Thermochemistry & Thermodynamics

Gibbs Free Energy

The thermodynamic potential whose change determines whether a process is spontaneous at constant temperature and pressure.

ΔG = ΔH − TΔS kJ/mol

Gibbs–Helmholtz Equation

The relation showing how the Gibbs free energy of a system varies with temperature.

(∂(ΔG/T)/∂T)_p = −ΔH/T² kJ/mol

Thermochemistry & Thermodynamics

Heat

Energy transferred between a system and its surroundings solely because of a temperature difference.

q = mcΔT J

Thermochemistry & Thermodynamics

Heat Capacity at Constant Pressure

The heat needed to raise a system's temperature by one kelvin while pressure is held constant.

C_p = C_V + R (ideal gas) J/(mol·K)

Thermochemistry & Thermodynamics

Heat Capacity at Constant Volume

The heat needed to raise a system's temperature by one kelvin while its volume is held fixed.

C_V = (∂U/∂T)_V J/(mol·K)

Thermochemistry & Thermodynamics

Helmholtz Free Energy

The thermodynamic potential that determines spontaneity at constant temperature and volume.

A = U − TS kJ/mol

Thermochemistry & Thermodynamics

Hess's Law

The total enthalpy change of a reaction is the same regardless of the route taken, provided the initial and final states are identical.

ΔH_total = ΣΔH_steps kJ/mol

Thermochemistry & Thermodynamics

Internal Energy

The total kinetic and potential energy of all the particles within a system.

ΔU = q + w J

Thermochemistry & Thermodynamics

Irreversible Process

A real process that passes through non-equilibrium states and cannot be reversed without leaving a permanent change in the surroundings.

ΔS_universe > 0 J/K

Thermochemistry & Thermodynamics

Isobaric Process

A process carried out at constant pressure.

q_p = ΔH J

Thermochemistry & Thermodynamics

Isochoric Process

A process carried out at constant volume, so that no expansion work is done.

w = 0, q_V = ΔU J

Thermochemistry & Thermodynamics

Isolated System

A system that exchanges neither energy nor matter with its surroundings.

ΔU = 0 Dimensionless

Thermochemistry & Thermodynamics

Isothermal Process

A process carried out at constant temperature, with heat exchanged as needed to maintain it.

ΔU = 0 (ideal gas), w = −nRT ln(V₂/V₁) J

Thermochemistry & Thermodynamics

Kirchhoff's Law

The relation describing how the enthalpy change of a reaction varies with temperature.

ΔH(T₂) = ΔH(T₁) + ΔC_p(T₂ − T₁) kJ/mol

Thermochemistry & Thermodynamics

Maximum Work

The greatest amount of work obtainable from a change of state, achieved only along a reversible path.

w_max = ΔA; w_max(non-pV) = ΔG J

Thermochemistry & Thermodynamics

Molar Heat Capacity

The heat required to raise the temperature of one mole of a substance by one kelvin.

C_m = q / (nΔT) J/(mol·K)

Thermochemistry & Thermodynamics

Open System

A system that can exchange both energy and matter with its surroundings.

Dimensionless

Thermochemistry & Thermodynamics

Path Function

A quantity whose value depends on the specific route taken between two states.

δq, δw J

Thermochemistry & Thermodynamics

Reversible Process

An idealised process carried out through a continuous series of equilibrium states, so it can be reversed by an infinitesimal change.

w_rev = −∫p dV J

Thermochemistry & Thermodynamics

Second Law of Thermodynamics

The total entropy of the universe increases in every spontaneous process.

ΔS_universe > 0 J/K

Thermochemistry & Thermodynamics

Specific Heat Capacity

The heat required to raise the temperature of one kilogram of a substance by one kelvin.

c = q / (mΔT) J/(kg·K)

Thermochemistry & Thermodynamics

Spontaneity

The tendency of a process to occur without any continuous external input of energy.

ΔG < 0 kJ/mol

Thermochemistry & Thermodynamics

Standard Enthalpy of Combustion

The enthalpy change when one mole of a substance burns completely in excess oxygen under standard conditions.

ΔH_c° kJ/mol

Thermochemistry & Thermodynamics

Standard Enthalpy of Formation

The enthalpy change when one mole of a compound forms from its elements in their standard states.

ΔH_f° kJ/mol