Energy Transfers

Internal Energy ($E$) is the sum of all kinetic and potential energies of the components within a system. While the absolute value of $E$ is difficult to measure, we can precisely determine the change in internal energy, $\Delta E = E_{final} - E_{initial}$.

Energy is exchanged between a system and its surroundings in two primary forms: Heat ($q$) and Work ($w$). This relationship is expressed by the fundamental equation: $\Delta E = q + w$

Sign Conventions are critical for tracking energy flow: $q$ is positive when the system absorbs heat (endothermic) and negative when it releases heat (exothermic). Similarly, $w$ is positive when work is done on the system (e.g., compression) and negative when work is done by the system (e.g., expansion).

Specific Heat Capacity ($C_s$) is an intrinsic property of a substance defined as the amount of heat required to raise the temperature of one gram of that substance by one degree Celsius (or one Kelvin). It represents a substance's resistance to temperature change.

The quantity of heat ($q$) transferred during a temperature change is calculated using the mass ($m$), the specific heat capacity ($C_s$), and the change in temperature ($\Delta T$): $q = m \cdot C_s \cdot \Delta T$

Substances with high specific heat capacities, like water, require significantly more energy to change temperature compared to substances with low heat capacities, such as metals.

During a phase transition, such as melting or boiling, the temperature of a substance remains constant even as heat is added. This is because the energy is being used to overcome intermolecular forces (potential energy) rather than increasing the speed of the particles (kinetic energy).

The Heat of Fusion ($\Delta H_{fus}$) is the energy required to convert a solid to a liquid at its melting point, while the Heat of Vaporization ($\Delta H_{vap}$) is the energy required to convert a liquid to a gas at its boiling point.

For any substance, the energy required for sublimation (solid to gas) is the sum of the energies for melting and vaporization: $\Delta H_{sub} = \Delta H_{fus} + \Delta H_{vap}$

Check the Signs: Always verify the direction of energy flow. If a system 'does work' or 'releases heat', the values for $w$ and $q$ must be entered as negative in the $\Delta E$ equation.

Temperature Units: When calculating $\Delta T$, the change is the same in both Celsius and Kelvin. You do not need to convert individual temperatures to Kelvin if you are only looking for the difference.

Heating Curve Slopes: On a graph of Temperature vs. Heat Added, a steeper slope indicates a lower specific heat capacity, as less heat is required to produce a large temperature change.

Units Consistency: Ensure that the units for mass (grams vs. moles) match the units of the heat capacity constant ($J/g\cdot K$ vs. $J/mol\cdot K$) being used.