A cylindrical rod having temperature T1 and T2 at its end. The rate of flow of heat Q1 cal/sec. If all the linear dimension are doubled keeping temperature constant, then rate of flow of heat Q2 will be

Question

A cylindrical rod having temperature T1 and T2 at its end. The rate of flow of heat Q1 cal/sec. If all the linear dimension are doubled keeping temperature constant, then rate of flow of heat Q2 will be (A) 4Q1 (B) 2Q1 (C) (Q1/4) (D) (Q1/2)

Tardigrade Admin · Accepted Answer

Heat flow rate (dQ/dt) = (KA(T1 - T2)/L) = Q When linear dimensions are double. A1 propto r21, L1 = L A2 propto 4r21, L1 = 2L so Q2 = 2Q1.

Q. A cylindrical rod having temperature $T_{1}$ and $T_{2}$ at its end. The rate of flow of heat $Q_{1}$ cal/sec. If all the linear dimension are doubled keeping temperature constant, then rate of flow of heat $Q_{2}$ will be

$4 Q_{1}$

$2 Q_{1}$

$\frac{Q _{1}}{4}$

$\frac{Q _{1}}{2}$

Heat flow rate $\frac{d Q}{d t} = \frac{K A ( T _{1} - T _{2} )}{L} = Q$
When linear dimensions are double.
$A_{1} \propto r_{1}^{2}, L_{1} = L$
$A_{2} \propto 4 r_{1}^{2}, L_{1} = 2 L$ so $Q_{2} = 2 Q_{1}$ .

Q. A cylindrical rod having temperature T1​ and T2​ at its end. The rate of flow of heat Q1​ cal/sec. If all the linear dimension are doubled keeping temperature constant, then rate of flow of heat Q2​ will be

4Q1​

2Q1​

4Q1​​

2Q1​​