Question

The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{\circ }C$. When the liquid is heated to a temperature T, the change in density will be

• A. $\frac{-\rho \gamma T}{(1+\gamma T)}$
• B. $\frac{\rho \gamma T}{(1+\gamma T)}$
• C. $-\frac{\rho (1+\gamma T)}{\gamma T}$
• D. $\frac{\rho (1+\gamma T)}{\gamma T}$

Answer 1

The correct option is A

$\frac{-\rho \gamma T}{(1+\gamma T)}$

The density of the liquid at temperature T is given by ${\rho }^{\prime }=\frac{\rho }{1+\gamma T}$
Now, change in density is ${\rho }^{\prime }-\rho =\frac{\rho }{1+\gamma T}-\rho$
$=-\frac{\gamma \rho T}{1+\gamma T}$
Hence, the correct choice is (a).