30 g of copper pellets are removed from a 300°C oven and immediately dropped into 100 mL of water at 20°C in an insulated cup. What will the new water temperature be?

Verified step by step guidance

1. Identify the specific heat capacities involved: Copper has a specific heat capacity, typically around 0.385 J/g°C, and water has a specific heat capacity of 4.186 J/g°C.
2. Set up the heat transfer equation assuming no heat is lost to the surroundings. The heat lost by the copper pellets should equal the heat gained by the water: $m_{ ext{Cu}}c_{ ext{Cu}}(T_{ ext{initial, Cu}} - T_{ ext{final}}) = m_{ ext{water}}c_{ ext{water}}(T_{ ext{final}} - T_{ ext{initial, water}})$.
3. Convert the mass of water from milliliters to grams (assuming the density of water is approximately 1 g/mL), which makes it easier to use in the heat transfer equation.
4. Substitute the known values into the equation: mass of copper, specific heat of copper, initial temperature of copper, mass of water, specific heat of water, and initial temperature of water.
5. Solve the equation for the final temperature, $T_{ ext{final}}$, which will give you the new temperature of the water after reaching thermal equilibrium.

Key Concepts

Heat Transfer

Heat transfer is the process of thermal energy moving from a hotter object to a cooler one until thermal equilibrium is reached. In this scenario, the copper pellets, initially at a high temperature, will transfer heat to the cooler water, causing the water's temperature to rise. This process is governed by the principles of conduction and convection.

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. Each material has a unique specific heat capacity, which influences how much its temperature changes when heat is added or removed. In this problem, the specific heat capacities of both copper and water will be crucial for calculating the final temperature.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this context, the heat lost by the copper pellets will equal the heat gained by the water, allowing us to set up an equation to find the final equilibrium temperature. This principle is fundamental in solving problems involving heat exchange.