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
A$4{Q_1}$
B$2{Q_1}$
C$\frac{{{Q_1}}}{4}$
D$\frac{{{Q_1}}}{2}$
AIPMT 2001, Medium
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B$2{Q_1}$
b (b)Rate of heat flow $\left( {\frac{Q}{t}} \right) = \frac{{k\pi {r^2}({\theta _1} - {\theta _2})}}{L} \propto \frac{{{r^2}}}{L}$
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