Two cylinders P and Q have the same length and diameter and are made of different materials having thermal conductivities in the ratio 2 : 3. These two cylinders are combined to make a cylinder. One end of P is kept at 100°C and another end of Q at 0°C. The temperature at the interface of P and Q is
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Temperature of interface $\theta = \frac{K_1 \theta_1 + K_2 \theta_2}{K_1 + K_2}$ where $K_1 = 2K$ and $K_2 = 3K \quad \left(\therefore \frac{K_1}{K_2} = \frac{2}{3}\right)$ $\Rightarrow \theta = \frac{2K \times 100 + 3K \times 0}{2K + 3K} = \frac{200K}{5K} = 40^\circ C$
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