Question

The temperature of the two systems differs by \[1{}^\circ \text{C}\]. How much will it differ on the Fahrenheit scale?
(A) \[\text{1}{}^\circ \text{F}\]
(B) \[\text{1}\text{.2}{}^\circ \text{F}\]
(C) \[\text{2}\text{.4}{}^\circ \text{F}\]
(D) \[\text{1}\text{.8}{}^\circ \text{F}\]

Answer 1

Hint: To find the difference on the Fahrenheit scale, we need to convert the temperature from the Celsius scale to the Fahrenheit scale. To convert the Celsius difference into the Fahrenheit difference, we need to find a common point between the two scales of temperature.

Formula Used:
\[\text{100 divisions on Celsius scale = 180 divisions on the Fahrenheit scale}\]

Complete step by step answer:
temperature is independent of the scale of measurement, this means that the readings on the two scales might be different but the temperature of the body remains the same.
There are divisions on the Celsius scale and divisions on the Fahrenheit scale. If the temperature of the body is to be kept independent of the scale of measurement, these divisions on the Celsius must be equal in value to the divisions on the Fahrenheit scale.
Mathematically, we can say that
\[\begin{align}
  & \text{100 divisions on Celsius scale = 180 divisions on the Fahrenheit scale} \\
 & \Rightarrow \text{1 division on Celsius scale = }\dfrac{\text{180}}{100}\text{ divisions on the Fahrenheit scale} \\
\end{align}\]
The above statement is a manifestation of the unitary method.
Solving the statement, we can say that \[\text{1 division on Celsius scale = }\dfrac{9}{5}\text{ divisions on the Fahrenheit scale}\]
Since the value of one division is a unit degree on the temperature scales, we can say that
\[\text{1}{}^\circ \text{C=}\dfrac{9}{5}{}^\circ F\]
Hence, we can conclude that the difference of \[\text{1}{}^\circ \text{C}\] on the Celsius is equal to a difference of \[1.8{}^\circ F\] on the Fahrenheit scale and the correct answer is option (D).

Note: The above method can only be used to convert the differences in temperature from one scale to another. If you have to convert the temperature from the Celsius scale to the Fahrenheit scale, do not multiply it by the factor obtained above; it will give you an incorrect answer. If you have to convert Celsius temperature to Fahrenheit, add thirty-two to the value obtained after multiplying the factor of \[1.8\] .