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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 ....... $cal\, s^{-1}$
$2.4$
$4.8$
$6.0$
$1.2$
Solution
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$
$\therefore \,\,{Q_{Copper}} = \frac{{0.92 \times 4 \times 60}}{{46}} = 4.8\,cal/s$
