Illustrated Physics
physics, drawn
Depth

Series

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.
Molecular speeds at 4 temperatures. The distribution of molecular speeds in a gas, with each curve enclosing the same area. Raising the temperature moves the peak right and lowers it: the same molecules, spread over a wider range of speeds.

Kinetic theory

  1. 1 The speeds in a still room
  2. 2 Pressure is a rate of arrival, and the gas law falls out of counting
  3. 3 Why the air thins with height, and why that is the same law as the speeds
  4. 4 How far a molecule gets
  5. 5 How far a neutrino gets
  6. +4 more
9 essays · thermodynamics Heating 1 kg of water from -20°C to 130°C. Temperature against heat added for 1 kilogram of water taken from -20 to 130 degrees Celsius. The two flat stretches are the melting and the boiling, where 334 and 2260 kilojoules go in and the temperature does not move. Melting costs as much as warming the water by 80 degrees; boiling costs as much as warming it by 541, which is 73 per cent of the whole journey.

Phase change

  1. 1 The heat that changes no temperature, and where it actually goes
  2. 2 A boiling point is a pressure, not a temperature
  3. 3 The part of the curve no fluid follows
  4. 4 The point at which the two become one
  5. 5 The barrier a new phase has to climb
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9 essays · thermodynamics Pushing one way and going another. The angle between an applied force and the acceleration it produces, against the angle between the force and the body's velocity, at four speeds. At 0° and 90° the two are parallel, because those are the two directions the γ³ and γ divisors do not mix. Everywhere between, they are not: at 0.99c the worst case is 73.9°, reached with the force at 8.0°. A body under a steady sideways-ish push does not travel along it.

Relativistic dynamics

  1. 1 The push that does not point where the body goes
  2. 2 The collision that wastes most of the energy
  3. 3 Nothing is allowed to be rigid
  4. 4 The centre that is not a place
  5. 5 The cone a decay cannot leave
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9 essays · relativity Single-slit diffraction at three slit widths. Intensity against angle behind a single slit, evaluated from the integral across the aperture, for slits two, six and twenty wavelengths wide. A wide slit throws a nearly sharp shadow; a narrow one spreads light through a wide angle.

Diffraction

  1. 1 Where rays stop being enough, and a shadow acquires a bright centre
  2. 2 How far apart two things have to be
  3. 3 What a thousand slits buy that two cannot
  4. 4 The grating that photographs itself
  5. 5 The fringes below the rainbow
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8 essays · optics A Carnot cycle on pressure–volume axes. Two isothermal steps joined by two adiabatic ones, forming a closed loop. The gas expands 9.6-fold in reaching the cold reservoir at 0.50 of the hot one, and the area enclosed is the net work done over one cycle.

Heat engines

  1. 1 The ceiling on every engine, set before it was designed
  2. 2 The engine that pays back more than it takes
  3. 3 The engine that has to finish
  4. 4 The engine a fluctuation cannot run
  5. 5 The temperature an engine really takes its heat at
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8 essays · thermodynamics Malus's law. The fraction of polarised light passing a filter, against the angle between the light's own direction of shaking and the filter's axis. It is the cosine squared: half at 45 degrees, nothing at 90.

Polarisation

  1. 1 The direction of the shaking, and the filter that only asks about it
  2. 2 The angle at which reflection picks a side
  3. 3 The crystal that answers twice
  4. 4 The rotation a return trip doubles
  5. 5 The phase that is only a shape
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8 essays · optics Surface at fixed volume. Four shapes of identical volume with their surface areas evaluated. The sphere's is the smallest at 4.836; the flattest shape drawn carries 1.91 times as much. Surface tension is an energy per unit area, so a free drop of liquid has an incentive to be the first of these and none at all to be any of the others.

Surface tension

  1. 1 The skin that is not a skin
  2. 2 The small bubble blows up the big one
  3. 3 The thread that cannot stay a thread
  4. 4 The surface that pulls toward the stronger side
  5. 5 The ring the drop leaves behind
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8 essays · fluids A travelling wave, caught at one instant. A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats. The ghosted curve is the same wave a moment later.

