Question

A long cylindrical vessel of volume V and linear coefficient of expansion $\alpha$ contains a liquid. The level of liquid has not changed on heating.The volume coefficient of real expansion of liquid is

• A. $\frac{V-a}{V}$
• B. $\frac{V+a}{V}$
• C. $\frac{v}{V-a}$
• D. 3a

Answer 1

The correct option is D 3a

Change in volume of the vessel upon heating $\Delta V=V{\alpha }_V\Delta T$
Change in volume of the liquid upon heating $\Delta V_b=V_b{\alpha }_{Vb}\Delta T$
where ${\alpha }_V$ and ${\alpha }_{Vb}$ are real volume expansion coefficients of the vessel and liquid, $V$ and $V_b$ are volume of the vessel and liquid before heating and $\Delta T$ is the change in temperature.
As the level of the liquid does not change, the coefficient of apparent expansion of the liquid is zero
So the coefficient of real volume expansion of the liquid is equal to volume expansion coefficient of vessel which is equal to $3\alpha$
option (D) is the correct answer