Properties Of Solids And Liquids Question 465
Question: A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length I- each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at $ 100{}^\circ C $ band that of steel at $ 9{}^\circ C $ then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel)
Options:
A) $ 99{}^\circ C $
B) $ 59{}^\circ C $
C) $ 19{}^\circ C $
D) $ 67{}^\circ C $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] From formula temperature of junction; $ \theta =\frac{k _{copper}{\theta _{copper}}l _{steel}\text{+}{{\text{K}} _{steel}}{\theta _{steel}}l _{copper}}{K _{copper}l _{steel}+k _{steel}l _{copper}} $
$ =\frac{9k\times 100\times \frac{L}{2}+k\times 0\times \frac{L}{2}}{9k\times \frac{L}{2}+k\times \frac{L}{2}}=\frac{\frac{900}{2}kL}{\frac{10kL}{2}}={{90}^{o}}C $
