Question

Three rods of copper , brass and steel are welded together to form a Y-shaped structure .Area of cross -section of each rod is $4cm^2$.End of copper rod is maintained at $100^{\circ}C$ whereas ends of brass and steel are kept at $0^{\circ C}$ Lengths of the copper, brass and steel rods are 46,13 and 12 cm respectively The rods are thermally insulated from surroundings except at ends.Thermal conductivities of copper , brass and steel are 092 , 0.26 and 0.12 in CGS units , respectively .Rate of heat flow throught cooper rod is

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

Answer 1

Answer: (C)

$Q= Q_{1}+Q_{2} $
$ \frac{0.92 \times 4(100-T)}{46}=\frac{0.26 \times 4 \times(T-0)}{13}+\frac{0.12 \times 4 \times T}{12} $
$\Rightarrow 200-2 T=2 T+T $
$\Rightarrow T=40^{\circ} C $
$\Rightarrow Q=\frac{0.92 \times 4 \times 60}{46}$
$=4.8\, cal / s$