If the temperature of a liquid can be measured in Kelvin units as x K and in Fahrenheit Class 9

If the temperature of a liquid can be measured in Kelvin units as x K and in Fahrenheit Class 9

Question 1.

If the temperature of a liquid can be measured in Kelvin units as x K and in Fahrenheit units as y °F, the relation between the two systems of measurement of temperature is given by the linear equation y = $\frac{9}{5}$ (x - 273) + 32. Class 9

i. Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313 K.

ii. If the temperature is 158 °F, then find the temperature in Kelvin.

Solution:

i. The linear equation relating x Kelvin and y° Fahrenheit is given by

y = $\frac{9}{5}$(x - 273) + 32 ...(i)

Substituting x = 313 in (i), we get

y = $\frac{9}{5}$ (313 - 273) + 32

∴ y = $\frac{9}{5}$ × 40 + 32

∴ y = 9 × 8 + 32

∴ y = 72 + 32 = 104

The temperature of the liquid is 104 °F.

ii. Substituting y = 158 in (i), we get

158 = $\frac{9}{5}$ (x - 273) + 32

158 - 32 = $\frac{9}{5}$ (x - 273)

∴ 126 = $\frac{9}{5}$ (x - 273)

∴ 126 × $\frac{9}{5}$ = x - 273

∴ 14 × 5 = x - 273

∴ 70 = x - 273

∴ x = 70 + 273

∴ x = 343 K

∴ The temperature of the liquid is 343 K.