System and Surroundings
A system in thermodynamics is that part of the universe in which observations are made; the remaining universe constitutes the surroundings. The surroundings include everything other than the system, so that the system and the surroundings together make up the universe:
$\text{The universe} = \text{The system} + \text{The surroundings}$
In practice the entire universe is not affected by changes inside the system. The surroundings are therefore taken to be that portion of the remaining universe which can actually interact with the system — usually the region of space in its immediate neighbourhood. If the reaction between two substances $\ce{A}$ and $\ce{B}$ is studied in a beaker, the reaction mixture in the beaker is the system and the room in which the beaker stands is the surroundings.
The system is separated from the surroundings by a boundary, a wall that may be real or imaginary. The boundary is what lets us control and keep track of all movements of matter and energy into or out of the system. A system may be defined by physical limits such as the walls of a beaker or test tube, or simply by a set of coordinates marking out a volume in space.
Types of System
Systems are classified according to whether matter and energy can move across the boundary. NCERT recognises three types — open, closed and isolated. An open system exchanges both matter and energy with the surroundings; reactants in an open beaker form an open system. A closed system permits exchange of energy but not matter; reactants in a sealed vessel of conducting material such as copper or steel form a closed system. An isolated system allows neither matter nor energy to cross its boundary; reactants in a thermos flask approximate an isolated system.
| Type of system | Matter exchange | Energy exchange | Typical example |
|---|---|---|---|
| Open | Yes | Yes | Reactants in an open beaker; plants and animals |
| Closed | No | Yes | Reactants in a sealed copper or steel vessel |
| Isolated | No | No | Reactants in a thermos flask / insulated vessel |
The State of a System
To make any useful calculation a system must be described quantitatively by specifying its properties — its pressure $(p)$, volume $(V)$, temperature $(T)$ and composition. Thermodynamics uses a much simpler concept of state than mechanics: it does not require the position and velocity of every particle, only the average measurable or macroscopic (bulk) properties. The state of a gas, for instance, is described by quoting $p$, $V$, $T$ and amount $(n)$.
It is not necessary to fix every property to define the state. Only a certain number of properties can be varied independently; once that minimum number of macroscopic properties is fixed, the others automatically take definite values. The number depends on the nature of the system. The state of the surroundings, by contrast, can never be completely specified — fortunately it need not be.
State Functions and Path Functions
Variables such as $p$, $V$ and $T$ are called state functions or state variables because their values depend only on the state of the system and not on how that state was reached. The NIOS supplement makes the contrast vivid: when a system changes from an initial state to a final state, the difference $p_2 - p_1$ or $T_2 - T_1$ is the same whichever path is followed, because pressure and temperature are state functions.
A path function, by contrast, depends on the route taken between two states. Heat $(q)$ and work $(w)$ are path functions: their individual values vary with how a change is carried out, even though the sum $q + w = \Delta U$ is fixed. The travel analogy is exact — the straight-line separation between two points is a state function, but the distance actually walked depends on the route and is a path function.
State function vs path function — know which quantity is which
Questions repeatedly ask candidates to classify quantities. State functions depend only on the state: $p$, $V$, $T$, internal energy $U$, enthalpy $H$, entropy $S$ and Gibbs energy $G$. Path functions depend on the route: heat $q$ and work $w$. A common trap is to mark heat or work as state functions because $\Delta U = q + w$ is path-independent — but $q$ and $w$ individually are not.
Rule: a change in a state function is written with $\Delta$ and is path-independent ($\Delta U$, $\Delta H$). Heat and work carry no $\Delta$ and are path-dependent.
Internal Energy as a State Function
When a chemical system gains or loses energy, the total energy of the system is represented by its internal energy, $U$ — the sum of all forms of energy (chemical, electrical, mechanical and others). The internal energy may change when heat passes into or out of the system, when work is done on or by the system, or when matter enters or leaves it.
Joule's experiments between 1840 and 1850 established that $U$ is a state function. Working with an adiabatic system (one whose wall permits no transfer of heat), he changed the state of water in two ways — by mechanical churning with paddles, and by an equal amount of electrical work through an immersion heater. The same amount of work produced the same change of state, measured by the same temperature change, irrespective of how the work was done. The adiabatic work needed to bring about a change of state therefore equals the difference in internal energy between the two states:
$\Delta U = U_2 - U_1 = w_{ad}$
Because this value depends only on the initial and final states, $U$ is a state function. By the IUPAC convention used in chemistry, $w_{ad}$ is positive when work is done on the system (internal energy rises) and negative when work is done by the system. Familiar state functions besides $U$ include $V$, $p$ and $T$: a change in temperature from 25 °C to 35 °C is $+10$ °C whether the system is taken straight up or cooled first and then heated.
