As shown in Fig. AB is 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^@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 `L_f=80 cal//g`)

Options

A. `84 mg//s`
B. `84 g//s`
C. `20mg//s`
D. `40mg//s`

Answer

D

Explanation

Thermal resistance (R) of `AC=(L)/(KA)=(0.1)/(336xx10^(-4))=(10^(3))/(336)`
Thermal resistance of `BC=(0.2)/(336xx10^(-4))=2R`
Also `H_(1)=(20)/(R),H_(2)=(40)/(2R)=(20)/(R)&H=H_(1)+H_(2)`
`=(40)/(R)=(40xx336)/(10^(3))=(13440)/(10^(3))=13.44W=(13.44)/(4.2)cal//s`
Rate of melting of ice `((dm)/(dt))=(H)/(L_(f))=(13.44//4.2)/(80)gms//s=40mg//s`