Two rods having thermal conductivity in the ratio of $5 : 3$ having equal lengths and equal cross-sectional area are joined by face to face. If the temperature of the free end of the first rod is $100°C$ and free end of the second rod is $20°C$ . Then temperature of the junction is...... $^oC$
Medium
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(a) Temperature of interface $\theta = \frac{{{K_1}{\theta _1} + {K_2}{\theta _2}}}{{{K_1} + {K_2}}}$
It is given that $\frac{{{K_1}}}{{{K_2}}} = \frac{5}{3}$
It is given that $\frac{{{K_1}}}{{{K_2}}} = \frac{5}{3}$
==> ${K_1} = 5K$ and ${K_2} = 3K$
$\theta = \frac{{5K \times 100 + 3K \times 20}}{{5K + 3K}}$$ = \frac{{560K}}{{8K}}=70°C$
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