NEET Physics Thermometry, Calorimetry & Thermal Expansion NEET PYQ-Thermometry, Calorimetry and Thermal Expansion

The value of coefficient of volume expansion of glycerin is \[5\times {{10}^{-4}}{{K}^{-1}}\]. The fractional change in the density of glycerin for a rise of \[40\,{}^\circ C\] in its temperature is                            [NEET (Re) 2015]

A) 0.015

B)      0.020

C) 0.025

D)      0.010

Correct Answer: B

Solution :

Given, the value of coefficient of volume expansion of glycerin is \[5\times {{10}^{-4}}{{K}^{-1}}\].

As, original density of glycerin,

\[\rho ={{\rho }_{0}}(1+Y\Delta T)\]

\[\Rightarrow \] \[\rho -{{\rho }_{0}}={{\rho }_{0}}Y\Delta T\]

Thus, fractional change in the density of glycerine for a rise of \[{{40}^{o}}C\] in its temperature,

\[\frac{\rho -{{\rho }_{0}}}{{{\rho }_{0}}}=Y\Delta T=5\times {{10}^{-4}}\times 40=200-\times {{10}^{-4}}=0.020\]