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

On a very 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 a grape-flavored drink, which she has mixed from a powder using room temperature water $\left(25^{\circ} \mathrm{C}\right) .$ How much grape-flavored drink will just melt all the ice?

Key Concepts

Latent Heat of Fusion

Latent heat of fusion is the energy required per unit mass to change a substance from solid to liquid at its melting point without changing its temperature. This concept is crucial when calculating the energy needed to melt ice, as it tells us how much energy must be absorbed to complete the phase change.

Specific Heat Capacity

Specific heat capacity is a property that indicates the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. This concept is key in determining how much energy a substance, such as a beverage, can release or absorb as it changes temperature, which is integral to heat exchange calculations.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In thermal problems, this means that the heat lost by one substance is equal to the heat gained by another. This principle is fundamental to setting up equations to calculate temperature changes and phase transitions.

Calorimetry

Calorimetry is the study of measuring the amount of heat involved in chemical reactions or physical changes. It provides the experimental and theoretical methods to quantify energy transfers during processes like melting or cooling, which is essential for solving problems involving heat exchange between substances.

Thermal Equilibrium

Thermal equilibrium occurs when separate objects or substances reach the same temperature such that there is no net heat flow between them. This concept is important for understanding and determining the final state in a system where two bodies at different initial temperatures exchange heat until they balance out.

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