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Question: When a Celsius thermometer read \( 90{}^\circ C \) faculty Fahrenheit thermometers read \( {{190}^{o...

When a Celsius thermometer read 90∘C90{}^\circ C faculty Fahrenheit thermometers read 190oF{{190}^{o}}F . The correction is made in the large scale is,
(A) + 2∘F+\text{ }2{}^\circ F
(B) −2∘F-2{}^\circ F
(C) −4∘F-4{}^\circ F
(D) 4∘F 4{}^\circ F~

Explanation

Solution

The degree Celsius is a unit of temperature that is originally thrown as a centigrade scale. It is the temperature scale based on 0∘0{}^\circ for freezing point of water and 100o{{100}^{o}} for the boiling point of water.
The Fahrenheit scale shows (32∘to 212∘)\left( 32{}^\circ \text{to }212{}^\circ \right) where
32∘32{}^\circ shows the freezing point of water.
212∘212{}^\circ shows the boiling point of water.
Establish the Relation b/w Celsius and Fahrenheit scale.

Formula Used: Relation between degree Celsius and
Fahrenheit scale,
C100=(F−32)180\frac{C}{100}=\frac{(F-32)}{180} .

Complete step by step solution
We have given,
Reading on Celsius scale, C = 90∘C90{}^\circ \text{C}
Reading on Fahrenheit scale, F = ?
C100=(F−32)180\frac{C}{100}=\frac{\left( F-32 \right)}{180}
91=F−3218\frac{9}{1}=\frac{F-32}{18}
18×9=F−3218\times 9=F-32
162=F−32162=F-32
F= 194∘F194{}^\circ F
But Given that
Reading on Faculty Fahrenheit thermometer
= 190∘F=\text{ }190{}^\circ F
Hence, error in faculty thermometer
\begin{array}{*{35}{l}} =\text{ }194{}^\circ F\text{ }-~190{}^\circ F \\\ =\text{ }4{}^\circ F \\\ \end{array}
Hence option (D) is correct.

Note
We should add 4∘F4{}^\circ F in 190∘F190{}^\circ F to make the correct Reading on Fahrenheit thermometer The formula for the conversion of Celsius scale into Fahrenheit scale is given by,
∘F=(95× ∘C)+32{}^\circ F=\left( \frac{9}{5}\times \text{ }{}^\circ C \right)+32
OR ∘C=(∘F−32)× 59{}^\circ C=({}^\circ F-32)\times \text{ }\frac{5}{9}
A modern Celsius scale has been adopted that is based on the triple point of Vienna standard mean ocean water and has improved with the concept of absolute zero.
The lowest defining point in the Fahrenheit scale is the temperature of a solution of brine with an equal amount of ice, water and salt(ammonium chloride).
Celsius scale is commonly used in areas that use metric system units and this is used for all scientific purposes.