Question

The co-efficient of thermal conductivity of copper, mercury and glass respectively are $K_c,K_m$ and $K_g$ such that $K_c>K_m>K_g$. If the same quantity of heat is flowing per sec per unit area through each and corresponding temperature gradient are $X_c,X_m$ and $X_g$. Then :

• A. $X_c=X_m=X_g$
• B. $X_c>X_m>X_g$
• C. $X_c<X_m<X_g$
• D. $X_m<X_c<X_g$

Answer 1

Answer: (C)

$X_c<X_m<X_g$

Heat flow is given by the formula: $\dot{Q}=KA\frac{dT}{dx}$
Where: $\frac{dT}{dx}$ is $X$ (The temperature gradient)
K is the coefficient of thermal conductivity, and A is the area of the cross section perpendicular to which the heat is flowing.
Given that heat flow and area is same for all 3 cases:

$KX=constant=K_c{X}_c=K_m{X}_m=K_g{X}_g$
So the temperature gradients must follow the reverse order of comparison.
If $K_c>K_m>K_g$ then $X_c<X_m<X_g$