The mercury column of height $\;0.8\;gm\;$ at $\;0^{0}C\;$ balances the mercury column of height $\;0.8144\;m\;$ at $\;100^{0}C\;$ . Calculate the coefficient of real expansion of mercury ?

$(a)\;0.0018/^{0}C\qquad(b)\;0.00018/^{0}C\qquad(c)\;0.018/^{0}C\qquad(d)\;0.0016/^{0}C$

Answer : $\;0.00018/^{0}C$
Explanation :
When 2 liquid columns balance each other , the processes exerted by them are equal to one another .
$h_{1} \rho_{1} g = h_{2} \rho_{2} g$
$\large\frac{\rho_{1}}{\rho_{2}}=\large\frac{h_{2}}{h_{1}}$
$\large\frac{\rho_{1}}{\rho_{2}}=\large\frac{0.811}{0.8}$
$1+ \bigtriangleup t=1.018$
$r=0.00018/^{0}C$