Question

An open container holds ice of mass 0.595 kg at a temperature of -10.3 ∘C . The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 870 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? 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

For ice to melt, its temperature must be 0* C.

Let

Q1 = heat required to raise the ice temp from -10.3 ^oC. to 0^oC.

Q2 = heat required to melt the ice

Q1 = M*Cp*(T)

Q2 = m(Hf)

where

M = mass of the ice = 0.595 kg (given)

Cp = specific heat of ice = 2100 J/kg K (given)

delta T = temperature change = 0 - (-10.3) = 10.3 ^oC.

Hf = heat of fusion of ice = 334 *10³ J/jg.

Substituting values,

Q1 = 0.595*(2100)*(10.3)

Q1 = 12869.85 joules

Q2 = 0.595*(334*10³)

Q2 = 198730 joules

Total heat required to melt the ice = Q1 + Q2 = 2,11,599.85 joules

Tmelt = Q1/870 = 12869.85/870 = 14.79 minute