Question

A thermometer graduated according to a linear scale reads a value $x_0$ when in contact with boiling water, and $x_0/3$ 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 $x_0/2$?

Answer 1

Let required temperature $= T^{\circ}C$

$\Rightarrow T^{\circ} C = \frac{x_0}{2} -\frac{x_0}{3} = \frac{x_0}{6}$
&$(x_0 - \frac{x_0}{3}) = (100 - 0^{\circ})$
$\Rightarrow \frac{2x_0}{3} = 100$
$\Rightarrow x_0 = \frac{300}{2}$
$\Rightarrow T^{\circ}C = \frac{x_0}{6} = \frac{150}{6} = 25^{\circ}C$