrenheit. If the obtained value in Fahrenheit is the same as that of the given question then there is no error. And if the value is more or less than the given value then it contains error.

Complete step by step answer:
Given Data: The temperature in degree Celsius is C=60∘CC = 60^\circ {\rm{C}} and the temperature in Fahrenheit shown by the thermometer is F=141∘FF = 141^\circ {\rm{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 12=F−329\begin{array}{c} \dfrac{{60}}{5} = \dfrac{{F - 32}}{9}\\\ 12 = \dfrac{{F - 32}}{9} \end{array}
Now, we perform cross multiplication in the above equation.
F−32=108 ⇒F=140∘F\begin{array}{c} F - 32 = 108\\\ \Rightarrow F = 140^\circ {\rm{F}} \end{array}
The conversion of 60 degree Celsius into Fahrenheit gives the value of 140∘F140^\circ {\rm{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∘F =1∘F\begin{array}{c} e = 141\,{\rm{^\circ F}} - 140{\rm{^\circ F}}\\\ {\rm{ = 1^\circ F}} \end{array}
The thermometer shows the error in the reading as 1∘F1^\circ {\rm{F}}.

So, the correct answer is “Option B”.

Note:
We know that the three temperature scales are used for the measurement of temperature. Two of the temperature scales are given in the question which are Celsius and Fahrenheit and the third one is Kelvin. Zero degree Celsius is equal to 273 Kelvin and if we want to convert degree Celsius into the units of Kelvin then we have to add 273 in the degree Celsius.