Systems & Surroundings

Thermodynamics is the branch of chemistry and physics that studies energy, its forms, and its transformations. Before analysing any energy change, we must define precisely what we are studying. Chemists draw an imaginary boundary around the region of interest and call everything inside the 'system'. Everything outside that boundary — the rest of the universe — is the 'surroundings'. The boundary can be real (the walls of a flask) or conceptual (an imaginary surface around a gas), but it always separates the system from the surroundings. Together, the system and its surroundings constitute the universe: Universe = System + Surroundings. Systems are classified by what can cross their boundary. An open system exchanges both matter and energy with the surroundings (a boiling pot without a lid). A closed system exchanges energy but not matter (the same pot with a tight lid). An isolated system exchanges neither matter nor energy with the surroundings (a perfect thermos flask, or the universe itself). Real laboratory apparatus approximates these ideals: a sealed calorimeter is nearly isolated, while a test tube open to air is an open system. Recognising the system type tells us immediately which conservation laws apply and which quantities may change. A second fundamental distinction is between state functions and path functions. A state function depends only on the current condition (state) of the system — not on how the system arrived there. Temperature T, pressure P, volume V, internal energy U, enthalpy H, entropy S, and Gibbs free energy G are all state functions. Their changes depend only on the initial and final states: ΔX = X_final − X_initial, regardless of the path taken. Path functions, by contrast, depend on the specific route taken: heat (q) and work (w) are path functions. The distinction has profound practical consequences: because enthalpy H is a state function, Hess's Law allows us to add chemical equations freely, something that would be impossible if reaction heat were path-dependent.

Key takeaways
  • Drawing the System Boundary
  • Three Types of System
  • State Functions vs Path Functions
  • Why the Distinction Matters in Practice
  • Extensive vs Intensive State Functions

Drawing the System Boundary

Choose what you want to study — a reaction mixture, a gas, a living cell — and draw an imaginary boundary around it. The boundary defines the system. You then ask: can matter cross this boundary? Can energy (heat or work) cross it? The answers determine which of the three system types applies.

Three Types of System

Open system: both matter (n) and energy (E) cross the boundary. Example: an open beaker of water evaporating — water molecules leave and heat flows in from the surroundings. Closed system: energy crosses but matter does not. Example: a sealed syringe of gas being compressed — work is done on the gas but no molecules escape. Isolated system: neither matter nor energy crosses. Example: an ideal Dewar flask (thermos) — the internal energy of its contents is constant, so ΔU = 0 for all processes inside.

State Functions vs Path Functions

A state function X satisfies: ΔX = X₂ − X₁, where X₁ and X₂ are the values at the initial and final states. The integral of a state function around any closed loop (cyclic process) is zero: ∮ dX = 0. This is a mathematical test for a state function. Heat q and work w do NOT satisfy this: ∮ δq ≠ 0 in general, which is why they are path functions written with an inexact differential symbol δ rather than d. However, their sum q + w = ΔU is a state function (First Law of Thermodynamics), which is a remarkable and deeply useful result.

Why the Distinction Matters in Practice

Because enthalpy H is a state function, the enthalpy change for a chemical reaction at constant pressure, ΔH°rxn, has a unique value that does not depend on mechanism or reaction sequence. We can therefore calculate ΔH°rxn from standard enthalpies of formation, or combine reactions using Hess's Law, confident that the result equals the directly measured value. If H were a path function, none of those shortcuts would work. Similarly, because entropy S is a state function, we can evaluate ΔS for an irreversible process by inventing any convenient reversible path between the same two states.

Extensive vs Intensive State Functions

State functions are further classified as extensive (proportional to the amount of matter: U, H, S, G, V, n) or intensive (independent of amount: T, P, density, molar quantities like Hₘ). When a system is divided into two equal parts, extensive properties are halved but intensive properties remain unchanged. Molar quantities (e.g., Uₘ = U/n in J mol⁻¹) convert extensive state functions into intensive ones, making them size-independent and directly tabulated in data books.

