Question

A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1:4$ . If the free face of brass is at $100 \,{}^{^\circ }C$ and that of copper at $0 \,{}^{^\circ }C$ , the temperature of the interface is

• A. $80^\circ C$
• B. $20^\circ C$
• C. $60^\circ C$
• D. $40^\circ C$

Answer 1

Answer: (A)

We know that $\frac{d Q}{d t}=\frac{K A \left(\left(\theta \right)_{2} - \left(\theta \right)_{1}\right)}{d}$
As slabs are in series, therefore
$\Rightarrow K_1\left(\theta_1-\theta_{\mathrm{C}}\right)=K_2\left(\theta_{\mathrm{C}}-\theta_2\right)$
$\Rightarrow 4K\left(100 - \theta \right)=K\left(\theta - 0\right)$
$\Rightarrow \, \, 400-4\theta =\theta $
$\Rightarrow \, \, \, \theta =80^\circ C$