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.
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
$158=\frac{9}{5}(x-273)+32$
$\Rightarrow$ $158=\frac{9(x-273)+32 \times 5}{5}$
$\Rightarrow$ $158 \times 5=9(x-273)+160$
$\Rightarrow$ $790=9(x-273)+160$
$\Rightarrow$ $790-160=9(x-273)$
$\Rightarrow$ $9(x-273)=630$
$\Rightarrow$ $x-273=\frac{630}{9}=70 \Rightarrow x-273=70$
$\because$ $x=70+273=343^{\circ} \mathrm{K}$
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