Question

The liquid with co-efficient of real expansion of $27\times {10}^{-6}{/}^{o}C$ is heated in a vessel with the coefficient of linear expansion$9\times {10}^{-6}{/}^{o}C$ . The level of the liquid :

• A. rises
• B. falls
• C. remains same
• D. first falls then rises

Answer 1

The correct option is C remains same

Let ${\gamma }_r=$ real volume expansion coefficient of liquid
Let ${\gamma }_a=$ apparent volume expansion coefficient of liquid
Let ${\gamma }_g=$ real volume expansion coefficient of the vessel
${\gamma }_r={\gamma }_a+{\gamma }_g$
$\therefore {\gamma }_a={\gamma }_r-{\gamma }_g$
But, ${\gamma }_g=3{\alpha }_g=3\ast 9\ast {10}^{-6}{/}^{0}C=27\ast {10}^{-6}{/}^{0}C$ where ${\alpha }_g$ is the linear expansion coefficient of the vessel.
${\gamma }_r=27\ast {10}^{-6}{/}^{0}C$ as given
$\therefore {\gamma }_a=0$ since ${\gamma }_r={\gamma }_g$
Hence, liquid level remains same.