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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.

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.
Coefficient of volume expansion $\gamma =\dfrac{\Delta p}{p\Delta T}=\dfrac{p_1-p_2}{p(\Delta \theta )}=\dfrac{10-9.7}{10\times (100-0)}$
$=3\times {{10}^{-4}}$