Question

The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{o}C$. When the liquid is heated to 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 $-\frac{\rho \gamma T}{(1+\gamma T)}$

Density of liquid at temperature T=$\frac{\rho }{1+\gamma T}$

$⟹$ Change in density of liquid$=\rho -\frac{\rho }{1+\gamma T}=-\frac{\rho \gamma T}{1+\gamma T}$