Question

An open container holds ice of mass 0.570 kg at a temperature of -13.7 ∘C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 730 J/minute. The specific heat of ice to is 2100 J/kg⋅K and the heat of fusion for ice is 334×10^3 J/kg.

A) How much time [tmelts] passes before the ice starts to melt?
B)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

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

Latent heat of fusion of ice = L = 334 x 10³ J/kg

Mass of ice in the container = m = 0.57 kg

Initial temperature of ice = T₁ = -13.7 ^oC

Melting point of ice = T₂ = 0 ^oC

Rate at which heat is supplied to the container = H = 730 J/min

Heat energy required for the ice to start melting = Q₁

The ice will start melting after all the ice in the container reaches 0 ^oC.

Q₁ = mC(T₂ - T₁)

Q₁ = (0.57)(2100)(0 - (-13.7))

Q₁ = 16398.9 J

Time required for the ice to start melting = t₁

Q₁ = Ht₁

16398.9 = (730)t₁

t₁ = 22.46 min

Heat energy required for the temperature to rise above 0 ^oC = Q₂

For the temperature to rise above 0 ^oC all of the ice should reach 0 ^oC and then all of the ice should melt.

Q₂ = mC(T₂ - T₁) + mL

Q₂ = (0.57)(2100)(0 - (-13.7)) + (0.57)(334x10³)

Q₂ = 206778.9 J

Time required for the temperature to rise above 0 ^oC = t₂

Q₂ = Ht₂

206778.9 = (730)t₂

t₂ = 283.3 min

A) Time period before the ice starts to melt = 22.46 min

B) Time period before the temperature begins to rise above 0 ^oC = 283.3 min