A 100 cm long cylindrical flask with inner and outer diameters 2 cm and 4 cm respectively is completely filled with ice as shown in the figure. The constant temperature outside the flask is 40°C. (Thermal conductivity of the flask is 0.693 W/m°C, $L_{i ce} = 80$ cal/gm.)

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Radial conduction: P = ln ( r 2 ​ / r 1 ​ ) 2 πk L Δ T ​ = ln 2 2 π ( 0.693 ) ( 1 ) ( 40 ) ​ = 80 π W (A). With L = 80 cal/g = 3.36 × 1 0 5 J/kg, m ˙ = 3.36 × 1 0 5 80 π ​ = 4200 π ​ kg/s (B).

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