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Question: The readings of a bath on Celsius and Fahrenheit thermometers are in the ratio \(2:5\). The temperat...

The readings of a bath on Celsius and Fahrenheit thermometers are in the ratio 2:52:5. The temperature of the bath is?
A. −26.66∘C - {26.66^ \circ }C
B. 40∘C{40^ \circ }C
C. 45.71∘C{45.71^ \circ }C
D. 26.66∘C{26.66^ \circ }C

Explanation

Solution

In order to answer this problem we should first get some idea about the temperature measure. The total kinetic energy of the particles in an object is measured by temperature. As the temperature rises, so does the motion of these particles.

Complete step by step answer:
Let us understand different ways of measuring temperature. The Fahrenheit (°F) scale, the Celsius (°C) scale, and the Kelvin (K) scale are the three most widely used temperature scales in the world today.In Fahrenheit Scale the freezing point of water is 32 degrees Fahrenheit and the boiling point is 212 degrees Fahrenheit on the Fahrenheit temperature scale.

The Celsius scale, also known as centigrade, is based on the freezing point of water being 0° and the boiling point of water being 100°. Because of the 100-degree interval between the specified points, it is often referred to as the centigrade scale. It was invented in 1742 by Swedish astronomer Anders Celsius.

Now let us understand the formula to convert Celsius to Fahrenheit vice versa:
C=59[F−32]C = \dfrac{5}{9}[F - 32]
Now, let us solve the problem: Celsius and Fahrenheit thermometers are in the ratio:
CF=25\dfrac{C}{F} = \dfrac{2}{5}
⇒C=2F5\Rightarrow C = \dfrac{{2F}}{5}
⇒C=0.4F\Rightarrow C = 0.4F........................[Equation−1][Equation - 1]
Now, as we saw earlier:
C=59[F−32]C = \dfrac{5}{9}[F - 32]
⇒0.4F=59[F−32]\Rightarrow 0.4F = \dfrac{5}{9}[F - 32]................[By using equation-11]
⇒3.6F=5F−160\Rightarrow 3.6F = 5F - 160
⇒F=114.28∘F\Rightarrow F = {114.28^ \circ }F
∴C=45.71∘C\therefore C = {45.71^ \circ }C

Hence, the correct answer is option C.

Note: There is a very interesting fact about the temperature calculation. When you convert −40∘F - {40^ \circ }Fto Celsius, it will come−40∘C - {40^ \circ }C. Temperature is essential in human and animal medicine, as well as food, beverages, and agriculture. In several ways, our overall well being is also influenced by temperature. It's crucial to keep medical cold storage areas at the right temperature.