JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Heat & Thermodynamics

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

^{0} C

, if this thermometer in the contact with the object reads

x_{0} /2

Answer: (A)

Solution

On a linear scale the temperature is fixed by where the reading falls between the ice point and the steam point,

t = \frac{x _{t} - x _{i ce}}{x _{s t e am} - x _{i ce}} \times 10 0^{\circ}

C. Here the steam point reads

x_{0}

, the ice point reads

x_{0} /3

, and the object reads

x_{0} /2

, so

t = \frac{\frac{x _{0}}{2} - \frac{x _{0}}{3}}{x _{0} - \frac{x _{0}}{3}} \times 100 = \frac{x _{0} /6}{2 x _{0} /3} \times 100 = \frac{1}{4} \times 100 = 2 5^{\circ}

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option