Question

The temperature on the Celsius scale is \[{25^{\text{o}}}\;{\text{C}}\]. What is the corresponding temperature on the Fahrenheit scale?
(A). \[{40^{\text{o}}}\;{\text{F}}\].
(B). \[{77^{\text{o}}}\;{\text{F}}\].
(C). \[{50^{\text{o}}}\;{\text{F}}\].
(D). \[{45^{\text{o}}}\;{\text{F}}\].

Answer 1

Hint:In this question, the concept of the conversion factor for the change in the scale of the temperature will be used. As we know that the relation between the Celsius and the Fahrenheit is given by the expression in which Fahrenheit is directly proportional temperature. Fahrenheit is the measurement of the temperature in a small unit of temperature.

Complete step by step solution:
-As we know that the Celsius and Fahrenheit are the measuring scale of temperature. In the Celsius scale, \[{100^{\text{o}}}{\text{C}}\] is the boiling point of the water and \[{0^{\text{o}}}{\text{C}}\] is the freezing point of the water. But in Fahrenheit scale, \[{212^{\text{o}}}{\text{F}}\] is the boiling point of the water and \[{32^{\text{o}}}{\text{F}}\] is the freezing point of the water. And represent by \[^{\text{o}}{\text{C}}\] and represent the Fahrenheit by \[^{\text{o}}{\text{F}}\].
-So, the relation between the Celsius and Fahrenheit is that they are directly proportional to each other. According to the question, we are given the temperature as,
\[ \Rightarrow {T_{\left( {^{\text{o}}{\text{C}}} \right)}} = {25^{\text{o}}}{\text{C}}\]
-Now we will calculate the corresponding temperature by using the relation,
\[ \Rightarrow {T_{\left( {^{\text{o}}{\text{F}}} \right)}} = {T_{\left( {^{\text{o}}{\text{C}}} \right)}} \times \dfrac{9}{5} + 32\]
-Now, we substitute the value of the Celsius temperature.
\[ \Rightarrow {T_{\left( {^{\text{o}}{\text{F}}} \right)}} = 25 \times \dfrac{9}{5} + 32\]
-Further solving the term, we get
\[ \Rightarrow {T_{\left( {^{\text{o}}{\text{F}}} \right)}} = 45 + 32\]
-Adding the values, we get
\[\therefore {T_{\left( {^{\text{o}}{\text{F}}} \right)}} = {77^{\text{o}}}{\text{F}}\]
-So, the corresponding temperature of the Fahrenheit scale is \[{77^{\text{o}}}\;{\text{F}}\].
Therefore, the option B is the correct option that is \[{77^{\text{o}}}\;{\text{F}}\].

Note:
As we know that the measuring scale which reads the temperature in Celsius and in Fahrenheit is the same at \[{40^{\text{o}}}\]. In Celsius, the temperature of the human body is \[{37^{\text{o}}}{\text{C}}\] and in Fahrenheit, the temperature of the human body is \[{98.6^{\text{o}}}\;{\text{F}}\].