Question

Two metallic slabs of same area of cross section and length having thermal conductivities $300{\text{W/m}}^{\circ }\text{C}$ and $200{\text{W/m}}^{\circ }\text{C}$ respectively are connected in series combination. Find the equivalent thermal conductivity (in ${\text{W/m}}^{\circ }\text{C}$)

• A. $240$
• B. $360$
• C. $250$
• D. $275$

Answer 1

The correct option is A $240$

Given , $A_1=A_2,l_1=l_2$
Thermal conductivity of slab 1 $\left(k_1\right)=300{\text{W/m}}^{\circ }\text{C}$
Thermal conductivity of slab 2 $\left(k_2\right)=200{\text{W/m}}^{\circ }\text{C}$
Equivalent thermal condictivity $\left(k_{eq}\right)=\frac{2k_1{k}_2}{k_1+k_2}$
$=\frac{2\times 200\times 300}{500}$
$=\frac{1200}{5}=240{\text{W/m}}^{\circ }\text{C}$