SATHEE: Properties Of Solids And Liquids Question 465

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; $θ = \frac{k_{c o p p e r} θ_{c o p p e r} l_{s t e e l} + K_{s t e e l} θ_{s t e e l} l_{c o p p e r}}{K_{c o p p e r} l_{s t e e l} + k_{s t e e l} l_{c o p p e r}}$

$= \frac{9 k \times 100 \times \frac{L}{2} + k \times 0 \times \frac{L}{2}}{9 k \times \frac{L}{2} + k \times \frac{L}{2}} = \frac{\frac{900}{2} k L}{\frac{10 k L}{2}} = 90^{o} C$

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Properties Of Solids And Liquids Question 465

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