Heat, pressure, sound, light and electricity

Particles, states of matter and density

Before explaining heating, it helps to choose a description of matter. In the microscopic model, substances consist of interacting particles such as atoms and molecules. In a solid, particles can vibrate around relatively stable positions; that does not mean they are absolutely motionless. In a liquid, they can rearrange while staying close enough to maintain an approximately defined volume. In a dilute gas, separations are larger and the material occupies the accessible volume.

These descriptions explain trends; they do not replace every property of real materials. A liquid can change volume with temperature and pressure, although it is much less compressible than a gas under common conditions. States and phase changes depend on conditions. Boiling temperature, for example, is not independent of pressure.

Density is ρ = m/V, with SI units kg/m³. It is neither the mass of a single particle nor a measure of “weight per size” without a defined reference. A homogeneous sample of mass 0,40 kg and volume 0,00050 m³ has density 800 kg/m³. If a fixed amount of material expands, volume increases without a proportional mass increase, and density falls.

During a phase change, transferred energy can alter microscopic organization and interactions without increasing temperature under suitable conditions. This is why we need to distinguish internal energy, temperature and heat before interpreting warming.

Temperature does not measure the total amount of energy

Temperature describes a system's thermal state and allows the direction of spontaneous energy transfer through contact to be predicted: from the higher-temperature body to the lower-temperature one. Two bodies in thermal equilibrium have the same temperature and no net energy transfer due to a temperature difference.

A thermometer must interact with the body long enough to approach equilibrium. The feeling in your hand is not a reliable measurement: metal and wood at the same temperature can feel different because they transfer energy from your hand at different rates. The reading also depends on where we place the thermometer and its response.

Thermodynamic temperature is measured in kelvin, K. The relationship with Celsius is T(K) = θ(°C) + 273,15. A difference of 1 °C has the same size as a difference of 1 K. However, 20 °C is not twice the absolute temperature of 10 °C. Zero kelvin is the origin of the absolute scale; it does not correspond to 0 °C.

Heat, warming and phase change

Internal energy is energy associated with the microscopic motions and interactions of a system's particles. Heat is energy being transferred because of a temperature difference. A body does not “contain heat” like a stored substance: it has internal energy, which can also change when work is done on it.

Without phase change and over an interval where specific heat capacity is approximately constant, Q = mcΔT. Q is transferred energy in J, m mass in kg, c specific heat capacity in J/(kg·K) and ΔT temperature change in K. The greater the mass or specific heat capacity, the more energy is needed for the same temperature change under the stated conditions.

During a phase change of a pure substance in equilibrium at constant pressure, energy can be transferred without a temperature change. We use Q = mL, where L is energy per mass for that transformation, in J/kg. When ice melts, energy changes microscopic organization and interactions; it does not necessarily increase average agitation. A heating curve can therefore have plateaus.

Three mechanisms of thermal transfer

In conduction, energy is transferred through microscopic interactions without macroscopic transport of material. One end of a metal spoon heats up when the other touches hot water. Materials differ in how readily they conduct energy; thickness, area and temperature difference also influence transfer rate.

In convection, the motion of a fluid itself transports energy. A heated region can expand, become less dense and rise under gravity, but the pattern depends on geometry and conditions. Fans and pumps can also force circulation. It is not “heat” that has a universal tendency to rise: matter is moving.

In radiation, energy propagates through electromagnetic waves and can cross a vacuum. Solar energy reaches Earth by this mechanism. A body emits and absorbs radiation, and the balance depends on its temperature and surface properties. All three mechanisms can occur simultaneously in one process; the goal is to recognize which dominates in the chosen model.

A force distributed over an area

Average pressure is p = F_⊥/A: force perpendicular to a surface divided by area. It is measured in pascals, Pa = N/m². The same force spread over a larger area produces lower average pressure. This explains why a wide strap can be more comfortable than a narrow one without changing the weight carried.

In a stationary liquid with approximately constant density, pressure increases with depth: p = p_surface + ρgh. Here ρ is density in kg/m³, g ≈ 9,8 m/s² in this lesson and h is vertical depth in m. Additional pressure comes from the weight of liquid above; it depends on depth, not only the total amount in the container.

