Question

The density of mercury is $13.6gc{m}^{-3}$ at $0^{\circ }C$ and its coefficient of cubical expansion is $1.82\times {10}^{-4}{}^{\circ }{C}^{-1}$. Calculate the density of mercury at ${50}^{\circ }C$

Answer 1

Let the mass of mercury m= 13.6 gm and volume be $V=1c{m}^3$.

Now change in volume when it is heated upto ${50}^{o}C$,

$\Delta V=V\alpha \Delta T$

$\Delta V=1\times 1.82\times {10}^{-4}\times 50$

$\Delta V=91\times {10}^{-4}c{m}^3$

New volume $V_1=V+\Delta V=1.0091c{m}^3$

New density $\rho =\frac{m}{V_1}=\frac{13.6}{1.0091}=13.48gc{m}^{-3}$