A linear scale thermometer reads x_0 when in contact with boiling water and x_0/3 when in contact with ice. If the thermometer reads x_0/2 when touching an object, what is the object's temperature in ^circtext C ?

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EEJ MAIN Physics QUESTION #7058

Question 1

A linear scale thermometer reads $x_0$ when in contact with boiling water and $x_0/3$ when in contact with ice. If the thermometer reads $x_0/2$ when touching an object, what is the object's temperature in $^\circ\text{C}$?

$25$✔️
$50$
$37.5$
$33.3$

Correct Answer Explanation

For a linear scale, the temperature $T$ is related to reading $x$ by: $\frac{T - T_{ice}}{T_{steam} - T_{ice}} = \frac{x - x_{ice}}{x_{steam} - x_{ice}}$

$\frac{T - 0}{100 - 0} = \frac{x_0/2 - x_0/3}{x_0 - x_0/3}$

$\frac{T}{100} = \frac{x_0/6}{2x_0/3} = \frac{1}{6} \times \frac{3}{2} = \frac{1}{4}$

$T = \frac{100}{4} = 25^\circ\text{C}$.

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