First Law of Thermodynamics — Core Principles

Core Principles

The First Law of Thermodynamics is a direct application of the principle of conservation of energy to thermodynamic systems. It states that the change in a system's internal energy ($Delta U$) is equal to the heat ($Q$) added to the system minus the work ($W$) done *by* the system on its surroundings, expressed as $Delta U = Q - W$.

Internal energy ($U$) is a state function, depending only on the system's current state (primarily temperature for ideal gases). Heat ($Q$) and work ($W$) are path functions, representing energy transfer mechanisms.

Crucial sign conventions dictate that $Q$ is positive for heat absorbed and negative for heat released, while $W$ is positive for work done by the system (expansion) and negative for work done on the system (compression).

This law helps analyze various thermodynamic processes: isochoric ($Delta U = Q_V$, $W=0$), isobaric ($Q_P = Delta U + PDelta V$), isothermal ($Delta U = 0$, $Q=W$ for ideal gases), and adiabatic ($Delta U = -W$, $Q=0$).

Mayer's relation, $C_P - C_V = R$, links specific heats for ideal gases. The First Law is fundamental to understanding energy conversion in engines, refrigerators, and all physical and biological systems.

Important Differences

vs Heat and Internal Energy

Aspect	This Topic	Heat and Internal Energy
Definition	Heat ($Q$) is energy transferred due to a temperature difference between a system and its surroundings.	Internal Energy ($U$) is the total energy contained within a system due to the microscopic motion and interactions of its particles.
Nature	Heat is energy in transit; it is a form of energy transfer.	Internal energy is a property of the system; it is energy stored within the system.
State vs. Path Function	Heat is a path function; its value depends on the specific process or path taken.	Internal energy is a state function; its value depends only on the initial and final states of the system, not the path.
Measurement	Heat is measured during a process (e.g., using calorimetry).	Internal energy itself cannot be directly measured, only changes in internal energy ($\Delta U$) can be determined.
Symbol & Units	$Q$, typically in Joules (J) or calories (cal).	$U$, typically in Joules (J).

While both heat and internal energy are forms of energy, they represent fundamentally different concepts in thermodynamics. Heat is the *transfer* of energy across a boundary due to a temperature gradient, making it a path-dependent quantity. A system does not 'contain' heat; it exchanges it. Internal energy, on the other hand, is an intrinsic property *of* the system, representing the total microscopic energy stored within it. It is a state function, meaning its value depends only on the system's current state, irrespective of how that state was achieved. The First Law of Thermodynamics links these two, showing how heat and work contribute to changes in a system's internal energy.