Question

In the figure shown below, two metallic slabs of same area of cross section and thickness having thermal conductivities $500{\text{W/m}}^{\circ }\text{C}$ and $600{\text{W/m}}^{\circ }\text{C}$ respectively are connected to the same temperature difference in parallel combination. Find the equivalent thermal conductivity (in ${\text{W/m}}^{\circ }\text{C}$)

• A. $600$
• B. $500$
• C. $550$
• D. $450$

Answer 1

The correct option is C $550$

Given,
$A_1=A_2=A,l_1=l_2=l$
Thermal conductivity of slab $1$ $\left(k_1\right)=500{\text{W/m}}^{\circ }\text{C}$
Thermal conductivity of slab $2$ $\left(k_2\right)=600{\text{W/m}}^{\circ }\text{C}$
Equivalent thermal conductivity $\left(k_{eq}\right)=\frac{k_1+k_2}{2}=\frac{500+600}{2}$
$=550{\text{W/m}}^{\circ }\text{C}$