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Question: A temperature difference of \[15{}^\circ \text{C}\] on the Fahrenheit scale is equal to a difference...

A temperature difference of 15∘C15{}^\circ \text{C} on the Fahrenheit scale is equal to a difference of:
A. 27∘F27{}^\circ \text{F}
B. 59∘F59{}^\circ \text{F}
C. −27∘F-27{}^\circ \text{F}
D. −59∘F-59{}^\circ \text{F}

Explanation

Solution

The temperature in Celsius is converted to Fahrenheit using the conversion formula. The given value, that is, 15∘C15{}^\circ \text{C} is substituted in the formula given below. Cross multiply and simplify the equation to find the value of F.
Formula used:
The formula for converting Celsius to Fahrenheit is given by,
C5=F−329\dfrac{C}{5}=\dfrac{F-32}{9}
Where, C = temperature in Celsius
F = temperature in Fahrenheit.

Complete answer:
Given,
∘C=15{}^\circ \text{C=15}
Substituting this value in the conversion formula, ∘F{}^\circ F can be calculated as follows:
 C5=F−329 ⇒155=F−329 ⇒3=F−329 ⇒F−32=27 ⇒F=27+32 ⇒F=59 \begin{gathered} & \text{ }\dfrac{C}{5}=\dfrac{F-32}{9} \\\ & \Rightarrow \dfrac{15}{5}=\dfrac{F-32}{9} \\\ & \Rightarrow 3=\dfrac{F-32}{9} \\\ & \Rightarrow F-32=27 \\\ & \Rightarrow F=27+32 \\\ & \Rightarrow F=59 \\\ \end{gathered}
Therefore, the temperature difference in Fahrenheit scale is 59∘F59{}^\circ \text{F}.

The correct answer is option B.

Additional information:
The S.I. The unit of temperature is Kelvin. To calculate temperature in Kelvin, we add 273 to the temperature in the Celsius scale. The divisions on the Celsius and the Kelvin scale are of the same size. The freezing point of water in Celsius scale is 0∘C0{}^\circ \text{C} and in Kelvin scale is 273 K. On the other hand, a temperature difference of 1∘1{}^\circ on Fahrenheit scale is 5/9∘5/9{}^\circ on the Celsius scale. The freezing point of water in Celsius scale is 0∘C0{}^\circ \text{C} and in Fahrenheit scale is 32∘C32{}^\circ \text{C}.

Note:
Another way of writing the conversion formula is:
F=C×1.8+32F=C\times 1.8+32
This formula is obtained by dividing 9 by 5 and transferring 32 to the other side in the mentioned formula for conversion. This formula can also be used for converting Fahrenheit to Celsius.
A trick for converting Celsius to Fahrenheit is multiplying the temperature by 2 and adding 30. For example:
 (15×2)+30 =30+30 =60∘F \begin{gathered} & \text{ }\left( 15\times 2 \right)+30 \\\ & =30+30 \\\ & =60{}^\circ \text{F} \\\ \end{gathered}
This will not provide us with accurate answers but give us an approximate value.