College physics 1

Question

How much heat in kcal is required to change 0.5 kg of ice, originally at - 10 degrees * C into steam at 110*C ? Show all your steps. Constants needed in the problem: Latent heat of fusion=79.7 kcal/kg; Specific heat of ice=0.5 kcal/kg/K ; Latent heat of vaporization=539 kcal/kg Specific heat of water 1.0 kal/kg/K; Specific heat of eam=0.480 kcal/kg

Answer 1

I will set this up for you, but YOU do the calculations. This problem has to be worked in 5 steps. (Be careful with your units!)

(1)

Heat the ice to the melting temperature of water.

m = mass of ice

c₁ = specific heat of ice

T₁ = initial temperature of ice

T₂ = fusion temperature of water (0°C)

Q₁ = mc₁(T₂ - T₁)

(2)

Melt the ice at a constant temperature of 0°C.

l_f = latent heat of fusion of water

Q₂ = ml_f

(3)

Heat the melted ice to the boiling temperature of water (100°C).

c₂ = specific heat of liquid water

T₃ = 100°C

Q₃ = mc₂(T₃ - T₂)

(4)

Vaporize the water at a constant temperature of 100°C (T₃).

l_v = latent heat of vaporization of water

Q₄ = ml_v

(5)

Heat the steam from T₃ (100°C) to the final temperature T₄ (110°C).

c₃ = specific heat of steam

Q₅ = mc₃(T₄ - T₃)

The total heat transfer is the sum of the 5 heat transfers.