See how heat and work change the internal energy and combine in the first law in Work, Heat and Internal Energy.
Extensive and Intensive Properties
The measurable properties of a system fall into two classes. An extensive property depends on the amount or size of the system — examples are mass, volume, internal energy, enthalpy and heat capacity. An intensive property is independent of the amount of matter present — examples are temperature, pressure, density, refractive index, viscosity and surface tension.
An extensive property can be converted into an intensive one by referring it to a unit amount of substance. Mass and volume are extensive, but mass per unit volume (density) and volume per unit mass (specific volume) are intensive. In general, dividing one extensive property by another extensive property yields an intensive property — the basis of molar quantities such as molar volume and molar heat capacity.
| Feature | Extensive property | Intensive property |
|---|---|---|
| Depends on amount of matter | Yes | No |
| On doubling the system | Value doubles | Value unchanged |
| Additive over parts | Yes | No |
| Examples | Mass, volume, $U$, $H$, $S$, $G$, heat capacity | Temperature, pressure, density, refractive index, molar volume, viscosity |
Molar and specific quantities are intensive
Total heat capacity is extensive, but molar heat capacity $(C_m)$ and specific heat are intensive because they are defined per unit amount. Likewise volume is extensive while molar volume is intensive. The test: split the system into two halves — if the property keeps the same value, it is intensive; if it halves, it is extensive.
Rule: extensive ÷ extensive = intensive (e.g. $U/n$, mass/volume). Temperature and pressure are always intensive.
Thermodynamic Processes
The method of bringing about a change in the state of a system is called a process. NCERT and NIOS define four processes by what is held constant, together with the reversible–irreversible distinction. An isothermal process keeps the temperature constant — the melting of ice at 273 K and 1 atm is isothermal because the temperature does not change while melting proceeds. An adiabatic process allows no exchange of heat between system and surroundings, as when an acid and base are mixed in a closed thermos flask; the temperature changes because the heat is retained.
An isobaric process occurs at constant pressure, and an isochoric process at constant volume. A change carried out so slowly that the system and surroundings remain in equilibrium at every instant is reversible; one that proceeds with finite, abrupt changes that disturb equilibrium is irreversible.
| Process | Quantity held constant | Condition | Example |
|---|---|---|---|
| Isothermal | Temperature, T | $\Delta T = 0$; heat added or removed to hold $T$ | Melting of ice at 273 K, 1 atm |
| Adiabatic | Heat (no transfer) | $q = 0$; $T$ changes | Acid–base mixing in a thermos flask |
| Isobaric | Pressure, p | $\Delta p = 0$ | Reaction open to the atmosphere |
| Isochoric | Volume, V | $\Delta V = 0$; no $pV$ work | Reaction in a sealed rigid bomb |
Classify each quantity and process: (i) enthalpy $H$, (ii) work $w$, (iii) density, (iv) mixing acid and base in a sealed thermos flask.
(i) $H$ is a state function and an extensive property. (ii) $w$ is a path function. (iii) Density is an intensive property (mass ÷ volume = extensive ÷ extensive). (iv) No heat crosses the insulated boundary, so the process is adiabatic, and because matter and energy are both confined the flask approximates an isolated system.
Standard States
Because a system is described by its state variables, comparing the energies of different compounds requires a fixed reference. The standard state refers to the condition of 1 bar pressure at any specified temperature, with the substance in its most stable form. Standard-state quantities are the basis of standard enthalpies of formation and reaction, which build directly on the state-function idea developed here.
Thermodynamic terms at a glance
- System + surroundings = universe, separated by a real or imaginary boundary.
- Open exchanges matter and energy; closed exchanges energy only; isolated exchanges neither.
- The state is fixed by macroscopic variables $p$, $V$, $T$, $n$; only a minimum independent set need be specified.
- State functions ($p$, $V$, $T$, $U$, $H$, $S$, $G$) are path-independent; path functions ($q$, $w$) are not.
- Internal energy $U$ is a state function: $\Delta U = w_{ad}$ for an adiabatic change (Joule).
- Extensive properties scale with amount (mass, volume, $U$, $H$); intensive do not (T, p, density, molar quantities).
- Four processes: isothermal (const. $T$), adiabatic ($q=0$), isobaric (const. $p$), isochoric (const. $V$).
- Standard state: 1 bar, specified temperature, most stable form.