question_answer

Two rods having thermal conductivity in the ratio of \[5:3\] having equal lengths and equal    cross-sectional area are joined face to face. If the temperature of the free end of the first rod is \[{{100}^{o}}C\] and free end of second rod is\[{{20}^{o}}C\], then the temperature of the junction is :

A)  \[{{70}^{o}}C\]          

B)  \[{{50}^{o}}C\]

C)  \[{{60}^{o}}C\]          

D)  \[{{90}^{o}}C\]

Correct Answer: A

Solution :

 Key Idea: In steady state rate of flow of heat is same in both the conductors. Let 6 be steady temperature of the interface, the rate of flow of heat is \[H=\frac{Q}{t}={{K}_{1}}\,A\frac{({{\theta }_{1}}-\theta )}{l}=\frac{{{K}_{2}}A(\theta -{{\theta }_{2}})}{l}\] Given, \[{{K}_{1}}:{{K}_{2}}=5:3,\,{{\theta }_{1}}={{100}^{o}}C,{{\theta }_{2}}={{20}^{o}}C\] \[\therefore \] \[5(100-\theta )=3(\theta -20)\] \[\Rightarrow \] \[500-5\theta =3\theta -60\] \[\Rightarrow \] \[8\theta =560\] \[\Rightarrow \] \[\theta ={{70}^{o}}C\]