Question

An open vessel is filled completely with oil which has the same coefficient of volume expansion as that of the vessel. On heating both oil and vessel
A. the vessel can contain more volume and more mass of oil
B. the vessel can contain same volume and same mass of oil
C. the vessel can contain same volume and more mass of oil
D. the vessel can contain more volume and same mass of oil

Answer 1

Hint: Firstly, you could recall that on applying heat both the vessel and the oil contained in it undergoes thermal expansion. Now, you could recall the expression for volume expansion. Analyzing the expression along with the given conditions in the question, you will be able find the true statement from the given options.

Formula used:
Volume expansion,
$\dfrac{\Delta V}{V}={{\alpha }_{v}}\Delta T$

Complete answer:
In the question, we are given an open vessel that is filled up to the brim with an oil of the same coefficient of volume expansion as that of the vessel in which it is kept. We are given certain statements in the options which are four possibilities of what may happen as the result of heating both oil and vessel.
We know that on heating a substance, be it solid, liquid or gas, it will undergo thermal expansion. So, the change in volume due to thermal expansion is given by the expression,
$\dfrac{\Delta V}{V}={{\alpha }_{v}}\Delta T$
In the given case, as the oil is filled up to the brim of the vessel, the volume of the vessel as well as the oil will be the same before thermal expansion. When heat is applied to the system, the resultant temperature change$\left( \Delta T \right)$ will be also same and we are also given that the coefficient of volume expansion $\left( {{\alpha }_{v}} \right)$ is same for both. Hence, we could conclude from the above expression that the volume expansion due to heat supplied will be the same for both oil and vessel. Or we could say that a vessel can easily contain the increased volume of oil with the same mass as the volume of the vessel is also increased by the same amount.

Hence, option D is found to be the correct answer.

Note:
The coefficient of thermal expansion actually gives us an idea of how the size of an object changes along with the change in temperature. Expansion or contraction occurs in all directions as the result of this temperature change. Volumetric expansion coefficient is found to be more significant in the case of liquids.