Question

In: Physics

An open container holds ice of mass 0.570 kg at a temperature of -13.7 ∘C. The...

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?

Solutions

Expert Solution

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


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