Question

In an experiment a solution of hydrochloric acid is to be kept between 25° and 30° celsius. What is the Range of temperature in degree fahrenheit? (f conversion formula is given by C = \(\frac{5}{9}\) (F - 32) where C and F represent temperature in degree celsius and degree fahrenheit respectively.

Answer 1

According to question:

25° < C < 30° ........ (i)

and C = \(\frac{5}{9}\) (F - 32) ........ (ii)

From equation (i) and (ii),

25 < \(\frac{5}{9}\) (F - 32) < 30

⇒ \(\frac{9}{5}\) × 25 < F - 32 < \(\frac{9}{5}\) × 30 (Multiplying by \(\frac{9}{5}\))

⇒ 45 < F - 32 < 54

⇒ 45 + 32 < F - 32 + 32 < 54 + 32 (Adding 32 on both sides)

⇒ 77 < F < 86

Thus, the required range of temperature is between 77°F and 86°F.