Question

A thermometer graduated according to a linear scale reads a value \(x_0\) when in contact with boiling water, and \(\dfrac{x_0}{3}\) when in contact with ice. What is the temperature of an object in \(^\circ 𝐶\), if this thermometer in the contact with the object reads \(\dfrac{x_0}{2}\) ?

Answer 1

We know that: \(\dfrac{T-T_{FP}}{T_{BP}-T_{FP}}=\text{constant}\)

Given: \(T_{BP}=x_0, T_{FP}=\dfrac{x_0}{3}\)
Let the temperature of the object in \({𝑇_c}^\circ C\) when the thermometer reads \(\dfrac{x_0}{2}\)

\(\dfrac{T-T_{FP}}{T_{BP}-T_{FP}}=\text{constant}\)

\(\dfrac{T_c-0}{100-0}=\dfrac{\dfrac{x_0}{2}-\dfrac{x_0}{3}}{x_0-\dfrac{x_0}{3}}\)

\(\dfrac{T_c}{100}=\dfrac{\dfrac{1}{6}}{\dfrac{2}{3}}\)

\(T_c=100\times \dfrac{1}{4}\)

\(=25^\circ C\)

Final Answer: (b)