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  •  Three rods of Copper, Brass and Steel are welded together to form a Y - shaped structure.  Area of cross - section of each    rod = 4 cm2. End of copper rod is

 Three rods of Copper, Brass and Steel are welded together to form a Y - shaped structure.  Area of cross - section of each    rod = 4 cm2. End of copper rod is maintained at 1000C where as ends of brass and steel are kept at 00C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :

 

Option: 1

1.2 cal/s


Option: 2

2.4 cal/s


Option: 3

4.8 cal/s


Option: 4

6.0 cal/s


Answers (1)

The arrangement of rods is shown in the above figure.

So using

\begin{array}{l} \frac{d Q}{d t}=\frac{d Q_{2}}{d t}+\frac{d Q_{3}}{d t} \\\\ \Rightarrow \frac{0.92(100-T)}{46}=\frac{0.26(T-0)}{13}+\frac{0.12(T-0)}{12} \\ \Rightarrow T=40^{\circ} \mathrm{C} \end{array}

So

\frac{d Q}{d t}=\frac{0.92 \times 4(100-40)}{40}=4.8 \mathrm{cal} / \mathrm{s}

 

 

Posted by

Sumit Saini

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