QUESTION 8
i
Easy
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 \(y = \frac{9}{5}(x − 273) + 32\). Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313 K.
SOLUTION
Substituting \(x = 313\) into the linear equation, we get
\(\begin{aligned} y &= \frac{9}{5}(313 − 273) + 32\\ &= \frac{9}{5}(40) + 32 \\ &= 72 + 31 \\ &= 104\end{aligned}\)
\(\begin{aligned} y &= \frac{9}{5}(313 − 273) + 32\\ &= \frac{9}{5}(40) + 32 \\ &= 72 + 31 \\ &= 104\end{aligned}\)
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Final Answer : Temperature of the liquid = \(104\) °\(F\).
Concept Note
We can solve the question simply by substitution.
The temperature scales are related by a linear equation because the increase in one scale corresponds to a proportional increase in the other.