Question

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PRACTICE IT Use the worked example above to help you solve this problem. A 4.90 kg block of ice at 0°C is added to an insulated container partially filled with 12.0 kq of water at 15.0°C. (a) Find the final temperature, neglecting the heat capacity of the container. -12.39 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.°C (b) Find the mass of the ice that was melted. 2.26 kg EXERCISE HINTS: GETTING STARTED I'M STUCK If 8.90 kg of ice at -5.00°C is added to 12.0 kg of water at 30°C, compute the final temperature. T C How much ice remains, if any? kg Neod Help? Talk to a Tutor

Answer 1

Subtract the heat lost by the cooling water from
the heat gained by the melting ice
the surplus is unmelted ice.
333.55kJ/kg×5kg = 1667.75kJ
4.186kJ/kgC×10kg×15C = 627.9kJ
1,667.75kJ - 627.9kJ = 1039.85kJ
1,039.85kJ/333.55kJ/kg = 3.1175kg ice unmelted
entire mixture at 0°C

We can approach this by simply subtracting the heat lost by the water from the heat gained by the ice.

The latent heat of fusion of ice = 333.55 kJ/kg

There fore Q_ice =  333.55 kJ/kg x 4.90 kg = 1634.39 kJ

The heat capacity of water is 4.186kJ/kgC

therefore heat lost by the water :

Q_water = 4.186kJ/kgC×12kg×15C = 753.48 kJ

Q_ice - Q_water = 1634.39 kJ - 753.48 kJ = 880.91 kJ

therefore 880.91 kJ / 333.55kJ/kg = 2.62 Kgs of melts and the remaining 1.38 Kgs is still frozen.

Therefore the mixture is at 0 degrees C