Thermal Dynamics: Ice Placed on Boiling Water (100°C)

When ice is placed in contact with boiling water at 100°C, several fascinating thermodynamic phenomena are observed. These phenomena depend on the amount of ice and water present. This article will explore the heat transfer involved in melting ice and evaluate the resulting temperature of the mixture.

Thermodynamics of Ice Melting

To melt 1 kg of ice from 0°C to 0°C, the water would need to supply enough heat to overcome the latent heat of fusion. This value for ice is approximately 334,000 J/kg. Let's consider a simplified scenario with 1 kg of ice and 10 kg of water at 100°C.

Calculating the Energy Required

The heat required to melt 1 kg of ice (Qmelt) is:

Qmelt 334,000 J/kg × 1 kg 334,000 J 334 kJ.

Heat Transfer from Water to Ice

Some of this heat (Qheat) will be used to cool the water from 100°C to the temperature of the melting ice (0°C). The heat transfer can be calculated using the formula:

Qheat mwater·cwater·ΔT 10 kg × 4200 J/kg·K × (100 - 0) 4,20,000 J 420 kJ.

Since the heat required to melt the ice (334 kJ) is less than the heat available (420 kJ), some heat remains after the ice has melted. This excess heat will increase the temperature of the water.

Final Temperature Calculation

We can use the formula for heat balance to find the final temperature of the mixture (Tfinal):

mice·cice·Tice mwater·cwater·ΔT (mice mwater)·cwater·Tfinal

1 kg × 2100 J/kg·K × 100°C 10 kg × 4200 J/kg·K × 0°C (1 kg 10 kg) × 4200 J/kg·K × Tfinal

210,000 J 0 11 kg × 4200 J/kg·K × Tfinal

Tfinal 210,000 J / (11 kg × 4200 J/kg·K) ≈ 356.6 K 83.6°C.

Real-world Observations

From a practical perspective, the ice will melt quickly due to the high temperature of the boiling water. The volume of the ice may decrease and possibly crack if it is a cube, as the volume of liquid water is less than the volume of ice. The overall temperature of the mixture will drop slightly below the initial boiling point of the water, as heat is used to melt the ice and warm the newly formed water.

Conclusion

The interaction between ice and boiling water demonstrates the principles of thermodynamics, particularly the concepts of latent heat and heat transfer. The final temperature of the mixture will be lower than the initial boiling point of the water, illustrating the energy required to melt the ice and the resulting temperature change.