Heat Capacity, Specific Heat, and Calorimetry

Heat Capacity: The amount of energy required to raise the temperature of a given sample by $1\,^\circ\text{C}$ .
Specific Heat: The amount of energy required to raise $1\,\text{g}$ of a substance by $1\,^\circ\text{C}$ .
Heat Capacity Equation: $q = C \times \Delta T$ , where $q$ is heat exchange, $C$ is heat capacity, and $\Delta T$ is the change in temperature.
Specific Heat Equation: $q = m \times c \times \Delta T$ , where $q$ is heat exchange, $m$ is mass in grams, $c$ is specific heat, and $\Delta T$ is the change in temperature.

Calorimetry: A process used to measure heat transfer in physical or chemical processes.
Coffee Cup Calorimeter: Serves as an effective insulator to prevent heat from escaping during measurements.
Experimental Procedure:
- A metal sample is heated in boiling water until it reaches the water's temperature.
- The hot metal is transferred to a coffee cup containing a known volume of room-temperature water equipped with a thermometer.
- Heat flows from the metal into the water, causing the water temperature to rise until thermal equilibrium is reached.

Heat Absorbed by Water:
- Calculated using $q_{\text{water}} = m_{\text{water}} \times c_{\text{water}} \times \Delta T_{\text{water}}$ .
- The volume of water in milliliters equals the mass in grams ( $1\,\text{mL} = 1\,\text{g}$ ).
Heat Conservation: Heat absorbed by the water is equal to the heat released by the metal ( $q_{\text{water}} = q_{\text{metal}}$ ).
Solving for Metal Specific Heat:
- Temperature change for the metal ( $\Delta T_{\text{metal}}$ ) is measured from the boiling water temperature to the final coffee cup temperature.
- Specific heat is calculated using $c_{\text{metal}} = \frac{q_{\text{metal}}}{m_{\text{metal}} \times \Delta T_{\text{metal}}}$ .
- Comparing the calculated specific heat to known values allows for the identification of unknown metals.