You take a diet cola from the refrigerator and pour 240 mL of it into a glass. The temperature o

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You take a diet cola from the refrigerator and pour 240 mL...

You take a diet cola from the refrigerator and pour $240 \mathrm{mL}$ of it into a glass. The temperature of the beverage is $10.5^{\circ} \mathrm{C}$. You then add one ice cube (45 g) at $0^{\circ}$ C. Which of the following describes the system when thermal equilibrium is reached? (a) The temperature is $0^{\circ} \mathrm{C},$ and some ice remains. (b) The temperature is $0^{\circ} \mathrm{C},$ and no ice remains. (c) The temperature is higher than $0^{\circ} \mathrm{C},$ and no ice remains. Determine the final temperature and the amount of ice remaining, if any.

You take a diet cola from the refrigerator and pour
$240 \mathrm{mL}$ of it into a glass. The temperature of the beverage is $10.5^{\circ} \mathrm{C}$. You then add one ice cube (45 g) at $0^{\circ}$ C. Which of the following describes the system when thermal equilibrium is reached?
(a) The temperature is $0^{\circ} \mathrm{C},$ and some ice remains.
(b) The temperature is $0^{\circ} \mathrm{C},$ and no ice remains.
(c) The temperature is higher than $0^{\circ} \mathrm{C},$ and no ice remains.
Determine the final temperature and the amount of ice remaining, if any.

Key Concepts

Thermal Equilibrium

Thermal equilibrium is the state in which all parts of a system reach a uniform temperature, so that no net heat exchange occurs between them. This concept is critical when various components at different temperatures (such as a warm liquid and cold ice) interact until they settle at a common temperature.

Energy Conservation in Heat Transfer

The principle of energy conservation in heat transfer asserts that in an isolated system, the total energy remains constant. Heat lost by warmer substances must be equal to the heat gained by cooler substances, including energy used during phase changes, which is essential for solving mixing problems involving different temperatures.

Specific Heat Capacity

Specific heat capacity is defined as the amount of energy required to change the temperature of a unit mass of a substance by one degree Celsius. This concept allows us to determine the amount of heat exchanged when a substance, such as a drink, cools down or warms up, and is crucial in calculating energy transfers.

Latent Heat of Fusion

Latent heat of fusion is the energy needed to change a unit mass of a substance from a solid to a liquid at its melting point without a temperature change. This concept is crucial in scenarios where ice is added to a warmer liquid, as it determines how much energy is required to melt the ice before any temperature rise in the mixture.

Phase Change

Phase change refers to the transformation of a substance from one state of matter to another, such as from solid (ice) to liquid (water). This concept plays an important role in thermal problems because energy absorbed during a phase change does not alter the temperature, which influences the final equilibrium state of the system.

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