Question

A Celsius thermometer and a Fahrenheit thermometer are put in a hot bath. The reading on Fahrenheit thermometer is just 3 times the reading on Celsius thermometer. The temperature of the hot bath is
A) \[26.67{{\text{ }}^{o}}C\]
B) \[36.67{{\text{ }}^{o}}C\]
C) \[46.67{{\text{ }}^{o}}C\]
D) \[56.67{{\text{ }}^{o}}C\]

Answer 1

Hint: Celsius and Fahrenheit are the scales of measurement units used to check the temperature. The temperature when measured in Celsius scale is denoted as degrees Celsius. The temperature when measured in Fahrenheit scale is denoted as degrees Fahrenheit. The relation between Celsius and Fahrenheit are proportional to each other. Hence, the relationship between the Fahrenheit (F) and Celsius (C) measurement unit is:
\[\dfrac{F-32}{180}=\dfrac{C}{100}\]

Complete step by step solution:
To start with the solution, we need to fill the value of the Fahrenheit temperature as Celsius as given in the question, the value of the Fahrenheit in terms of Celsius is \[F=3C\].
Now placing the value of the Fahrenheit in terms of the Celsius in the formula of conversion is:
\[\dfrac{F-32}{180}=\dfrac{C}{100}\]
\[\dfrac{3C-32}{180}=\dfrac{C}{100}\]
Solving the equation for the variable of \[C\], we have:
\[\Rightarrow 100\left( 3C-32 \right)=C\times 180\]
\[\Rightarrow 300C-180C=3200\]
\[\Rightarrow C=\dfrac{3200}{120}\]
\[\Rightarrow C={{26.67}^{o}}C\]
Therefore, the temperature conversion with Fahrenheit being three times that of the Celsius is \[{{26.67}^{o}}C\].

So, option A is correct

Note: By definition, Celsius scale, or centigrade scale, measures temperature based on freezing and boiling point of water. Whereas Fahrenheit scale measures temperature based on freezing and boiling point of water which ranges from \[{{32}^{o}}F\] to \[{{212}^{o}}F\]. The conversion of Celsius to Fahrenheit is \[\left( C\times 1.8 \right)+32=F\] and from Fahrenheit to Celsius is \[\dfrac{F-32}{180}=\dfrac{C}{100}\].