Topic 2: B. The particulate nature of matter

Matter is made of vast numbers of particles in constant motion, and many large-scale properties such as temperature, pressure and heat capacity emerge from the average behaviour of those particles. This theme links the microscopic picture to measurable quantities and shows how energy moves between objects and through circuits. It closes with the thermodynamic rules that govern how that energy may be transformed.

Temperature and the kinetic picture

Temperature is a measure of the average random kinetic energy of the particles in a substance, not a measure of how much energy is stored overall. Two objects placed in contact reach thermal equilibrium when their temperatures are equal, meaning no further net flow of energy occurs between them. The Celsius and Kelvin scales differ by an offset of 273: a change of one degree is the same size on both, but only the Kelvin scale starts at absolute zero, where particle motion is at a theoretical minimum. Because the Kelvin scale is absolute, it is the scale that must appear in the gas laws and in any equation where temperature is proportional to energy.

Internal energy and thermal energy transfer

Internal energy is the total of the random kinetic energies of all the particles plus the potential energies stored in the bonds and forces between them. Heating a substance increases its internal energy, and so can doing work on it, for example by compression or by friction. Thermal energy moves spontaneously from a hotter region to a colder region by three mechanisms: conduction, where energy passes through a material as particles collide; convection, where heated fluid rises and carries energy with it; and radiation, where energy travels as electromagnetic waves and needs no medium. The direction of net flow is always from high temperature to low temperature until equilibrium is reached.

Specific heat capacity and latent heat

The specific heat capacity c is the energy needed to raise the temperature of one kilogram of a substance by one Kelvin, used in Q = m c (delta T). Latent heat is the energy absorbed or released during a change of state, when the temperature does not change because the energy goes into breaking or forming bonds rather than speeding particles up; here Q = m L, where L is the specific latent heat of fusion or vaporisation. Worked example: heating 0.50 kg of water from 20 degrees Celsius to 100 degrees Celsius, with c = 4200 J per kg per K. Q = m c (delta T) = 0.50 x 4200 x (100 - 20) = 0.50 x 4200 x 80 = 168000 J, or 168 kJ. To then boil all of it into steam with L = 2.3 x 10^6 J per kg requires Q = m L = 0.50 x 2.3 x 10^6 = 1.15 x 10^6 J, showing that vaporisation demands far more energy than the heating did.

The greenhouse effect and energy balance

The Earth receives short-wavelength radiation from the Sun, absorbs much of it, and re-emits energy at longer infrared wavelengths because the surface is much cooler than the Sun. Greenhouse gases such as carbon dioxide, methane and water vapour absorb a portion of this outgoing infrared radiation and re-radiate it in all directions, including back toward the surface, which raises the average surface temperature above what it would otherwise be. Energy balance means that, on average, the power radiated away by the planet equals the power absorbed from the Sun; when the concentration of greenhouse gases rises, the balance shifts and the equilibrium temperature increases. The albedo, or fraction of incoming radiation reflected, also affects how much energy is available to be absorbed.

The gas laws

For a fixed mass of gas, three experimental relationships connect pressure, volume and temperature. Boyle's law states that at constant temperature pressure is inversely proportional to volume, so p V is constant. Charles's law states that at constant pressure volume is proportional to absolute temperature. The pressure law states that at constant volume pressure is proportional to absolute temperature. These can be combined into the relation p V over T being constant for a fixed amount of gas, which is useful for comparing a gas before and after a change of conditions. Remember that temperature in all of these must be in Kelvin, because the relationships pass through the origin only on the absolute scale.

The ideal gas equation

An ideal gas is a model in which particles have negligible volume and exert forces on one another only during collisions, which are perfectly elastic. Its behaviour is captured by the ideal gas equation pV = nRT, where p is pressure in Pa, V is volume in cubic metres, n is the amount of substance in moles, R is the universal gas constant of about 8.31 J per mol per K, and T is the absolute temperature in Kelvin. The equation links the macroscopic state of a gas to the number of particles present, since one mole contains Avogadro's number of them. Real gases approximate ideal behaviour best at low pressure and high temperature, where the particles are far apart and intermolecular forces are weak.

Electric current and resistance

Electric current is the rate of flow of charge, measured in amperes, where one A is one coulomb of charge passing a point each second. A source such as a battery provides an electromotive force, or emf, which is the energy given to each unit of charge by the source. Resistance, measured in ohms, opposes the flow of charge and is defined by R = V over I; a component is ohmic if its resistance stays constant so that current is proportional to voltage. In a series circuit the same current flows through every component and resistances add directly, while in a parallel circuit the voltage across each branch is the same and the total resistance is less than the smallest individual resistance.

Electrical power and circuits

The power delivered or dissipated by an electrical component is P = V I, which can be rewritten using Ohm's law as P = I^2 R or P = V^2 over R depending on which quantities are known. A real cell has internal resistance, so the terminal voltage available to the external circuit is less than the emf when current flows, because some energy is dissipated inside the cell itself. Kirchhoff's rules help analyse circuits: the junction rule states that current into a junction equals current out, expressing conservation of charge, and the loop rule states that the sum of emfs around a loop equals the sum of voltage drops, expressing conservation of energy.

The first law of thermodynamics (HL)

The first law of thermodynamics is a statement of energy conservation for a gas: the increase in internal energy of a system equals the heat added to it plus the work done on it, often written as Q = (delta U) + W when W is the work done by the gas. If a gas expands it does positive work on its surroundings, and if it is compressed work is done on it. Particular processes simplify the law: in an isothermal process the temperature and hence internal energy stay constant, so any heat added equals the work done; in an adiabatic process no heat is exchanged, so any work done changes the internal energy and the temperature directly.

The second law and entropy (HL)

The second law of thermodynamics states that the total entropy of an isolated system never decreases over time, and increases for any spontaneous process. Entropy is a measure of the number of microscopic arrangements consistent with a system's macroscopic state, often described informally as a measure of disorder. This law explains why heat flows spontaneously from hot to cold but never the reverse without external work, and why no heat engine can be perfectly efficient: some energy must always be transferred to a colder reservoir. The arrow of time, the observation that natural processes have a preferred direction, is a direct consequence of entropy tending to rise.