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Q.

In the figure shown AB is a rod of length 30 cm and area of cross-section $1.0 c m^{2}$ and thermal conductivity 336 S.I. Units. The ends A&B are maintained at temperatures $20^{0} C$ and $40^{0} C$ respectively. A point C of this rod is connected to a box D, containing ice at $0^{0} C$ through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is ___ (in mg/s) [Assume latent heat of fusion for ice $L_{f} = 80 c a l / g m]$
[ Take 1cal = 4.2 J ]

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Detailed Solution

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$(\frac{m}{t}) L_{i c e} = \frac{K A}{10^{- 2}} [\frac{(20 - 0)}{10} + \frac{(40 - 0)}{20}]$ $(\frac{m}{t}) \times 80 \times 4200 = \frac{336 \times 10^{- 4}}{10^{- 2}} [2 + 2]$

$\frac{m}{t} = 4 \times 10^{- 5} k g / \sec = 40 m g / \sec$

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In the figure shown AB is a rod of length 30 cm and area of cross-section 1.0 cm2 and thermal conductivity 336 S.I. Units. The ends A&B are maintained at temperatures 200C and 400C respectively. A point C of this rod is connected to a box D, containing ice at 00C through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is ___ (in mg/s) [Assume latent heat of fusion for ice Lf=80cal/gm][ Take 1cal = 4.2 J ]