Three rods of Copper, Brass and Steel are welded together to form 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 ofbrass and steel are kept at \(0^o C\). Lengths of the copper, brass and steel rods are \(46, 13\) and \(12\ cms\) respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are \(0.92, 0.26\) and \(0.12\ CGS\) units respectively. Rate ofheat flow through copper rod is ....... \(cal\, s^{-1}\)

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Answer & Solution

Correct Answer

(B) \(4.8\)

Detailed explanation

Rate of heat flow is given by,

\(Q = \frac{{KA\left( {{\theta _1} - {\theta _2}} \right)}}{l}\)

Where, \(K=coefficient\,of\,thermal\,conductivity\)

\(l=length\,of\,rod\,and\,A=Area\,of\,cross-section\,of\,rod\)

If the junction temperature is \(T\), then

\({Q_{Copper}} = {Q_{Brass}} + {Q_{Steel}}\)

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

\(\frac{{0.12 \times4\times \left( {T - 0} \right)}}{{12}}\)

\( \Rightarrow 200 - 2T = 2T + T\)

\( \Rightarrow T = {40^ \circ }C\)

\(\therefore \,\,{Q_{Copper}} = \frac{{0.92 \times 4 \times 60}}{{46}} = 4.8\,cal/s\)

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