An 8.5-g ice cube is placed into 255 g of water. Calculate the temperature change in the water upon the complete melting of the ice. Assume that all of the energy required to melt the ice comes from the water.

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Identify the heat required to melt the ice using the formula: \( q = m \cdot \Delta H_f \), where \( m \) is the mass of the ice and \( \Delta H_f \) is the heat of fusion for ice.

Calculate the heat \( q \) needed to melt the 8.5 g of ice using the heat of fusion for ice, which is approximately 334 J/g.

Recognize that the heat lost by the water is equal to the heat gained by the ice, so set the heat lost by water equal to the heat gained by the ice: \( q_{water} = -q_{ice} \).

Use the formula for heat change in water: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the water, \( c \) is the specific heat capacity of water (4.18 J/g°C), and \( \Delta T \) is the change in temperature.

Solve for \( \Delta T \) by rearranging the equation: \( \Delta T = \frac{-q_{ice}}{m_{water} \cdot c} \), and substitute the known values to find the temperature change.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat Transfer

Heat transfer is the process by which thermal energy moves from one object to another due to a temperature difference. In this scenario, the warmer water transfers heat to the colder ice cube, causing the ice to melt. Understanding this concept is crucial for calculating the temperature change in the water as it loses energy.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required to change a substance from solid to liquid at its melting point without changing its temperature. For ice, this value is approximately 334 J/g. This concept is essential for determining how much energy the water must provide to completely melt the ice cube.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. Water has a specific heat capacity of about 4.18 J/g°C. This concept is important for calculating the resulting temperature change in the water after it has transferred energy to the ice.