Chemical Thermodynamics - First Law of Thermodynamics

Thermodynamics deals with the energy changes accompanying physical and chemical processes.

A System is the part of the universe under observation, while the Surroundings comprise the rest of the universe.

Types of Systems: Open (exchange of matter and energy), Closed (exchange of energy only), and Isolated (no exchange of matter or energy).

Internal Energy ($U$): The total energy contained within a system. It is a state function and an extensive property.

First Law of Thermodynamics: Energy can neither be created nor destroyed; it can only be converted from one form to another. Mathematically: $\Delta U = q + w$.

Sign Convention (IUPAC): Heat absorbed by the system ($q$) is positive ($+$); heat released is negative ($-$). Work done on the system ($w$) is positive ($+$); work done by the system is negative ($-$).

Work ($w$): For an irreversible process against constant external pressure, $w = -P_{ext} \Delta V$. For a reversible isothermal process, $w_{rev} = -2.303 nRT \log \frac{V_2}{V_1}$.

Enthalpy ($H$): The total heat content of a system at constant pressure, defined as $H = U + PV$. The change in enthalpy is given by $\Delta H = \Delta U + P\Delta V$.

Relation between $\Delta H$ and $\Delta U$: For reactions involving gases, $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in the number of moles of gaseous products and reactants.

Heat Capacity: The amount of heat required to raise the temperature of a substance by $1^{\circ}C$ (or $1 K$). At constant volume, it is $C_v$, and at constant pressure, it is $C_p$. For one mole of an ideal gas, $C_p - C_v = R$.