Define specific heat capacity, explain why metals are good conductors of heat, and describe the method of mixtures for determining specific heat capacity.

Task 1.1:
Specific heat capacity ($c$) is the heat energy needed to raise the temperature of 1 kilogram of a substance by 1 Kelvin, measured in J kg$^{-1}$ K$^{-1}$. It indicates a substance's resistance to temperature change; materials with high specific heat capacity require more energy to change temperature.

Metals are typically good heat conductors because their free electrons efficiently transfer thermal energy throughout the material. Metals like copper exhibit high thermal conductivity. Materials lacking these free electrons, such as non-metals, are poor conductors or insulators. While some metals conduct better than others, all metals are relatively good conductors compared to non-metallic insulators.

The method of mixtures uses the principle of energy conservation to determine specific heat capacity. A hot object of known mass and initial temperature is placed into a cooler liquid (e.g., water) of known mass and temperature in a calorimeter. Heat transfers until thermal equilibrium is reached. By measuring the final temperature and knowing the specific heat capacities of the liquid and calorimeter, the heat lost by the object is equated to the heat gained by the liquid and calorimeter. This allows calculation of the unknown specific heat capacity using the formula $m_1 c_1 \Delta T_1 = m_2 c_2 \Delta T_2$.

$$\boxed{\text{Specific heat capacity is the heat energy required to raise the temperature of 1 kg of a substance by 1 K. Metals are good heat conductors due to free electrons. The method of mixtures determines specific heat capacity by equating heat lost by a hot object to heat gained by a cooler liquid and calorimeter, based on the conservation of energy.}}$$

Task 1.2:

$$\boxed{\text{If an unknown metal is heated and then mixed with water in a calorimeter, then its specific heat capacity can be determined by assuming that the heat lost by the metal equals the heat gained by the water and calorimeter.}}$$