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The density of a substance at $0{}^\circ C$is $10\dfrac{g}{cc}$ and at $100{}^\circ C$, its density is $9.7\dfrac{g}{cc}$. The coefficient of volume expansion of the substance is
(A) $2\times {{10}^{-2}}$
(B) $3\times {{10}^{-4}}$
(C) $4\times {{10}^{-6}}$
(D) $6\times {{10}^{-3}}$

Last updated date: 29th May 2024
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Hint: We know that thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic energy of a substance. The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, the change in size or volume of a given mass with temperature. Railroad tracks and bridges, for example, have expansion joints to allow them to freely expand and contract with temperature changes.

Complete step-by step answer:

Volume expansion is defined as the increase in the volume of the solid on heating. With a change in temperature $\Delta t$ the change in volume of a solid is given by $\Delta v={{V}_{y}}\Delta t$ where the coefficient of volume expansion is y.
Thus, we can say that the volumetric thermal expansion coefficient is the most basic thermal expansion coefficient, and the most relevant for fluids. In general, substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions.
Coefficient of volume expansion $\gamma =\dfrac{\Delta p}{p\Delta T}=\dfrac{p_1-p_2}{p(\Delta \theta )}=\dfrac{10-9.7}{10\times (100-0)}$
$=3\times {{10}^{-4}}$

Hence, the correct answer is Option B.

Note: It should be known to us that thermal expansion is caused when seawater expands because of the higher temperature of the water. Since the oceans absorb heat from the atmosphere, when the atmosphere becomes warmer so will the oceans. The increased volume will cause the level of the water in the oceans to rise. The amount by which it expands depends on three factors: its original length, the temperature change, and the thermal or heat properties of the metal itself. Some substances simply expand more easily than others.
We can also say that the warming of Earth is primarily due to accumulation of heat-trapping greenhouse gases, and more than 90 percent of this trapped heat is absorbed by the oceans. As this heat is absorbed, ocean temperatures rise and water expands. This thermal expansion contributes to an increase in global sea level.