Revise Thermal energy transfers for IB Physics (B.1)

Temperature is a measure of the average random kinetic energy of the particles in a substance: the faster they jiggle, the higher the temperature. It is not the same as the total energy the substance holds. That total is the internal energy — the sum of the random kinetic energy of the particles (their motion) AND the potential energy stored in the forces between them (how far apart they are held). A large, cool object can have far more internal energy than a small, hot one, because internal energy depends on how MANY particles there are, while temperature only reflects their average energy.

For quantitative work physicists use the Kelvin scale, an absolute scale whose zero point, $0$ K (absolute zero, about $-273\,^{\circ}$C), is the temperature at which particles have their minimum possible energy. To convert, use $T/\text{K} = \theta/^{\circ}\text{C} + 273$. A crucial fact: because the two scales rise in step, a CHANGE of $1\,^{\circ}$C is identical to a change of $1$ K. So a temperature difference $\Delta T$ is the same number on either scale — but an absolute temperature (a single value of $T$) is not.

Put a hot object in contact with a cold one and energy is transferred from the hotter to the colder — never spontaneously the other way. This transferred energy is what we call heat (thermal energy transfer). The flow continues until both objects reach the same temperature, at which point there is no longer any net transfer between them: they are in thermal equilibrium. Equilibrium does not mean the particles have stopped exchanging energy — collisions still happen — but that the exchanges balance, so the NET flow is zero. The single rule to remember is that heat flows down a temperature gradient, from high temperature to low.

Different substances need different amounts of energy to warm up. The specific heat capacity $c$ of a substance is the energy required to raise the temperature of 1 kg of it by 1 K (equivalently 1 °C), measured in J kg⁻¹ K⁻¹. Water has an unusually large value, $c = 4180$ J kg⁻¹ K⁻¹, which is why it takes so long to heat and why it is used as a coolant. The energy needed for a given temperature change is:

$Q = mc\Delta T$

where $Q$ is the energy transferred (J), $m$ is the mass (kg), $c$ is the specific heat capacity (J kg⁻¹ K⁻¹) and $\Delta T$ is the temperature change. Because $\Delta T$ is a difference, you may keep it in °C or K — the value is the same. This equation applies ONLY while the substance stays in one state; the moment it starts to melt or boil, the temperature stops changing and this formula no longer describes what is happening.

To melt a solid or boil a liquid you must supply energy, yet the temperature does not rise while it happens. The energy required to change the state of 1 kg of a substance at constant temperature is its specific latent heat $L$, in J kg⁻¹. There are two kinds: the specific latent heat of fusion $L_f$ (melting or freezing) and the specific latent heat of vaporisation $L_v$ (boiling or condensing). For water, $L_f = 3.34 \times 10^{5}$ J kg⁻¹ and $L_v = 2.26 \times 10^{6}$ J kg⁻¹ — vaporisation needs far more energy, because boiling separates the particles completely rather than merely loosening them. The energy for a phase change is:

Q = mL

with $Q$ in joules, $m$ in kilograms and $L$ in J kg⁻¹. Notice there is no $\Delta T$ term: because the temperature is constant during the change, the only variables are how much substance changes state and the latent heat of that substance. Use $L_f$ for melting or freezing, and $L_v$ for boiling or condensing.

Plot the temperature of a solid as it is heated steadily and you get a heating curve with two flat plateaus. The sloping parts are where $Q = mc\Delta T$ applies — energy raises the kinetic energy of the particles, so the temperature climbs. The flat parts are the phase changes, at the melting point and the boiling point, where $Q = mL$ applies. Here the supplied energy goes entirely into the POTENTIAL energy of the particles: it pulls them apart and breaks the bonds holding the state together. Because the average kinetic energy is not increasing, the temperature stays constant — that is the key reason a plateau appears. A cooling curve is the mirror image: energy is released at each plateau as bonds reform, again at constant temperature.

Conduction is the transfer of thermal energy through a substance without any bulk movement of the substance itself. When one region is heated, its particles gain kinetic energy and vibrate more vigorously, colliding with their cooler neighbours and passing energy along — like a chain reaction through the material. In metals the process is far faster because a 'sea' of free (delocalised) electrons carries energy rapidly through the lattice, which is why metals feel cold to the touch (they conduct heat away from your hand quickly). Conduction requires a medium and is dominant in solids; gases, whose particles are far apart, conduct poorly and make good insulators.

Convection is the transfer of thermal energy through the bulk movement of a fluid — a liquid or a gas. When part of a fluid is heated it expands, becomes less dense and rises; cooler, denser fluid sinks to take its place, is heated in turn, and the cycle repeats, setting up a circulating convection current that carries energy through the whole fluid. This is how a radiator warms a room and how water heats in a pan. Convection cannot occur in a solid, because the particles are locked in place and cannot flow.

Radiation is the transfer of thermal energy by electromagnetic waves, chiefly in the infrared. Uniquely, it needs no medium at all and so travels through a vacuum — which is how energy from the Sun crosses empty space to reach the Earth. Every object above absolute zero emits thermal radiation, and the hotter it is the more it radiates. The surface matters: dark, matt surfaces are good emitters and good absorbers, while shiny, light-coloured surfaces are poor emitters and good reflectors, which is why survival blankets are silvered and why a black car heats up fastest in the Sun.

This is the showcase for a calculation topic. In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) for a correct step, or an answer mark (A) for the correct final value with its unit. Crucially, method marks and error-carried-forward (ECF) mean that a wrong number early on does not automatically cost you every mark that follows — but only if your method is written down. Study how each mark below is earned by a specific line of a two-stage calculation.