Systems and Processes
Thermochemistry starts with a shared vocabulary: what counts as the system, how it exchanges energy with its surroundings, and how that exchange is tracked.
Thermochemistry is the study of the heat released or absorbed during chemical and physical change, and it starts with a shared vocabulary: what counts as the system, how that system exchanges energy with its surroundings, and how that exchange is tracked using internal energy, heat, and work. These definitions — along with the distinction between state and path functions and the four idealized thermodynamic processes — set up every calculation later in this chapter, from enthalpy to entropy to Gibbs free energy.
Key Takeaways
Energy is the capacity to do work or produce heat, and it's conserved — never created or destroyed, only converted between potential and kinetic forms.
The system is the reactants/products under focus; the surroundings are everything else. Systems are isolated (no energy or matter exchange), closed (energy only), or open (both energy and matter).
Internal energy (E) is the total kinetic and potential energy of a system's particles; ΔE tracks its change, and the first law of thermodynamics says ΔE(system) = −ΔE(surroundings).
ΔE = q + w: heat (q) transfers energy via a temperature difference, work (w) transfers energy via force through a distance. Both are positive when added to/done on the system, negative when removed from/done by the system.
State functions (temperature, pressure, volume, energy) depend only on the current state; path functions (heat, work) depend on the path taken to get there.
The four thermodynamic processes — isothermal (constant T), adiabatic (no heat exchange), isobaric (constant P), isochoric (constant V) — each trace a distinct shape on a P-V diagram.
P-V work: w = −PΔV. Expansion does negative work (system on surroundings); compression does positive work (surroundings on system). 101.3 J = 1 L·atm.
Energy: Potential, Kinetic, and Conserved
Energy is the capacity to do work or produce heat. One of its most important properties is that it's conserved: the law of conservation of energy states that energy can be converted from one form to another, but it can never be created or destroyed — the total energy of the universe is constant.
Energy comes in two broad categories:
Potential energy — energy due to position or composition:
Gravitational potential energy: stored by an object's position above Earth's surface.
Elastic potential energy: stored when an object is stretched or compressed.
Nuclear potential energy: stored in the bonds holding a nucleus together.
Chemical potential energy: stored in the bonds between atoms and molecules.
Kinetic energy — energy due to motion:
Motion (mechanical) energy: the energy of an object in motion.
Sound energy: mechanical energy carried by sound waves through a medium.
Thermal energy: the collective motion of particles within a substance, which contributes to its temperature.
Electrical energy: carried by moving charges (typically electrons) through a conductor.
The kinetic energy of a moving object is KE = ½mv².
The SI unit of energy is the joule (J). The other common unit is the calorie (cal) — the heat required to raise the temperature of 1 g of water by 1°C — where 1 cal = 4.184 J. The nutritional "Calorie" (capital C) is equal to 1000 of these lowercase calories.
System vs. Surroundings
In thermodynamics, the universe is divided into two parts:
The system is the part of the universe under focus — for a chemical reaction, that's the reactants and products.
The surroundings are everything else — the reaction container, the room, and so on.
Systems are classified by how they exchange energy and matter with their surroundings:
Isolated system: exchanges neither energy nor matter with the surroundings. Example: an insulated bomb calorimeter.
Closed system: exchanges energy but not matter. Example: a steam radiator.
Open system: exchanges both energy and matter. Example: a pot of boiling water.
Internal Energy and the First Law of Thermodynamics
The internal energy of a system is the combined kinetic and potential energy of every particle in it — far too much to calculate directly, even for a simple system. What's usually tracked instead is ΔE, the change in internal energy (final minus initial):
If ΔE is negative, the system loses energy.
If ΔE is positive, the system gains energy.
This leads directly to the first law of thermodynamics (also called the law of conservation of energy): energy can be converted from one form to another, but it can't be created or destroyed. The total energy of the universe stays constant, so any energy lost by the system is gained by the surroundings, and vice versa:
ΔE(system) = −ΔE(surroundings)
Heat and Work: Two Ways to Transfer Energy
Restating energy formally: it's the capacity to do work or transfer heat, which gives the first law its working equation:
ΔE = q + w
(Some sources write ΔE = q − w — same information, different sign convention for work. This article uses q + w throughout.)
Heat (q) is the flow of energy that occurs because of a temperature difference, and it always flows from the hotter object to the colder one. Heat is not the same as temperature: temperature measures the kinetic energy of a system, while heat measures the transfer of that kinetic energy between systems. Heat also isn't itself a form of energy — it's one of the two ways energy can be transferred.
Work (w) is the second way energy transfers — the result of a force acting through a distance: w = F × d.
The sign of q and w is always defined from the system's point of view:
Quantity | Positive (+) | Negative (−) |
|---|---|---|
Heat (q) | Added to the system | Removed from the system |
Work (w) | Done on the system by the surroundings | Done by the system on the surroundings |
State Functions vs. Path Functions
A state function is a property determined only by the current state (or condition) of a system — it doesn't depend on how the system got there. Temperature, pressure, volume, concentration, and energy are all state functions (as is enthalpy, covered later in this chapter).
