• # question_answer Two rods having thermal conductivity in the ratio of $5:3$ having same length area equal cross-sectional area are join by face to face. If the temperature of the free end of the first rod is ${{100}^{o}}C$ and the temperature of free end of the second rod is ${{20}^{o}}C$. Then temperature of junction will be: A)  ${{85}^{o}}C$                 B)  ${{90}^{o}}C$C)  ${{50}^{o}}C$              D)  ${{70}^{o}}C$

Thermal conductivity of first rod ${{K}_{1}}=5\alpha$ and thermal conductivity of second rod ${{K}_{2}}=3\,\alpha$ Temperature of the first rod ${{T}_{1}}={{100}^{o}}C$ and Temperature of second rod ${{T}_{2}}={{20}^{o}}C$. In the steady state, the rate of heat transfer in  both the conductors will be same $\therefore$  $\frac{{{K}_{1}}A({{T}_{1}}-T)}{d}=\frac{{{K}_{2}}A(T-{{T}_{1}})}{d}$ Where T is the temperature of the junction) $\Rightarrow$               ${{K}_{1}}({{T}_{1}}-T)={{K}_{2}}(T-{{T}_{2}})$ $\Rightarrow$               $5\alpha (100-T)=3\alpha (T-20)$ $\Rightarrow$               $5(100-T)=3\,(T-20)$ $\Rightarrow$               $500-5T=3T-60$ $\Rightarrow$               $8T=560$ $\Rightarrow$               $T={{70}^{o}}C$