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Mechanical Properties Of Fluids

Question
CBSEENPH11020648
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The value of the coefficient of volume expansion of glycerin is 5 x 10-4 K-1. The fractional change in the density of glycerin for a rise of 400C in its temperature is 

  • 0.015

  • 0.020

  • 0.025

  • 0.010

Solution

B.

0.020

Given the value of coefficient of volume expansion of glycerin  is  5 x 10-4 K-1
As, original density of glycerine 
bold rho bold space bold equals bold space bold rho subscript bold o bold space left parenthesis 1 plus space straight Y increment straight T right parenthesis bold rightwards double arrow bold space bold rho bold space bold minus bold space bold rho subscript bold o space equals space straight rho subscript straight o straight Y increment straight T space
Thus, fractional change in the density of glycerine for a rise of 40o C in its temperature,

fraction numerator bold rho bold space bold minus bold rho subscript bold o over denominator bold p subscript bold o end fraction bold space equals space Y increment T space equals space 5 space x space 10 to the power of negative 4 end exponent space x space 40 space equals space 200 space x space 10 to the power of negative 4 end exponent space equals space 0.020

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