Question

A metallic container is completely filled with liquid. The coefficient of linear expansion of the metal is $2.0 \times 10^{-6}$ per $^{\circ} C$ and the coefficient of cubical expansion of the liquid is $6.0 \times 10^{-6}$ per ${ }^{\circ} C$. On heating the vessel :

• A. The liquid will overflow
• B. The level of the liquid will fall
• C. The level of the liquid will remain unchanged
• D. The level of liquid will rise or fall depending on the nature of the metal and of the liquid

Answer 1

Answer: (C)

Coefficient of cubical expansion of container,
$\gamma_{c} =3 \alpha_{c}=3 \times 2 \times 10^{-6}\, {}^{\circ}C ^{-1}$
$=6 \times 10^{-6}\,{}^ {\circ} C ^{-1}$
Coefficient of cubical expansion of liquid,
$\gamma_{l}=6 \times 10^{-6}\, {}^{\circ}C ^{-1}$
Thus, both container and liquid will expand to same extent and level of liquid remain unchanged.