A 0.3-L glass of water at 20^∘ C is to be cooled with ice to 5^∘ C. Determine how much ice needs

step 1 Hi everyone here it is given a 0 .3 litre glass of water so volume of water is given 0 .3 liter

A 0.3-L glass of water at 20^∘ C is to be cooled with ice to...

A $0.3-\mathrm{L}$ glass of water at $20^{\circ} \mathrm{C}$ is to be cooled with ice to $5^{\circ} \mathrm{C}$. Determine how much ice needs to be added to the water, in grams, if the ice is at $(a) 0^{\circ} \mathrm{C}$ and $(b)-20^{\circ} \mathrm{C}$ Also determine how much water would be needed if the cooling is to be done with cold water at $0^{\circ} \mathrm{C}$. The melting temperature and the heat of fusion of ice at atmospheric pressure are $0^{\circ} \mathrm{C}$ and $333.7 \mathrm{kJ} / \mathrm{kg}$, respectively, and the density of water is $1 \mathrm{kg} / \mathrm{L}$.

Key Concepts

Calorimetry

Calorimetry is the measurement and calculation of the heat transferred in physical and chemical processes. This technique involves setting up energy balances between objects or substances at different temperatures and phases, enabling the determination of unknown quantities like the mass of ice or water needed to reach thermal equilibrium.

Latent Heat of Fusion

Latent heat of fusion is the energy required to change a substance from solid to liquid at its melting point without changing its temperature. For ice, this energy must be supplied to melt it into water. In problems involving phase changes, the latent heat must be accounted for in addition to any energy required to change temperatures.

Conservation of Energy

This principle states that energy can neither be created nor destroyed, only transferred between systems. In thermal processes, the heat lost by one substance is equal to the heat gained by another. In calorimetry problems, setting up an energy balance allows us to calculate unknown quantities, such as the amount of ice required to achieve a certain temperature change.

Specific Heat Capacity

The specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a key factor in calculating the energy involved in changing the temperature of a substance without a phase change. In cooling and heating problems, the equation Q = mc?T (where m is mass, c is the specific heat capacity, and ?T is the temperature change) is routinely used.

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