Density of water at 20^oC is 0.998, gm/cm^3 and at 40^oC is 0.992, gm/cm^3 . mean coefficient o

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10-1.Thermometry, Thermal Expansion and Calorimetry

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The density of water at $20^oC$ is $0.998\, gm/cm^3$ and at $40^oC$ is $0.992\, gm/cm^3$. The mean coefficient of cubical expansion (in per $^oC$) is :-

A

$1 \times 10^{-4}$

B

$2 \times 10^{-4}$

C

$3 \times 10^{-4}$

D

$6 \times 10^{-4}$

Solution

$\rho_{2}-\rho_{1}=\left(\mathrm{t}_{2}-\mathrm{t}_{1}\right) \rho_{1} \gamma$

$\gamma =\frac{\rho_{2}-\rho_{1}}{\left(\mathrm{t}_{2}-\mathrm{t}_{1}\right) \rho_{1}} $

$ = \frac{{0.998 – 0.992}}{{(40 – 20) \times 0.998}} = \frac{{0.006}}{{20 \times 0.998}} = 3 \times {10^{ – 4}}{\,^\circ }{\rm{C}}$

Standard 11

Physics

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