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

Answer

A, B

Explanation

Integrating we have
`H=(KAd theta)/(dr)=K(2pirL)(d theta)/(dr)`
`int_(r1)^(r2)(dr)/(r)=(2piKL)/(H)int_(theta1)^(theta2)d theta`
`implies (dQ)/(dt)=H=(2piKL(theta_(2)-theta_(1)))/(In(r_(2)/(r_(1))))=80 theta`
`implies (dm)/(dt)L=80pi`
`implies (dm)/(dt)=(8pi)/(L)+(80pi)/(80xx4200)`
`=(pi)/(4200)Kg//s`