Question

Three rods of copper, brass and steel are welded together to form a Y - shaped structure. Area of cross - section of each rod $=4{\text{cm}}^2$. End of copper rod is maintained at ${100}^{\circ }C$ where as ends of brass and steel rods are kept at $0^{\circ }C$. Lengths of the copper, brass and steel rods are $46,13\text{and}12\text{cm}$ 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. $2.4\text{cal/s}$
• B. $6.0\text{cal/s}$
• C. $1.2\text{cal/s}$
• D. $4.8\text{cal/s}$

Answer 1

The correct option is D $4.8\text{cal/s}$


Let temperature at junction be $T$

Using electric analogy of thermal current,

$I_1+I_2+I_3=0$

$\frac{K_1(T-0)}{l_1}+\frac{K_2(T-0)}{l_2}+\frac{K_3(T-100)}{l_3}=0$

$\frac{0.12}{12}T+\frac{0.26}{13}T+\frac{0.92}{46}(T-100)=0$

$T={40}^{\circ }C$

Now $\frac{dQ}{dt}$ through copper is $=\frac{0.92\times 4}{46}(100-40)$
$=4.8\text{cal/s}$