Question

An accurate Celsius scale and faulty Fahrenheit thermometer read \[65\]\[^{\circ }C\]and \[154\]\[^{\circ }F\]respectively when placed in a hot liquid. Find the error in the latter.

Answer 1

Hint: When attempting questions based on Celsius or Fahrenheit or any temperature scale remember the formulas and the process on how to convert the Fahrenheit scale to the Celsius scale and vice versa because Fahrenheit is used mostly in the US and in contrast Celsius is used worldwide and you can get values in either.

Complete step-by-step solution:
Before attempting this question let's have a simple understanding of what the Fahrenheit and Celsius scale are.
Fahrenheit scale is mostly used in the United States but actually it is named after a German Physicist. It’s unit is \[F\]. The lower defining point \[{{0}^{\circ }}F\] is the freezing temperature of a solution of brine.
This solution of brine comprises ice, water, and ammonium chloride. Moreover, the melting point of ice on this scale takes place at\[{{32}^{\circ }}F\]. Furthermore, the boiling point of water on this scale is \[{{212}^{\circ }}F\].
The Celsius scale refers to a temperature scale that is used by the international system of units (\[SI\]). It is popular almost everywhere in the world except the United States and a few other places. The degree Celsius symbol \[^{\circ }C\]can refer to a particular temperature on this scale. The scale is named after Anders Celsius who was a Swedish astronomer.
Most noteworthy, the freezing point of water on this scale is \[{{0}^{\circ }}C\], while the boiling point of water is \[{{100}^{\circ }}C\]. Furthermore, this takes place at \[1atm\] pressure. Sometimes, the Celsius scale is also called the centigrade scale.
To find our answer, we need to keep in mind the conversion formula for Fahrenheit and Celsius.
\[C=\dfrac{5}{9}\times (F-32)\]
Where \[C\]is Celsius, and \[F\]denotes Fahrenheit.
In question we are given that Celsius scale is accurate, and the scale reads \[65\]\[^{\circ }C\]so putting that in the given formula we get;
\[\Rightarrow 65=\dfrac{5}{9}\times (F-32)\]
\[\Rightarrow 65\times 9=5\times (F-32)\]
On solving we get the value of \[F\]to be \[{{149}^{\circ }}\]
But in question we are given the value of \[F\]to be \[154\]\[^{\circ }F\]
So the error in scale reading is;
\[{{154}^{\circ }}F-{{149}^{\circ }}F={{5}^{\circ }}F\]
So the answer is that the faulty Fahrenheit scale has an error of \[{{5}^{\circ }}F\]

Note: Other than Fahrenheit and Celsius, another commonly used temperature scale is that of Kelvin, also denoted as \[K\]. A mathematical equation to give the relationship between Celsius and Kelvin is; \[K{{=}^{\circ }}C+273\]. This scale is also called the SI scale of temperature and is used mostly by the scientific community.