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 ...... $^oC$
Medium
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(b) Temperature of interface $\theta = \frac{{{K_1}{\theta _1} + {K_2}{\theta _2}}}{{{K_1} + {K_2}}}$
where $K_1 = 2K and K_2 = 3K$ $\left( {\because \,\frac{{{K_1}}}{{{K_2}}} = \frac{2}{3}} \right)$
==> $\theta = $$\frac{{2K \times 100 + 3K \times 0}}{{2K + 3K}}$$ = \frac{{200K}}{{5K}} = 40^\circ C$
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