Classical Mechanics

# Phase changes

If $$8.00 \text{ kg}$$ of ice at $$-9.00^\circ\text{C}$$ is added to $$25.00 \text{ kg}$$ of water at $$40.00^\circ\text{C},$$ what is the approximate temperature of the water at equilibrium, assuming that the specific heats of ice and water are $$2220 \text{ J/kg}\cdot\text{K}$$ and $$4187 \text{ J/kg}\cdot\text{K},$$ respectively and the latent heat of fusion of water is $$3.33 \times 10^5 \text{ J/kg}?$$

If we absorb $$65.0 \text{ kJ}$$ of energy from $$650 \text{ g}$$ of liquid water at $$0^\circ\text{C},$$ approximately how much water remains as liquid state, assuming that the latent heat of fusion of water is $$3.33 \times 10^5 \text{ J/kg}?$$

If $$7.00 \text{ kg}$$ of ice at $$0.0^\circ\text{C}$$ is added to $$14.00 \text{ kg}$$ of water at $$14.0^\circ\text{C},$$ approximately how much ice can melt at equilibrium, assuming that the ice-water system is isolated and the specific heat of water is and $$4187 \text{ J/kg}\cdot\text{K},$$ and the latent heat of fusion of water is $$3.33 \times 10^5 \text{ J/kg}?$$

If $$70.0 \text{ g}$$ of steam at $$100.0^\circ\text{C}$$ is mixed with $$350.0 \text{ g}$$ of ice at $$0.0^\circ\text{C},$$ in a thermally isolated container, what is the approximate temperature of the mixture at equilibrium?

The specific heat of water is $$c_w=4187 \text{ J/kg}\cdot\text{K},$$ and the latent heat of fusion and vaporization of water are $$L_f=333 \text{ kJ/kg}$$ and $$L_v=2336 \text{ kJ/kg},$$ respectively.

How much heat must be absorbed by ice of $$8.00 \text{ kg}$$ at $$-17 ^\circ\text{C}$$ for the ice to become liquid state water at $$0^\circ\text{C},$$ assuming that the specific heat of ice is $$2220 \text{ J/kg}\cdot\text{K}$$ and the latent heat of fusion of water is $$3.33 \times 10^5 \text{ J/kg}?$$

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