Question

A liquid which has coefficient of volumetric expansion of$\gamma ,$is heated till there is a temperature change of$\Delta T.$ The density of the liquid after heating is.
$\left(\mathrm{initial}\mathrm{density}\rho \right)$

• A. ${\rho }^{\prime }=\rho (1+\gamma \Delta T)$
• B. ${\rho }^{\prime }=\rho -\gamma \Delta T$
• C. ${\rho }^{\prime }=\rho (1-\gamma \Delta T)$
• D. ${\rho }^{\prime }=\rho +\gamma \Delta T$

Answer 1

The correct option is C ${\rho }^{\prime }=\rho (1-\gamma \Delta T)$

We know that
$m=\rho V=Constant\Rightarrow {\rho }^{\prime }{V}_f={\rho }_i{V}_i\Rightarrow \rho V={\rho }^{\prime }\left\{V\right(1+\gamma \times \Delta T\left)\right\}{\rho }^{\prime }=\frac{\rho }{1+\gamma \Delta T}{\rho }^{\prime }=\rho (1-\gamma \Delta T)$
Becasue $\gamma \Delta T<<1$