A compound slab is made of two parallel plates of copper and brass of the same thickness and having thermal conductivities in the ratio $4: 1$. The free face of copper is at $0^{\circ} \mathrm{C}$. The temperature of the interface is $20^{\circ} \mathrm{C}$. What is the temperature of the free face of brass?

• A

  $0^{\circ} \mathrm{C}$
• B

  $20^{\circ} \mathrm{C}$
• C

  $40^{\circ} \mathrm{C}$
• Correct answer
  D

  $100^{\circ} \mathrm{C}$

Solution

Given, $K_{\text {copper }}: K_{\text {brass }}=4: 1$ $$ \Rightarrow \quad \frac{K_{\text {copper }}}{K_{\text {brass }}}=\frac{4}{1} $$ Let the temperature of the free surface of brass $=\theta$ Rate of flow of heat will be equal in both the plates as connected in series.

i.e. $H=K_{\text {brass }} \frac{A(\theta-20)}{l}=K_{\text {copper }} \frac{A(20-0)}{l}$ $$ \begin{array}{cl} \Rightarrow \quad \frac{\theta-20}{20} & =\frac{K_{\text {copper }}}{K_{\text {brass }}}=\frac{4}{1} \\ \Rightarrow \quad \theta-20 & =80 \\ \theta & =100^{\circ} \mathrm{C} \end{array} $$

Hence, the correct answer is option: 'D'.