Energy and Conservation of Energy

What Energy Means in (Physical) Chemistry

In everyday language, “energy” is often associated with strength, electricity, or fuel. In physical chemistry, the term is used more precisely, but the core idea is similar:

Energy is the capacity of a system to do work or to transfer heat.

• A system is the part of the world we are focusing on (e.g. the contents of a beaker).
• The surroundings are everything else.

In thermodynamics, we do not ask what energy “really is” but rather:

• In which forms does it appear?
• How can it be transferred?
• How can we account for it quantitatively?

Later subsections will treat the first and second laws and Gibbs energy in detail. Here we focus on the basic forms and the conservation (bookkeeping) of energy.

Forms of Energy Relevant in Chemistry

Real systems contain many forms of energy at once. For chemical thermodynamics it is useful to distinguish:

• Kinetic energy – associated with motion:
• Macroscopic motion (e.g. a moving piston).
• Microscopic motion: random motion of atoms and molecules, which is closely linked to temperature.

For a particle of mass $m$ moving at speed $v$:
$$ E_\text{kin} = \frac{1}{2}mv^2 $$

• Potential energy – associated with position in a field:
• Gravitational potential energy (usually negligible for chemistry at the lab scale).
• Electrical potential energy (very important in electrochemistry and for ions).

Near Earth’s surface:
$$ E_\text{pot,grav} = mgh $$
with $g$ the gravitational acceleration and $h$ the height.

• Internal energy ($U$) – the total energy contained within a system due to:
• Motions of all particles (translations, rotations, vibrations).
• Interactions between particles (chemical bonds, intermolecular forces, etc.).
• Electronic energies, nuclear energies (at the chemistry level, often included implicitly).

Internal energy is a state function (explained below): it depends only on the current state of the system, not on how that state was reached.

In chemical thermodynamics we are primarily concerned with changes in internal energy $\Delta U$, because absolute values are usually not directly measurable.

System, Surroundings, and Types of Systems

For energy considerations, it is essential to define the boundary between system and surroundings.

• Open system: can exchange matter and energy with surroundings (e.g. an open beaker).
• Closed system: can exchange energy but not matter (e.g. a sealed, but not perfectly insulated, flask).
• Isolated system: ideally no exchange of matter or energy (e.g. an ideal, perfectly insulated container). Real isolated systems are approximations.

The classification affects how we think about energy changes. For example:

• In a closed system, the number of moles in the system is fixed, but energy can be gained or lost as heat or work.
• In an isolated system, the total energy is constant. Any change inside must be balanced by another change inside.

Work and Heat as Modes of Energy Transfer

Energy can cross the boundary between system and surroundings in only two broad ways in classical thermodynamics:

• Work ($w$) – energy transfer associated with organized motion at the boundary (e.g. a gas pushing a piston, stirring, electrical work).
• Heat ($q$) – energy transfer driven by a temperature difference between system and surroundings; associated with disordered molecular motion.

Important:

• $q$ and $w$ are not properties of the system; they are path-dependent quantities:
• They depend on how the process is carried out (slowly, quickly, under constant pressure, etc.).
• They are not state functions.
• In contrast, the change in internal energy $\Delta U$ is a state function; it depends only on initial and final states.

Sign convention (chemistry/physics convention, which will be used in later chapters):

• $q > 0$: the system absorbs heat from surroundings.
• $q < 0$: the system releases heat to surroundings.
• $w > 0$: work is done on the system (energy enters the system as work).
• $w < 0$: work is done by the system on the surroundings (energy leaves the system as work).

State Functions vs. Path Functions

Understanding the distinction between different types of thermodynamic quantities is crucial:

• State functions depend only on the current state of the system (defined by variables like temperature $T$, pressure $p$, volume $V$, amount of substance $n$). Examples:
• Internal energy $U$
• Enthalpy $H$ (introduced in the First Law chapter)
• Entropy $S$ (introduced in the Second Law chapter)
• Gibbs free energy $G$ (introduced later)

For any state function $X$:
$$ \Delta X = X_\text{final} - X_\text{initial} $$
is independent of the path between initial and final states.

• Path functions depend on how the change occurs:
• Heat $q$
• Work $w$

There is no $\Delta q$ or $\Delta w$ defined as a property of state; we only talk about “heat supplied” or “work done” during a specific process.

In energy accounting, the key idea is:

Different paths between the same initial and final states can involve different amounts of heat and work, but the total change in internal energy $\Delta U$ is always the same.

The Principle of Conservation of Energy

The conservation of energy is a fundamental principle: in an isolated system, energy can neither be created nor destroyed, only converted from one form to another.

In words:

• The total energy of an isolated system is constant.
• Any energy lost by one part of the system is gained by another part.

Applied to a closed system (that can exchange heat and work, but not matter) we focus on changes in internal energy $U$:

• If the system receives energy as heat or work, its internal energy increases.
• If the system loses energy as heat or work, its internal energy decreases.

Quantitatively, for a process from state 1 to state 2:
$$ \Delta U = U_2 - U_1 $$

Energy bookkeeping then demands that the change in internal energy equals the net energy transfer into the system as heat and work. The explicit formulation connecting $\Delta U$, $q$, and $w$ is treated systematically in the chapter on the First Law of Thermodynamics; here we focus just on the conceptual meaning:

• You can track all energy transfers as heat and work.
• Whatever is not leaving or entering as heat or work must be reflected in the internal energy of the system.
• When system and surroundings are considered together as an isolated whole, total energy is conserved.

Energy Conversion in Chemical Processes (Conceptual View)

Chemical reactions and physical processes often involve the interconversion of energy forms, for example:

• Chemical energy (associated with bonds and molecular structure) can be converted into:
• thermal energy (heating the surroundings),
• mechanical work (gas expansion moving a piston),
• electrical work (in electrochemical cells).
• Conversely, electrical or mechanical energy can be used to:
• drive non-spontaneous chemical reactions (e.g. electrolysis),
• change phase (melting, vaporization) if sufficient energy is supplied as heat.

From the standpoint of conservation:

• The total energy before and after the process (system + surroundings) is the same.
• What changes is the distribution between internal energy (especially chemical and thermal parts) and energy stored/manifested as work or heat in surroundings.

Energy Units in Chemistry

The standard SI unit of energy is the joule (J).

Commonly used multiples and related units in chemistry include:

• $1\ \text{kJ} = 10^3\ \text{J}$
• $1\ \text{MJ} = 10^6\ \text{J}$
• Calorie (cal): historically used in calorimetry (heat measurements).
• By definition:
  $$ 1\ \text{cal} = 4.184\ \text{J} $$
• Nutritional “Calories” (with capital C) are actually kilocalories:
  $$ 1\ \text{Cal} = 1\ \text{kcal} = 1000\ \text{cal} \approx 4184\ \text{J} $$

In thermodynamic equations and tables in this course, energies will generally be expressed in joules or kilojoules per mole (J/mol or kJ/mol).

Summary of Key Ideas

• Energy is the capacity to do work or transfer heat.
• In chemistry we mostly track internal energy $U$ and its changes.
• Energy is transferred as heat ($q$) or work ($w$), which are path-dependent.
• State functions (like $U$, $H$, $S$, $G$) depend only on the state; their changes are path-independent.
• The conservation of energy states that total energy is constant in an isolated system; energy is neither created nor destroyed, only converted.
• In any physical or chemical process, including reactions, we can account for all energy transformations using this principle.

The detailed mathematical expression of energy conservation in terms of internal energy, heat, and work is formulated and used systematically in the chapter on the First Law of Thermodynamics.