First Law of Thermodynamics — Core Principles

Core Principles

The First Law of Thermodynamics is fundamentally the law of conservation of energy applied to thermodynamic systems. It states that energy cannot be created or destroyed, only transformed. Mathematically, it's expressed as $Delta U = q + w$, where $Delta U$ is the change in the system's internal energy, $q$ is the heat exchanged, and $w$ is the work done.

Internal energy ($U$) is a state function, depending only on the system's current state. Heat ($q$) and work ($w$) are path functions, depending on the process. Key sign conventions: $q > 0$ for heat absorbed, $q < 0$ for heat released; $w > 0$ for work done *on* the system, $w < 0$ for work done *by* the system.

Different thermodynamic processes (isochoric, isobaric, isothermal, adiabatic, cyclic) lead to specific simplifications of the First Law, allowing for calculations of energy changes. Enthalpy ($Delta H = q_p$) is a crucial concept derived from the First Law for constant pressure processes.

Important Differences

vs Internal Energy vs. Enthalpy

Aspect	This Topic	Internal Energy vs. Enthalpy
Definition	Internal Energy ($U$): Total energy contained within a system (kinetic + potential energy of molecules).	Enthalpy ($H$): A thermodynamic potential defined as $H = U + PV$ (Internal energy + Pressure-Volume work).
Nature	State function. Its change ($Delta U$) depends only on initial and final states.	State function. Its change ($Delta H$) depends only on initial and final states.
Measurement	Change in internal energy ($Delta U$) is equal to heat exchanged at constant volume ($q_v$). $Delta U = q_v$.	Change in enthalpy ($Delta H$) is equal to heat exchanged at constant pressure ($q_p$). $Delta H = q_p$.
Relevance	Most relevant for processes occurring at constant volume (isochoric processes), or when considering total energy changes irrespective of pressure-volume work.	Most relevant for processes occurring at constant pressure (isobaric processes), which are common in chemical reactions conducted in open vessels.
Relation to First Law	Directly appears in the First Law: $Delta U = q + w$.	Derived from the First Law under constant pressure conditions: $Delta H = Delta U + PDelta V = (q_p + w) + PDelta V = q_p - PDelta V + PDelta V = q_p$.

While both internal energy and enthalpy are state functions representing energy within a system, they differ in their practical application and definition. Internal energy ($U$) represents the total microscopic energy, and its change ($Delta U$) directly equals heat exchanged at constant volume ($q_v$). Enthalpy ($H$), defined as $U+PV$, is particularly useful for constant pressure processes, where its change ($Delta H$) directly corresponds to the heat exchanged ($q_p$). This distinction is crucial for correctly analyzing energy changes in different experimental conditions.