The enthalpy of fusion of water is 6.01 kJ/mol. Sunlight striking Earth's surface supplies 168 W per square meter (1 W = 1 watt = 1 J/s). (b) The specific heat capacity of ice is 2.032 J/g°C. If the initial temperature of a 1.00 square emter patch of ice is -5.0°C, what is its final temperature after being in sunlight for 12 h, assuming no phase changes and assuming that sunlight penetration uniformly to a depth of 1.00 cm?

Verified step by step guidance

1. First, we need to convert the power of sunlight from watts per square meter to joules per second per square centimeter. We know that 1 W = 1 J/s and 1 m² = 10,000 cm². So, we can convert 168 W/m² to 0.0168 J/s/cm².
2. Next, we need to calculate the total energy absorbed by the ice in 12 hours. We know that 1 hour = 3600 seconds, so 12 hours = 43,200 seconds. The total energy absorbed by the ice is the power of the sunlight times the time, which is 0.0168 J/s/cm² * 43,200 s.
3. Then, we need to calculate the mass of the ice. We know that the density of ice is approximately 0.92 g/cm³. The volume of the ice is the area times the depth, which is 1 cm² * 1 cm = 1 cm³. So, the mass of the ice is 0.92 g/cm³ * 1 cm³ = 0.92 g.
4. Now, we can calculate the change in temperature of the ice using the formula for heat transfer: Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. We can rearrange this formula to solve for ΔT: ΔT = Q/(mc). We know that Q is the total energy absorbed by the ice, m is the mass of the ice, and c is the specific heat capacity of ice, which is 2.032 J/g°C.
5. Finally, we can calculate the final temperature of the ice by adding the change in temperature to the initial temperature. The initial temperature of the ice is -5.0°C.

Key Concepts

Enthalpy of Fusion

The enthalpy 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 water, this value is 6.01 kJ/mol, indicating that this amount of energy is needed to convert one mole of ice at 0°C to liquid water at the same temperature. Understanding this concept is crucial for analyzing phase changes and energy transfers in thermodynamic processes.

Specific Heat Capacity

Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For ice, the specific heat capacity is 2.032 J/g°C, meaning that 2.032 joules are needed to increase the temperature of one gram of ice by one degree. This concept is essential for calculating temperature changes in materials when heat is added or removed.

Energy Transfer from Sunlight

Energy transfer from sunlight can be quantified in terms of power, measured in watts, where 1 watt equals 1 joule per second. In this scenario, sunlight provides 168 W/m², meaning that each square meter receives 168 joules of energy every second. Over a period of time, this energy can be calculated to determine how much heat is absorbed by the ice, which is necessary for calculating the final temperature after exposure to sunlight.