A $\mathrm{KCl}$ solution of conductivity $0.14 \mathrm{S}{ \mathrm{m}}^{-1}$ shows a resistance of $4.19\mathrm{\Omega }$ in a conductivity cell. If the same cell is filled with an $\mathrm{HCl}$ solution, the resistance drops to $1.03\Omega$. The conductivity of the HCl solution is ____$\times {10}^{-2} \mathrm{S}{ \mathrm{m}}^{-1}$. (Round off to the Nearest Integer).

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by $\mathrm{\kappa }$, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity

$\mathrm{\kappa }=\frac{1}{\mathrm{R}}·{\mathrm{G}}^{*}$

For same conductivity cell, ${\mathrm{G}}^{*}$ is constant and hence $\mathrm{\kappa }·\mathrm{R}.=$ constant.

$\therefore 0.14\times 4.19=\kappa \times 1.03$

or, $=\frac{0.14\times 4.19}{1.03}$

$=0.5695{\mathrm{Sm}}^{-1}$

$=56.95\times {10}^{-2}{\mathrm{Sm}}^{-1}\approx 57\times {10}^{-2}{\mathrm{Sm}}^{-1}$