Absolute pressure is measured relative to a vacuum; gauge pressure is the difference from local atmospheric pressure. If the surface is exposed to air, ρgh gives gauge pressure, while absolute pressure includes p_atm. Pressure in a stationary fluid acts in all directions at a point; it is not a single arrow pointing only downward.

Sound: a disturbance that needs a medium

A sound source vibrates a medium, producing pressure variations that propagate. In air, compression and rarefaction regions move while particles oscillate around their average positions. The wave carries energy; air need not travel from source to listener. Without a material medium, sound does not propagate.

Period T is the duration of one oscillation and is measured in s. Frequency f is the number of oscillations per second and is measured in hertz, Hz = s⁻¹; f = 1/T. Wavelength λ is the distance between consecutive equivalent regions and is measured in m. Propagation speed obeys v = λf: in one period, the disturbance advances one wavelength.

Higher frequency generally corresponds to higher-pitched sound; greater amplitude is associated with greater intensity in the same medium under the same conditions. Do not confuse musical pitch with loudness. Sound speed depends on the medium and its conditions, such as temperature. Reflection can produce an echo; measured time includes travel to the obstacle and back.

Light, reflection and refraction

Light is an electromagnetic wave and propagates through a vacuum, unlike sound. In a vacuum, its speed is approximately c = 3,00 × 10⁸ m/s. To study mirrors and paths at the scale of objects large compared with wavelength, we can use rays: lines representing propagation direction.

In reflection, the angle of incidence equals the angle of reflection. Both are measured relative to the normal, a line perpendicular to the surface at the incidence point. A rough surface can scatter rays in several directions because local normals vary, although the law remains valid locally.

In refraction, light changes speed when passing between media. It can also change direction when incident obliquely. Refractive index is n = c/v and is dimensionless. On entering a higher-index medium, an oblique ray bends towards the normal; on leaving, it bends away. At normal incidence, speed can change without direction changing. Color should not be explained merely as “stronger light”.

Charge, current, voltage and resistance

Electric charge is measured in coulombs, C. Average current is I = Δq/Δt, in amperes, A = C/s: the amount of charge crossing a section per duration. Conventional current points in the direction positive charges would move. In metals, electrons move in the opposite direction. Current is not the speed of those electrons.

Potential difference, or voltage, indicates energy transferred per unit charge: U = E/q, in volts, V = J/C. A source maintains a potential difference through energy conversion, for example chemical energy in a battery. In a closed circuit, charges already present in conductors can move in an organized way; they are neither created nor consumed by the lamp.

For an ohmic resistor at approximately constant temperature, U = RI. Resistance R is measured in ohms, Ω = V/A. A lamp whose filament heats up may not keep constant resistance. In a simple series circuit without branches, current is the same at every point; energy per charge is what transforms in the components. Work with appropriate low-voltage diagrams and models; this lesson does not provide mains-wiring instructions.

Connect the ideas without mixing the models

Electrical power transferred to a component is P = UI, in W. Over a constant-power interval, E = PΔt, in J. In a resistor, this transfer can increase internal energy and then produce thermal transfers to the surroundings. Electricity does not turn into a substance called heat: energy changes form and crosses boundaries.

A unit resolves many ambiguities: J for energy; W for power; K for absolute temperature; Pa for pressure; Hz for frequency; A for current. Two expressions can use the same letter for different quantities, so always state its meaning. The period T, for example, is not automatically temperature T.

To study a phenomenon, first identify the question, system and scale. If the question is an echo's time, use propagation and path; if it is water heating, use energy transfer and thermal properties; if it is current in a resistor, use circuit relationships. Connections become useful when differences are clear too.

Worked examples, without skipping steps

Follow the reasoning first. Then cover the solution and try to reconstruct it in your own words.

Now try it yourself

There is no timer. Write what you know, choose a relationship and justify each step. Hints and solutions are available whenever you need them.

Mistakes worth avoiding

A body contains an amount of heat.

Heat means energy being transferred due to a temperature difference; the body has internal energy.

Pressure in a liquid depends only on total mass.

In the hydrostatic model it depends on depth, density, gravity and surface pressure.

Sound carries all the air from source to ear.

The disturbance and energy propagate while the medium oscillates locally.

Reflection angles are measured from the surface.

The law's convention uses the normal.

The lamp consumes current.

Charges circulate; the lamp transforms electrical energy.