The Key Equation

ΔU=q+w\Delta U = q + w
  • ΔU — Change in internal energy (J (joules)): A state function: depends only on initial and final states. ΔU = U_final − U_initial.
  • q — Heat (J (joules)): A path function: energy transferred as heat across the system boundary. Positive when heat flows into the system (endothermic).
  • w — Work (J (joules)): A path function: energy transferred as work. Using the IUPAC sign convention, w is positive when work is done on the system (e.g., compression). For expansion against external pressure: w = −P_ext ΔV.

Worked Example

Problem. A gas in a sealed piston–cylinder device (closed system) absorbs 850 J of heat from the surroundings while expanding against a constant external pressure of 1.20 × 10⁵ Pa. The volume increases from 2.00 L to 5.50 L. (a) Classify the system. (b) Calculate the work done by the gas using w = −P_ext ΔV. (c) Calculate ΔU for the gas. (d) State whether internal energy U is a state or path function, and explain what this means for your answer.

w=−Pext ΔV=−(1.20×105 Pa)(3.50×10−3 m3)=−420 J;ΔU=q+w=850+(−420)=+430 Jw = -P_{\text{ext}}\,\Delta V = -(1.20\times10^5\,\text{Pa})(3.50\times10^{-3}\,\text{m}^3) = -420\,\text{J};\quad \Delta U = q + w = 850 + (-420) = +430\,\text{J}

Answer. The system is closed; w = −420 J; ΔU = +430 J. U is a state function, so ΔU is path-independent.

Figure
Diagram
Types of Thermodynamic SystemsOPENMatter ✓Energy ✓SystemExample:Open beakerof boiling waterCLOSEDMatter ✗Energy ✓SystemExample:Sealed syringebeing compressedISOLATEDMatter ✗Energy ✗SystemExample:Ideal Dewar(thermos flask)Blue arrows = energy transfer; green arrow = matter transfer
Origins · 1 minRudolf Clausius and how this was discovered
RC
Rudolf Clausius
1822–1888 · German

Clausius was the first to give a clear mathematical formulation of both the First and Second Laws of Thermodynamics. In his 1850 paper he introduced the concept of internal energy as a state function and stated that energy is conserved in an isolated system. In 1865 he coined the word 'entropy' (from the Greek tropē, meaning 'transformation') and defined it precisely as dS = δq_rev / T — an exact differential, confirming entropy as a state function. His famous summary: 'The energy of the universe is constant; the entropy of the universe tends toward a maximum.' Clausius derived many of his results using thought experiments involving idealised frictionless, leakproof machinery — techniques that closely parallel the modern system/surroundings framework taught in introductory chemistry today.

  • Internal Energy (U) & Work — Internal energy U is the most fundamental state function. Understanding the system boundary is a prerequisite for applying the First Law ΔU = q + w correctly.
  • Enthalpy (H) — Enthalpy H = U + PV is a state function defined for constant-pressure processes in closed systems. The system/surroundings framework determines when H or U is the appropriate energy quantity to use.
  • Heat Capacity — Heat capacity connects the path function q to measurable temperature changes. The distinction between C_P (constant pressure, open/closed system) and C_V (constant volume, closed system) follows directly from the system-type classification.
  • Calorimetry — A calorimeter is a practical attempt to construct an isolated or adiabatic system. Understanding system classification is essential for setting up the energy balance q_system + q_surroundings = 0.
  • Reaction Enthalpies — Standard reaction enthalpies are tabulated because H is a state function. This concept flows directly from the state-function/path-function distinction introduced here.
  • Bond Enthalpy — Bond enthalpies are treated as state-function quantities that can be combined arithmetically — a practice that is only valid because enthalpy is a state function.
  • Hess's Law — Hess's Law is the direct thermochemical consequence of enthalpy being a state function: ΔH for a reaction is the same regardless of the pathway, so equations may be added freely.
  • Entropy (S) — Entropy is a state function defined within the system boundary. Its spontaneous increase in an isolated system (ΔS_universe ≥ 0) depends on correctly identifying what constitutes the isolated system.
  • Gibbs Free Energy (G) — G = H − TS is a composite state function that predicts spontaneity for processes in closed systems at constant T and P. Its definition relies on both the system boundary and the state-function nature of H and S.
  • Coupled Reactions — Coupling reactions is valid precisely because G is a state function: ΔG values for separate reactions may be added to give ΔG for the combined process, regardless of mechanism.