JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Topic Test - Thermometry, Thermal Expansion and Calorimetry (3-5-21)

A constant pressure air thermometer gave a reading of 47.5 units of volume when immersed in ice cold water, and 67 units in a boiling liquids. The boiling point of the liquid will be

A) \[135{}^\circ C\]

B) \[125{}^\circ C\]

C) \[112{}^\circ C\]

D) \[100{}^\circ C\]

Correct Answer: C

Solution :

Initial volume \[{{V}_{1}}=47.5\] units

Temperature of ice cold water \[{{T}_{1}}=0{}^\circ C=273\,K\]

Final volume of \[{{V}_{2}}=67\] units

Applying Charles law, we have \[\frac{{{V}_{1}}}{{{T}_{1}}}=\frac{{{V}_{2}}}{{{T}_{2}}}\]

(where temperature \[{{T}_{2}}\] is the boiling point)

or \[{{T}_{2}}=\frac{{{V}_{2}}}{{{V}_{1}}}\times {{T}_{1}}=\frac{67\times 273}{47.5}=385\,K=112{}^\circ C\]