QUESTION 8
ii
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 \(y =\) \( \frac{9}{5} \)\((x − 273) + 32\). If the temperature is 158 °F, then find the temperature in Kelvin.
SOLUTION
Substituting \(y = 158\) into the linear equation, we get
\(158 = \frac{9}{5}(x − 273) + 32\)
⇒ \(126 = \frac{9}{5}(x − 273)\)
⇒ \(x − 273 = \frac{126 × 5}{9}\)
⇒ \(x = 70 + 273\)
⇒ \(x = 343\)
\(158 = \frac{9}{5}(x − 273) + 32\)
⇒ \(126 = \frac{9}{5}(x − 273)\)
⇒ \(x − 273 = \frac{126 × 5}{9}\)
⇒ \(x = 70 + 273\)
⇒ \(x = 343\)
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Final Answer : Temperature of the liquid = \(343\) \( K\).
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.