question_answer

Three rods of equal lengths and cross-sectional areas are joined in series. The thermal conductivities are in the ratio 2 : 4 : 3. The free ends consisting of the rods of least and second highest thermal conductivities are maintained at +473 K and \[18{}^\circ C\] respectively. Under steady conditions, the temperature at the junctions are

A)  \[{{116}^{o}}C,\,{{27}^{o}}C\]  

B)  \[{{116}^{o}}C,\,{{74}^{o}}C\]

C)  \[{{74}^{o}}C,\,{{27}^{o}}C\]                     

D)  \[{{100}^{o}}C,\,{{27}^{o}}C\]

Correct Answer: B

Solution :

Rate of flow of heat should be same in all the three segments. \[+473\text{ }K=+473-273=200{}^\circ C\] \[H=\frac{{{\theta }_{2}}-{{\theta }_{1}}}{{{R}_{Th}}}=k({{\theta }_{2}}-{{\theta }_{1}})\frac{\ell }{A}\] \[\therefore \,\,2(200-{{\theta }_{1}})=4({{\theta }_{1}}-{{\theta }_{2}})=3({{\theta }_{2}}-18)\] \[\Rightarrow \,{{\theta }_{1}}={{116}^{o}}C,\,\,{{\theta }_{2}}={{74}^{o}}C\]