A 4.00-kg silver ingot is taken from a furnace, where its temperature is 750.0°C, and placed on a large block of ice at 0.0°C. Assuming that all the heat given up by the silver is used to melt the ice, how much ice is melted?

Verified step by step guidance

1. Calculate the heat lost by the silver as it cools from 750.0°C to 0.0°C. Use the formula: \(Q = mc\Delta T\), where \(m\) is the mass of the silver, \(c\) is the specific heat capacity of silver, and \(\Delta T\) is the change in temperature.
2. Look up the specific heat capacity of silver, which is typically around 0.235 J/g°C. Convert the mass of silver from kilograms to grams because the specific heat capacity is in J/g°C.
3. Compute the change in temperature, \(\Delta T\), by subtracting the final temperature of the ice (0.0°C) from the initial temperature of the silver (750.0°C).
4. Calculate the total amount of heat lost by the silver using the values from the previous steps.
5. Use the heat lost by the silver to find out how much ice is melted. Use the formula: \(m_{\text{ice}} = \frac{Q}{L_f}\), where \(L_f\) is the latent heat of fusion of ice (approximately 334 J/g). Solve for \(m_{\text{ice}}\) to find the mass of ice melted in grams.

Key Concepts

Heat Transfer

Heat transfer is the process by which thermal energy moves from a hotter object to a cooler one until thermal equilibrium is reached. In this scenario, the silver ingot, initially at a high temperature, transfers heat to the ice, causing the ice to melt. This process is governed by the principles of thermodynamics, specifically the conservation of energy.

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. For the silver ingot, its specific heat capacity determines how much heat it can release as it cools from 750.0°C to 0.0°C. This value is crucial for calculating the total heat lost by the silver during the cooling process.

Latent Heat of Fusion

Latent heat of fusion is the amount of heat required to change a substance from solid to liquid at its melting point without changing its temperature. In this case, the heat absorbed by the ice to melt into water is quantified by the latent heat of fusion. This concept is essential for determining how much ice can be melted by the heat lost from the silver ingot.