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  4. As shown in diagram, AB is a rod of length 30 cm and area of cross section 1.0 cm2 and thermal conductivity 336 SI units . The ends A and B are maintained at temperatures 20 ° C and 40 ° C , respectively. A point C of this rod is connected to a box D , containing ice at 0 ° C , through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is (assume latent heat of fusion for ice Lf=80 cal g- 1 ) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-oesqn5uvcs3k.png />

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Q. As shown in diagram, $AB$ is a rod of length $30 \, cm$ and area of cross section $1.0 \, cm^{2}$ and thermal conductivity $336 \, SI \, units$ . The ends $A$ and $B$ are maintained at temperatures $20 \,{}^\circ C$ and $40 \,{}^\circ C$ , respectively. A point $C$ of this rod is connected to a box $D$ , containing ice at $0 \,{}^\circ C$ , through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is (assume latent heat of fusion for ice $L_{f}=80 \, cal \, g^{- 1}$ )

Question

NTA AbhyasNTA Abhyas 2020Thermal Properties of Matter

Solution:

Thermal resistance of $\text{AC} = \frac{\text{L}}{\text{KA}} = \frac{\text{0.1}}{3 3 6 \times 1 0^{- 4}} = \frac{1 0^{3}}{3 3 6} = \text{R} \left(\text{let}\right)$
Solution
Thermal resistance of $\text{BC} = \frac{\text{0.2}}{3 3 6 \times 1 0^{- 4}} = 2 \text{R}$
Heat flow rates are
$\text{H}_{1} = \frac{2 0}{\text{R}} \text{; } \text{H}_{2} = \frac{4 0}{2 \text{R}} = \frac{2 0}{\text{R}}$
undefined
$= \frac{1 3 4 4 0}{1 0^{3}} = \text{13.44 W}$
Rate of melting of ice
$=\frac{\text{H}}{\text{L}_{\text{f}}}=\frac{\text{13.44/4.2}}{8 0} \, \text{g s}^{\text{-1}}=40 \, mg \, s^{- 1}$