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

Answer

D

Explanation

Thermal resistance of `AC=(L)/(KA)=(0.1)/(336xx10^-4)=(10^3)/(336)`
`=R(say)`
Thermal resistance of `BC=(0.2)/(336xx10^-4)=2R`
Heat flow rates are
`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`
Rate of melting of ice
`=(H)/(L_f)=(13.44//4.2)/(80)g//s=40 mg//s`