Question

Question 5
If the temperature of a liquid can be measured in Kelvin units as $x^{\circ }$ K or in Fahrenheit units as $y^{\circ }$ 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 313 k.

(ii) If the temperature is ${158}^{\circ }$ F, then find the temperature in Kelvin.

Answer 1

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

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

$y=\frac{9}{5}(313-273)+32$
$=\frac{9}{5}\times 40+32$
$=72+32={104}^{\circ }F$


(ii) Given, $y={313}^{\circ }$ F, then from Eq(i); we get,

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