Question

In an experiment, a solution of hydrochloric acid is to be kept between 30° and 35° Celsius. What is the range of temperature in degree Fahrenheit if conversion formula is given by $\mathrm{C}=\frac{5}{9}$ (F – 32), where C and F represent temperature in degree Celsius and degree Fahrenheit, respectively.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{As}\mathrm{C}=\frac{5}{9}\left(\mathrm{F}-32\right) \\ \Rightarrow \mathrm{F}-32=\frac{9\mathrm{C}}{5} \\ \Rightarrow \mathrm{F}=\frac{9\mathrm{C}}{5}+32 \\ \mathrm{When}\mathrm{temperature}=30°\mathrm{C} \\ \mathrm{F}=\frac{9\left(30\right)}{5}+32=\frac{270}{5}+32=\frac{270+160}{5} \\ =\frac{430}{5}=86°\mathrm{F} \\ \mathrm{When}\mathrm{temperature}=35°\mathrm{C} \\ \mathrm{F}=\frac{9\left(35\right)}{5}+32=\frac{315}{5}+32=\frac{315+160}{5} \\ =\frac{475}{5}=95°\mathrm{F} \\ \mathrm{Range}\mathrm{of}\mathrm{temperature}86°\mathrm{F}<\mathrm{temperature}<95°\mathrm{F} \end{gathered}$$
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