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Question: At what temperature do the Celsius and Fahrenheit scales coincide....

At what temperature do the Celsius and Fahrenheit scales coincide.

Explanation

Solution

In this question, we have been asked to calculate the temperature at which the Celsius and Fahrenheit scales give the same reading. We know that the Celsius and Fahrenheit scales are two different units of temperature based on different scales. Therefore, we shall discuss both the scales and also understand why the Celsius and Fahrenheit scales are different. Later, we shall discuss the relation between two scales. Therefore, using this relation we will calculate our answer.

Formula Used:
(∘F−32)180=∘C100\dfrac{({}^\circ F-32)}{180}=\dfrac{{}^\circ C}{100}

Complete step by step answer:

Celsius scale was introduced by Andres Celsius. In Celsius scale water is taken as the base and certain standard values are set with respect to water, for example the boiling point of water is 100 degree Celsius and melting point of ice is 0 degree Celsius.

The Fahrenheit scale was introduced by Daniel Gabriel Fahrenheit. According to this scale the boiling point of water is taken as 212 degree Fahrenheit and the melting point of ice as 32 degree Fahrenheit. This gives the exact difference of 180.

The relation between the Fahrenheit and Celsius scale is given by the equation.

⇒(∘F−32)180=∘C100\Rightarrow \dfrac{({}^\circ F-32)}{180}=\dfrac{{}^\circ C}{100}

Now, let us assume that Fahrenheit and Celsius scale coincide at x∘x{}^\circ . Therefore,

⇒(∘x−32)180=∘x100\Rightarrow \dfrac{({}^\circ x-32)}{180}=\dfrac{{}^\circ x}{100}

On solving,

We get,

⇒59(∘x−32)=∘x\Rightarrow \dfrac{5}{9}({}^\circ x-32)={}^\circ x

Therefore,

⇒x=−40∘\Rightarrow x=-40{}^\circ

Therefore, Celsius and Fahrenheit scale coincide at -40 degrees.

Note:

The difference between both scales is the base measurement. The Celsius scale has a melting point of ice as 0 degrees and Fahrenheit scale has 32 degrees. The other factor differentiating them is the acceptance. The Celsius scale is simple and widely used. The Fahrenheit scale is used in the USA and few other countries. The Celsius scale is not accepted in few regions where the Kelvin is used as a measurement unit of temperature. All the scales are convertible to one another.