A copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at 20.0°C. A 0.250-kg block of iron at 85.0°C is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the surroundings.

Verified step by step guidance

1. Identify the specific heat capacities for copper, water, and iron. The specific heat capacity is the amount of heat required to change the temperature of one kilogram of a substance by one degree Celsius. For copper, it is approximately 0.385 J/g°C, for water it is 4.186 J/g°C, and for iron, it is about 0.449 J/g°C.
2. Convert the masses of the copper pot, water, and iron block from kilograms to grams because the specific heat capacities are given in J/g°C.
3. Set up the heat transfer equation assuming no heat loss to the surroundings. The heat gained by the copper pot and water should equal the heat lost by the iron block. Use the formula: \(m_c c_c (T_f - T_{c_i}) + m_w c_w (T_f - T_{w_i}) = m_i c_i (T_{i_i} - T_f)\), where \(m\) is mass, \(c\) is specific heat capacity, \(T_f\) is the final temperature, and subscripts \(c\), \(w\), and \(i\) refer to copper, water, and iron respectively.
4. Solve the equation for the final temperature \(T_f\). This involves combining like terms and isolating \(T_f\) on one side of the equation.
5. Check the physical plausibility of your answer, ensuring that the final temperature is between the initial temperatures of the substances involved (between 20.0°C and 85.0°C) and that the direction of heat flow is from the hotter iron to the cooler water and copper pot.

Key Concepts

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, heat will flow from the hot iron block to the cooler copper pot and water until thermal equilibrium is reached, meaning all components will eventually have the same final temperature.

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 heat it can absorb or release. In this problem, the specific heat capacities of copper, water, and iron will be essential 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 iron block will equal the heat gained by the copper pot and water, allowing us to set up an equation to solve for the final temperature of the system.