A 100 cm long cylindrical flask with inner and outer diameter 2 cm and 4 cm respectively is completely filled with ice at 0°C as shown in the figure. The constant temperature outside the flask is 40°C

Question

A 100 cm long cylindrical flask with inner and outer diameter 2 cm and 4 cm respectively is completely filled with ice at 0°C as shown in the figure. The constant temperature outside the flask is 40°C. (Thermal conductivity of the flask is $0.693 W / m^{\circ} C, L_{ice} = 80 cal / gm & ℓ n 2 = 0.693$ ). (Flat faces are thermally insulated)

TestHub · Accepted Answer

​ R eq ​ = ∫ r 1 ​ r 2 ​ ​ k .2 π r ℓ dr ​ = k .2 π ℓ ℓ n 2 ​ ​ ∴ Heat current = R eq ​ T S ​ − T ice ​ ​ = ℓ n 2 40 ​ k 2 π ℓ = 80 π J / sec ​ Also, dt dm ice ​ ​ L f ​ = 80 π ​ ⇒ dt dm ice ​ ​ = 80 × 4.2 × 1000 80 π ​ = 4200 π ​ kg / sec ​

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