Heat and work are not state functions — they're path functions. Their values depend on the path taken between the initial and final states, not just on the two states themselves, because heat and work describe the process of change rather than a property that exists in either the initial or final state.
The Four Thermodynamic Processes
Systems can be constrained in different ways as they change. Four idealized processes — isothermal, adiabatic, isobaric, and isochoric — describe how a system behaves under each constraint, and each has a distinct signature on a pressure-volume (P-V) diagram.
Isothermal (constant temperature): heat added to the system is exactly balanced by work done by the system, so temperature never changes. On a P-V diagram, this traces a hyperbolic curve — since PV = nRT at constant T, pressure and volume are inversely proportional. Example: slow compression or expansion of an ideal gas in a container that exchanges heat with its surroundings, staying in thermal equilibrium throughout.
Adiabatic (no heat exchange): the system is perfectly insulated, so any change in internal energy comes entirely from work. The P-V curve is steeper than an isothermal curve, because without heat exchange, temperature does change as the gas expands or compresses. Examples: a gas expanding rapidly in an insulated container (does work on the surroundings, so internal energy and temperature drop) or being compressed rapidly (internal energy and temperature rise) — as in the compression stroke of an internal combustion engine, or air rushing out of a bicycle pump.
Isobaric (constant pressure): volume changes while pressure stays fixed, shown as a horizontal line on a P-V diagram. Heat added at constant pressure changes both internal energy and does work. Example: heating a gas in a piston free to expand or contract while pressure stays constant.
Isochoric (constant volume): volume is fixed, so no work is done (there's no distance to push through) — shown as a vertical line on a P-V diagram. Heat added goes directly into internal energy, which changes pressure. Example: heating a gas in a rigid, sealed container, where pressure rises because the volume can't expand to accommodate the added energy.
Pressure-Volume Work
Most reactions run in the lab happen in open containers at constant pressure — this is pressure-volume (P-V) work. For a movable piston, compressing it means the surroundings are doing work on the system, giving w a positive sign. Working through the math gives:
w = −PΔV
If the gas expands, ΔV is positive, so w is negative — the system does work on the surroundings.
If the gas contracts, ΔV is negative, so w is positive — the surroundings do work on the system.
Useful conversion factor: 101.3 J = 1 L·atm.
Common MCAT Mistakes
Treating heat and temperature as interchangeable. Temperature is a state function describing a system's average particle kinetic energy at a moment in time; heat is a path function describing energy transfer driven by a temperature difference.
Losing track of the sign convention for q and w. Both are always defined from the system's point of view — heat added to the system and work done on the system by the surroundings are positive; heat leaving the system and work the system does on the surroundings are negative.
Assuming heat and work are state functions because energy is. Internal energy, temperature, pressure, and volume are state functions, but heat and work are path functions — their values depend on the specific process, not just the initial and final states.
Mixing up adiabatic with isothermal. Adiabatic means no heat is exchanged (q = 0), not that temperature stays constant — an adiabatic process can and usually does change temperature, since any energy change must come entirely from work.
MCAT-Style Concept Check
Question: A rigid, sealed metal container of gas is heated with a Bunsen burner. The container's volume cannot change, but its internal pressure rises steadily. Which thermodynamic process does this describe, and how much work is done?
A) Isobaric; w = 0
B) Isochoric; w = 0
C) Isothermal; w ≠ 0
D) Adiabatic; w ≠ 0
Answer: B
Explanation: A rigid, sealed container fixes the volume, so ΔV = 0 — this is an isochoric process. Since w = −PΔV, a ΔV of zero means no work is done (w = 0) regardless of how much the pressure or internal energy changes. All of the heat added goes directly into raising the system's internal energy, which is what drives the pressure increase.
FAQ
What's the difference between heat and work?
Both are ways of transferring energy, but heat (q) transfers energy because of a temperature difference between a system and its surroundings, while work (w) transfers energy through a force acting over a distance. Together, ΔE = q + w accounts for every way a system's internal energy can change.
What's the difference between a state function and a path function?
A state function — like temperature, pressure, volume, or internal energy — depends only on a system's current condition, not on how it got there. A path function — like heat or work — depends on the specific process taken between the initial and final states, so two different paths between the same two states can produce different amounts of heat or work even though ΔE is the same either way.
What does the first law of thermodynamics say?
The first law states that energy can be converted between forms but never created or destroyed, so the total energy of the universe is constant. Applied to a system and its surroundings, this means any energy lost by one is gained by the other: ΔE(system) = −ΔE(surroundings).
Why is work negative when a gas expands?
Work is defined as w = −PΔV, from the system's point of view. When a gas expands, ΔV is positive, making w negative — the system is losing energy by doing work on its surroundings (pushing them back). When a gas is compressed, ΔV is negative, making w positive, since the surroundings are now doing work on the system.
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