Question

Three rods of Copper, Brass and Steel were welded together to from a Y-shaped structure. Area of cross-section of each rod $=4{cm}^2$. End of copper rod is maintained at ${100}^{o}C$ where as ends of brass and steel are kept at $0^{o}C$. Lengths of the copper, brass and steel rods are $46,13$ and $12cms$ 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:

• A. $4.8cal/s$
• B. $6.0cal/s$
• C. $1.2cal/s$
• D. $2.4cal/s$

Answer 1

The correct option is A $4.8cal/s$

$\frac{d{Q}_1}{dt}=\frac{d{Q}_2}{dt}+\frac{d{Q}_3}{dt}$
$\Rightarrow \frac{0.92(100-T)}{46}=\frac{0.26(T-0)}{13}+\frac{0.12(T-0)}{12}\Rightarrow T={40}^{o}C$
$\frac{d{Q}_1}{dt}=\frac{0.92\times 4(100-40)}{40}=4.8cal/s$