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`)

Explanation

Thermal resistance of AC `(=(L)/(KA))=(0.1)/(336xx1xx10^(-4))=(10^(3))/(336)=R` (suppose)
thermal resistance of BC `=(0.2)/(336xx10^(-4))=2R`
`thereforeH_(1)=(20)/(R),H_(2)=(40)/(2R)=(20)/(R)`
`thereforeH=H_(1)+H_(2)=(40)/(R)=(40xx336)/(10^(3))=(13440)/(10^(3))=13.44` watt
Rate of melting of ice `=(H)/(L_(f))=(13.44//4.2)/(80)g//s=40mg//s`