Question

As shown in diagram, $AB$ is a rod of length $30cm$ and area of cross section $1.0c{m}^2$ and thermal conductivity $336SIunits$ . 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 $L_f=80cal{g}^{-1}$ )

• A. $84mg{s}^{-1}$
• B. $84g{s}^{-1}$
• C. $20mg{s}^{-1}$
• D. $40mg{s}^{-1}$

Answer 1

Answer: (D)

Thermal resistance of $\text{AC}=\frac{\text{L}}{\text{KA}}=\frac{\text{0.1}}{336\times 10^{-4}}=\frac{10^3}{336}=\text{R}\left(\text{let}\right)$

Thermal resistance of $\text{BC}=\frac{\text{0.2}}{336\times 10^{-4}}=2\text{R}$
Heat flow rates are
${\text{H}}_1=\frac{20}{\text{R}}\text{; }{\text{H}}_2=\frac{40}{2\text{R}}=\frac{20}{\text{R}}$
undefined
$=\frac{13440}{10^3}=\text{13.44 W}$
Rate of melting of ice
$=\frac{\text{H}}{{\text{L}}_{\text{f}}}=\frac{\text{13.44/4.2}}{80}{\text{g s}}^{\text{-1}}=40mg{s}^{-1}$