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. ${12}^{0}C$
• C. ${14}^{0}C$
• D. ${16}^{0}C$

Answer 1

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

We have the equation for converting temperature in degree Fahrenheit to temperature in degree Celsius as,

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

Let the initial atmospheric temperature be $T_F=x^{0}F$

Hence,

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

or

$T_C=(x-32)(\frac{5}{9}{)}^{0}C$

If temperature rises by ${18}^{0}F$,

Then, final temperature, $T_{F1}=(x+18{)}^{0}F$

Hence,

$\frac{T_{C1}-0}{100}=\frac{x+18-32}{180}$

or

$T_{C1}=(x-14)(\frac{5}{9}{)}^{0}C$

Therefore, rise in temperature,

$T_{C1}-T_C=(x-14-x+32)\left(\frac{5}{9}\right)={10}^{0}C$