Question

If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation

`y = 9/5 (x - 273) + 32`

1. Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313°K.
2. If the temperature is 158°F, then find the temperature in Kelvin.

Answer 1

Given relation is `y = 9/5 (x - 273) + 32`  ...(i)

i. Given, x = 313°K, then from equation (i), we get

`y = 9/5 (313 - 273) + 32`

= `9/5 xx 40 + 32`

= 9 × 8 + 32

= 72 + 32

= 104°F

ii. Given, y = 158°F, then from equation (i), we get

`158 = 9/5 (x - 273) + 32`

⇒ `158 = (9(x - 273) + 32 xx 5)/5` 

⇒ 158 × 5 = 9(x – 273) + 160

⇒ 790 = 9(x – 273) + 160

⇒ 790 – 160 = 9(x – 273)

⇒ 9(x – 273) = 630

⇒ `x - 273 = 630/9 = 70`

⇒ x – 273 = 70

∵ x = 70 + 273 = 343°K