Two rectangular blocks $A$ and $B$ of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of $A$ is $100°C$ and that of $B$ at the other end is $0°C$ . If the ratio of their thermal conductivity is $1 : 3$ , then under steady state, the temperature of the junction in contact will be ........ $^oC$
Medium
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(a) It is given that $\frac{{{K_1}}}{{{K_2}}} = \frac{1}{3}$ ==> ${K_1} = K$ then ${K_2} = 3K$
the temperature of the junction in contact
$\theta = \frac{{{K_1}{\theta _1} + {K_2}{\theta _2}}}{{{K_1} + {K_2}}}$$ = \frac{{1 \times 100 + 3 \times 0}}{{1 + 3}} = \frac{{100}}{4}$= $25°C$
the temperature of the junction in contact
$\theta = \frac{{{K_1}{\theta _1} + {K_2}{\theta _2}}}{{{K_1} + {K_2}}}$$ = \frac{{1 \times 100 + 3 \times 0}}{{1 + 3}} = \frac{{100}}{4}$= $25°C$
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