A `100 cm` long cylindrical flask with inner and outer diameter `2 cm` and `4cm` respectively is completely filled with ice as shown in the The constant temperature outside the flask is `40^(@)C`
(Thermal conductivity of the flask is `0.693 W// m^(@)C, L_(ice) = 80cal// gm & In 2=0.693)`

Options

A. Rate of heat flow from outside to the flask is `80 piJ//s`
B. The rate at which ice melts is `(pi)/(4200) kg//s`
C. The rate at which ice melts is `100pi kg//s`
D. Rate of heat flow from outside to flask is `40piJ//s`

Answer

A, B

Explanation

`R_(eq)=underset(n)overset(r^(2))int(dr)/(k.2pirl)=(1n2)/(k.2pil)`
`:.` heat current ` = (T_(S)-T_(ice))/(R_(eq)) = (40)/(ln2) k2pil =80piJ//sec`
Also, `(dm_(ice))/(dt) L_(f) = 80pi`
`rArr (dm_(ice))/(dt) = (80pi)/(80 xx 4.2 xx 1000) = (pi)/(4200)kg//sec`
.