A 25.0 g piece of granite at 100.0°C was added to 100.0 g of water of 25.0°C, and the temperature rose to 28.4°C. What is the specific heat capacity of the granite? (The specific heat capacity for water is 4.18 J/(g•°C).) (LO 9.10) (a) 0.563 J/(g•°C) (b) 1.53 J/(g•°C) (c) 0.992 J/(g•°C) (d) 0.794 J/(g•°C)

Verified step by step guidance

1. Calculate the heat gained by the water using the formula: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the water, \( c \) is the specific heat capacity of water, and \( \Delta T \) is the change in temperature of the water.
2. Assume that the heat lost by the granite is equal to the heat gained by the water, due to the principle of conservation of energy.
3. Calculate the change in temperature of the granite, which is the difference between its initial temperature and the final equilibrium temperature.
4. Use the formula \( q = m \cdot c \cdot \Delta T \) to express the heat lost by the granite, substituting the mass of the granite and its change in temperature.
5. Solve for the specific heat capacity of the granite, \( c \), by rearranging the formula to \( c = \frac{q}{m \cdot \Delta T} \) using the heat lost by the granite calculated in step 2.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a material property that varies between different substances, influencing how they absorb and transfer heat. In this problem, the specific heat capacity of granite needs to be calculated based on the heat exchange with water.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object to another due to a temperature difference. In this scenario, heat is transferred from the hot granite to the cooler water until thermal equilibrium is reached. The principle of conservation of energy dictates that the heat lost by the granite equals the heat gained by the water.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this context, it involves calculating the heat exchanged between the granite and water using their respective masses, specific heat capacities, and temperature changes. The formula used is q = mcΔT, where q is heat, m is mass, c is specific heat capacity, and ΔT is the change in temperature.