 # If the temperature of a liquid can be `
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.

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

(i) find the temperature of the liquid in fahrenheit, if the temperature of the liquid is 313K.

(ii) If the temperature is 158°F, then find the temperature in kelvin.

Solution:

Given relation is $y=\frac{9}{5}(x-273)+32$ $\ldots$ (i)

(i) Given, $x=313^{\circ} \mathrm{K}$, then from Eq. (i), we get

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

$=\frac{9}{5} \times 40+32=9 \times 8+32=72+32=104^{\circ} \mathrm{F}$

(ii) Given, $y=158^{\circ} \mathrm{F}$, then from Eq. (i), we get

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

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

$\Rightarrow$ $158 \times 5=9(x-273)+160$

$\Rightarrow$ $790=9(x-273)+160$

$\Rightarrow$ $790-160=9(x-273)$

$\Rightarrow$ $9(x-273)=630$

$\Rightarrow$ $x-273=\frac{630}{9}=70 \Rightarrow x-273=70$

$\because$ $x=70+273=343^{\circ} \mathrm{K}$