question_answer

Three bars of equal lengths and equal areas of cross-section are connected in series. Their thermal conductivities are in the ratio of 2 : 4 : 3. If the open ends of the first and the last bars are at temperatures \[200{}^\circ C\] and \[18{}^\circ C\] respectively in the  steady state,  the temperature of the two junctions is

A)  \[60{}^\circ C,\text{ }50{}^\circ C\]         

B) \[116{}^\circ C,\text{ }74{}^\circ C\]

C) \[55{}^\circ C,\text{ }65{}^\circ C\] 

D) \[160{}^\circ C,\text{ }80{}^\circ C\]

Correct Answer: B

Solution :

                 The rate of flow of heat is same                                 \[H=(2K)A\frac{(200-{{\theta }_{1}})}{L}\]                 \[=(4K)A\frac{({{\theta }_{1}}-{{\theta }_{2}})}{L}\]                 \[=(3K)A\frac{{{\theta }_{2}}-{{18}^{o}}}{L}\] \[\Rightarrow \]               \[2({{200}^{o}}-{{\theta }_{1}})=4\,({{\theta }_{1}}-{{\theta }_{2}})\]                                 \[=3({{\theta }_{2}}-{{18}^{o}})\] \[\Rightarrow \]               \[{{\theta }_{1}}={{116}^{o}}C\],               \[{{\theta }_{2}}{{74}^{o}}C\]