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The coefficients of thermal conductivity of copper, mercury and glass are respectively $Kc, Km$ and $Kg$ such that $Kc > Km > Kg$ . If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $Xc, Xm$ and $Xg$ , then
${X_c} = {X_m} = {X_g}$
${X_c} > {X_m} > {X_g}$
${X_c} < {X_m} < {X_g}$
${X_m} < {X_c} < {X_g}$
Solution
(c) $\frac{Q}{{At}} = K\frac{{\Delta \theta }}{l}$ ==> $K\frac{{\Delta \theta }}{l}$= constant ==> $\frac{{\Delta \theta }}{l} \propto \frac{1}{K}$
Hence If ${K_c} > {K_m} > {K_g}$, then
${\left( {\frac{{\Delta \theta }}{l}} \right)_c} < {\left( {\frac{{\Delta \theta }}{l}} \right)_m} < {\left( {\frac{{\Delta \theta }}{l}} \right)_g} \Rightarrow {X_c} < {X_m} < {X_g}$
because higher $ K$ implies lower value of the temperature gradient.
