A cylindrical rod having temperature ${T_1}$ and ${T_2}$ at its ends. The rate of flow of heat is ${Q_1}$ $cal/sec$. If all the linear dimensions are doubled keeping temperature constant then rate of flow of heat ${Q_2}$ will be
AIPMT 2001, Medium
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(b)Rate of heat flow $\left( {\frac{Q}{t}} \right) = \frac{{k\pi {r^2}({\theta _1} - {\theta _2})}}{L} \propto \frac{{{r^2}}}{L}$
$\therefore$ $\frac{{{Q_1}}}{{{Q_2}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}\left( {\frac{{{l_2}}}{{{l_1}}}} \right) = {\left( {\frac{1}{2}} \right)^2} \times \left( {\frac{2}{1}} \right) = \frac{1}{2}$
==> ${Q_2} = 2{Q_1}$
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