Question

The ratio of the coefficient of volume expansion of glass container to that of a viscous liquid kept in it is 1:4. What fraction of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?

Answer 1

The volume fraction is 1/4

Given:

Coefficient of volume expansion of glass to viscous liquid = 1:4

To find:

Volume fraction = ?

Formula:

Volume expansion:

$\bold{\Delta V=V_0\beta\Delta T}$

Where,

$\bold{V_0}$ = Initial Volume

$\bold{\beta}$ = Coefficient of volume expansion

$\bold{\Delta T}$ = Change in temperature

Solution:

Volume expansion of glass:

$\bold{\Delta V=V_g\beta_g \Delta T}$

$\bold{\Delta V = V_g\times 1\times \Delta T}$

Volume expansion of viscous liquid:

$\bold{\Delta V=V_v\beta_v \Delta T}$

$\bold{\Delta V=V_v \times 4 \times \Delta T}$

We need to find the fraction and there is no change in temperature and volume, so,

$\bold{\frac{\Delta V}{\Delta V}=\frac{V_v\times4\times\Delta T}{V_g\times1\times\Delta T}}$

$\bold{1=\frac{V_v\times4}{V_g\times1}}$

$\bold{\therefore \frac{V_v}{V_g}=\frac{1}{4}}$