On a hot summer day, Daphne is off to the park for a picnic....

On a hot summer day, Daphne is off to the park for a picnic. She puts $0.10 \mathrm{kg}$ of ice at $0^{\circ} \mathrm{C}$ in a thermos and then adds tea initially at $25^{\circ} \mathrm{C}$. How much tea will just melt all the ice?

Key Concepts

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required to change a substance from a solid to a liquid at its melting point without changing its temperature. It explains the energy needed to melt ice into water and is a crucial constant in energy balance problems involving phase transitions.

Specific Heat Capacity

Specific heat capacity is the amount of heat per unit mass required to raise the temperature of a substance by one degree. It is essential for calculating the energy exchange when a substance (such as tea or water) changes temperature, and it plays a critical role in problems where different materials equilibrate at a common temperature.

Energy Conservation in Heat Transfer

Energy conservation in heat transfer refers to the principle that the energy lost by a warmer substance must equal the energy gained by a cooler substance when they come into thermal contact. This concept is used to set up equations that balance the heat gained by melting ice with the heat lost by the tea as it cools, thus allowing the determination of an unknown variable such as the mass of tea required.

Thermal Equilibrium

Thermal equilibrium is the state in which two substances in contact with each other reach the same temperature and no net heat transfer occurs between them. In mixing problems like this, achieving thermal equilibrium requires accounting for both sensible heat changes and latent heat changes during phase transitions.

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