Question

In: Physics

An open container holds ice of mass 0.535 kg at a temperature of -16.7 ?C ....

An open container holds ice of mass 0.535 kg at a temperature of -16.7 ?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.

1. How much time tmelts passes before the ice starts to melt? in minutes

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

Expert Solution

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

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

Rate at which heat is supplied = H = 770 J/min

Mass of ice = m = 0.535 kg

Initial temperature of ice = T₁ = -16.7 ^oC

Melting point of ice = T₂ = 0 ^oC

Heat energy required so that the ice starts to melt = Q₁

For the ice to start melting all of the ice should reach 0 ^oC.

Q₁ = mC(T₂ - T₁)

Q₁ = (0.535)(2100)(0 - (-16.7))

Q₁ = 18762.45 J

Time period before the ice starts to melt = t₁

Q₁ = Ht₁

18762.45 = (770)t₁

t₁ = 24.37 min

Heat required before the temperature begins to rise above 0 ^oC = Q₂

For the temperature to rise above 0 ^oC the whole ice should reach 0 ^oC and the whole ice should melt into water.

Q₂ = mC(T₂ - T₁) + mL

Q₂ = (0.535)(2100)(0 - (-16.7)) + (0.535)(334x10³)

Q₂ = 197452.45 J

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

Q₂ = Ht₂

197452.45 = (770)t₂

t₂ = 256.4 min

a) Time taken for the ice to start melting = 24.37 min

b) Time taken for the temperature to rise above 0 ^oC = 256.4 min

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