Question

The density of a liquid at ${100}^0$C is $8.0gm/c{m}^3$ and at ${10}^0$C is $8.4gm/c{m}^3$. The coefficient of cubical expansion of the liquid is nearly :

• A. ${10}^{-4}{/}^0{C}^{-1}$
• B. $5\times {10}^{-4}{/}^0{C}^{-1}$
• C. $8\times {10}^{-4}{/}^0{C}^{-1}$
• D. $4\times {10}^{-4}{/}^0{C}^{-1}$

Answer 1

The correct option is B $5\times {10}^{-4}{/}^0{C}^{-1}$

Here,

${\rho }_o=8gm/c{m}^3$,

$\rho =8.4gm/c{m}^3$,

$\Delta T=10-100=-{90}^{o}C$,

Coefficient of cubical expansion$=\gamma$

The relation between densities of liquid at different temperatures and Coefficient of cubical expansion is given by,

$\rho =\frac{{\rho }_o}{1+\gamma \Delta T}$

Putting the values we get,

$8.4=\frac{8}{1+\gamma \times (-90)}$

$\therefore \gamma =5.29\times {10}^{-4}\approx 5\times {10}^{-4}{/}^{o}C$ is the coefficient of cubical expansion of the liquid.