The value of 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 40°C in its temperature, is:

 

  • Option 1)

    0.020

  • Option 2)

    0.025

  • Option 3)

    0.010

  • Option 4)

    0.015

 

Answers (1)

As we learnt

Variation of Density with Temperature -


ho=frac{
ho}{(1+gamma Delta 	heta)}=
ho(1-gamma Delta 	heta)

- wherein

Delta 	heta=Change in temperature

 

 

\gamma =5\times 10^{-4}K^{-1}

\rho=\frac{\rho _{o}}{1+\gamma \Delta T} \: \: =\rho _{o}(1-\gamma \Delta T)

\Rightarrow \rho =\rho _{o}-\rho _{o}\gamma \Delta T \: \: \: or \: \: \: \: \frac{\rho _{o}-\rho }{\rho _{o}}=\gamma \Delta T

\frac{\rho _{o}-\rho }{\rho _{o}} \: = \: Fractional \: change \: in \: the \: density \: of \: glycerin

             =\gamma \Delta T=5\times 10^{-4}\times 40

             = .02

                    


Option 1)

0.020

This option is correct

Option 2)

0.025

This option is incorrect

Option 3)

0.010

This option is incorrect

Option 4)

0.015

This option is incorrect

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