Question

An open container holds ice of mass 0.530 kg at a temperature of -17.7 ∘C . The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 770 J/minute . The specific heat of ice to is 2100 J/kg⋅K and the heat of fusion for ice is 334×103J/kg.

How much time tmelts passes before the ice starts to melt?

From the time when the heating begins, how much time trise does it take before the temperature begins to rise above 0∘C?

Answer 1

Mass of ice = m = 0.53 kg

Initial temperature of ice = T₁ = -17.7^oC

Melting temperature of ice = T₂ = 0^oC

Specific heat of ice = C = 2100 J/(kg.K)

Heat of fusion for ice = L = 334 x 10³ J/kg = 334000 J/kg

Heat supplied to the container = H = 770 J/minutes

Time taken for ice to start to melt = t₁

Time taken so that the temperature begins to rise above 0^oC = t₂

The ice will start melting when all of the ice is at 0^oC

Ht₁ = mC(T₂ - T₁)

(770)t₁ = (0.53)(2100)(0 - (-17.7))

t₁ = 25.58 minutes

The temperature will begin to rise above 0^oC after all of the ice has melted.

Ht₂ = mC(T₂ - T₁) + mL

(770)t₂ = (0.53)(2100)(0 - (-17.7)) + (0.53)(334000)

t₂ = 255.48 minutes

Time before ice starts melting = 25.58 minutes

Time before temperature starts to rise above 0^oC = 255.48 minutes