A cylindrical rod with one end in a steam chamber and the other end is in ice. It is found that $1$ gm of ice melts per second. If the rod is replaced by another one of the same material but of double length and double area of cross section, the mass of ice that melts per second is :

2 gm

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4 gm

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1 gm

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0.5 gm

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Solution

The correct option is D 1 gm
Thermal conduction in a metal bar is given by:
$Q = \frac{K A (Δ θ) t}{l} = m_{i} L_{i}$
$m_{i} \propto \frac{A}{l}$
$\frac{m_{2}}{m_{1}} = \frac{A_{2}}{A_{1}} \times \frac{l_{1}}{l_{2}} = \frac{2 A}{A} \times \frac{l}{2 l} = 1$
$m_{2} = m_{1} = 1 g m$

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