Three rods `AB, BC` and `BD` of same length l and cross-sectionsl area `A` are arranged as shown . The end `D` is immersed in ice whose mass is `440 gm` Heat is being supplied at constant rate of `200cal//sec` from the end Time in which whole ice will melt (Latent heat of fusion of ice is `80cal//gm`
.

Options

A. `40//3 min`
B. `700 sec`
C. `20//3 min`
D. indefiniely long time

Answer

A

Explanation

Givne k (theraml conductivity)
`=100 cal//m//sc//C, A =10 cm^(2), l =1m`
If `theta` temperature of `B`
`then(2kA(theta-100))/(l)+((k//2)A(theta-0))/(l)=200`
Substituting value
`theta =880^(@)C :. phi_(1) =mL, (kA(880-0))/(2l) xx t = 440 xx 80`
`t =(80 xx 1xx 2xx440)/(100xx10xx10^(-4)xx880)=800sec=40//3min` .