Three rods of Copper, Brass and Steel are welded together to from a Y-shaped structure. Area of cross section of each rod $=4\mathrm{~cm}^{2}$. End of copper rod is maintained at $100^{\circ}\mathrm{C}$ where as ends of brass and steel are kept at $0^{\circ}\mathrm{C}$. 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:

(A) $4.8\mathrm{~cal}/\mathrm{s}$

(B) $6.0\mathrm{~cal}/\mathrm{s}$

(C) $1.2\mathrm{~cal}/\mathrm{s}$

(D) $2.4\mathrm{~cal}/\mathrm{s}$

JEE Main · 2014 · 06 Apr 2014 · Offline · Heat & Thermodynamics

Three rods of Copper, Brass and Steel are 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

10 0^{\circ} C

where as ends of brass and steel are kept at

0^{\circ} C

. 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:

(A) $4.8 cal / s$ ✓ Correct
(B) $6.0 cal / s$
(C) $1.2 cal / s$
(D) $2.4 cal / s$

Answer: (A)

Solution

At the welded junction the heat arriving along the copper splits into the brass and steel arms, so

\frac{d Q _{1}}{d t} = \frac{d Q _{2}}{d t} + \frac{d Q _{3}}{d t}

. Writing each as

\frac{k A Δ T}{L}

and letting the junction sit at temperature

T

\frac{0.92 \times 4 ( 100 - T )}{46} = \frac{0.26 \times 4 ( T - 0 )}{13} + \frac{0.12 \times 4 ( T - 0 )}{12}

. This gives

T = 4 0^{\circ}

C, and the copper rod then carries

\frac{0.92 \times 4 ( 100 - 40 )}{46} = 4.8

cal/s.

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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JEE Main · 2014 · 06 Apr 2014 · Offline · Heat & Thermodynamics

Solution

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