Question

During the day time, the atmospheric temperature rises by ${18}^{0}F$. What is the corresponding rise on Celsius scale?

• A. ${10}^{0}C$
• B. ${20}^{0}C$
• C. ${30}^{0}C$
• D. ${40}^{0}C$

Answer 1

The correct option is A ${10}^{0}C$

We have relation between Celsius scale and Fahrenheit scale ,

$\frac{T_C-0}{100}=\frac{T_F-32}{180}$ ,

Let the initial atmospheric temperature be $T_F=x^{o}F$ ,

Hence , $\frac{T_C-0}{100}=\frac{x-32}{180}$ ,

or $T_C=\left(5/9\right)(x-32{)}^{o}C$ ,

If temperature rises by ${18}^{o}F$ ,

Then final temperature , $T_F^{\prime }=(x+18{)}^{o}F$

Hence , $\frac{T_C^{\prime }-0}{100}=\frac{x+18-32}{180}$ ,

or $T_C^{\prime }=\left(5/9\right)(x-14{)}^{o}C$ ,

Therefore rise in temperature ,

$T_C^{\prime }-T_C=\left(5/9\right)(x-14-x+32)={10}^{o}C$