Question

You have $mkgs$ of a certain liquid in a vessel, which is heated till there is a temperature change of $\Delta T$. If the coefficient of volume expansion is $\gamma$, what is the density of the liquid after heating, if the initial density was $\rho$?

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

Answer 1

The correct option is D

${\rho }^{\prime }$ = $\rho (1-\gamma \Delta T)$

We know that
$m=\rho V=Constant\Rightarrow {\rho }_1{V}_2={\rho }_2{V}_2\Rightarrow \rho V={\rho }^1\left\{V\right(1+\gamma \times \Delta T\left)\right\}{\rho }^1=\frac{\rho }{1+\gamma \Delta T}{\rho }^1=\rho (1-\gamma \Delta T)$