Wave motion

  1. 1 A wave is a shape that travels, and nothing else does
  2. 2 The medium decides the speed, and the source only decides the note
  3. 3 How a wave thins out
  4. 4 The equation that lets a shape travel
  5. 5 The correction that took a century
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8 essays · waves A spike, spreading. The solution of the diffusion equation at three times, with a seeded random walk histogrammed behind it. The area under every curve is the same because nothing is lost; only the width changes, and it grows as the square root of the time.

Diffusion

  1. 1 The equation that only runs forwards, and the walk underneath it
  2. 2 The jiggle that proved atoms
  3. 3 The walk that comes home
  4. 4 The second experiment that cannot disagree
  5. 5 The summer that reaches the cellar in December
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7 essays · thermodynamics Wavefronts from a moving source. Circles showing where each crest has reached, centred on where the source was when it emitted them. Ahead of the source the crests are closer together and the frequency heard is higher; behind, they are spread out and it is lower.

Doppler

  1. 1 The note that changes on approach, and the two ways of getting it
  2. 2 The shift that survives at right angles
  3. 3 The sky that crowds into a cone
  4. 4 The cone the source leaves behind
  5. 5 The brightness that is not the same for everyone
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7 essays · waves Ways to arrange 10 coins. The number of distinct arrangements giving each number of heads, for 10 coins. Every individual arrangement is equally likely; the middle wins because there are more ways to reach it.

Entropy

  1. 1 Entropy is a count, and the arrow of time is arithmetic
  2. 2 The entropy that lives on a surface
  3. 3 The exponential that decides everything
  4. 4 What a system actually minimises
  5. 5 Mixing what is already mixed
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7 essays · thermodynamics The staircase equipartition cannot climb. The heat capacity of hydrogen at constant volume, in units of R, against temperature on a logarithmic axis. The three translational directions contribute 3/2 at every temperature. The two rotations switch on near 85.4 K — the temperature at which kT matches the first rotational step — taking the total to 5/2, computed here by summing the rigid rotor's partition function over two hundred levels rather than by assuming the plateau. The vibration switches on near 6332 K, taking it to 7/2. At 50 K the value is 2.469; at 300 K the value is 2.502; at 5000 K the value is 3.376. Classical equipartition predicts 7/2 at every temperature, including at four kelvin, and the size of the steps is set by ħ — which is how a heat capacity measures a quantum constant.

Equipartition

  1. 1 Half a kT for every way of moving
  2. 2 The share that is not half a kT
  3. 3 The temperature a molecule does not have
  4. 4 The energy that refuses to be shared
  5. 5 The condition three modes never meet
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7 essays · thermodynamics The stress that stops growing with depth. Vertical stress against depth in a silo of radius 0.5 m holding grain of bulk density 1500 kg/m³, with a wall friction coefficient of 0.5 and Janssen's ratio K = 0.5. The straight line is what a liquid of the same density would do — ρgz, with no length in it anywhere. The curve is what grains do: wall friction, mobilised by the sideways stress the grains themselves exert, removes weight from the column at a rate proportional to the stress, so the stress saturates at ρgλ over a screening length λ = R/2μK = 1.00 m. Read off the drawn curve at the 8 m base, the stress is 14.7 kPa against the 117.7 kPa the liquid delivers — 88 per cent of the weight is standing on the walls. Another twenty metres of grain would move the floor's reading by less than a pascal.

Granular matter

  1. 1 The silo that does not weigh what it holds
  2. 2 The angle that does not know the size of the heap
  3. 3 The heap that becomes a solid
  4. 4 The big one comes to the top
  5. 5 The hourglass that keeps time
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7 essays · fluids The pendulum's phase portrait. Angle plotted against angular velocity. Closed loops are swinging back and forth; the open curves above and below are rotating all the way round; the dashed curve between them is the separatrix.

Pendulum

  1. 1 The pendulum, and the small lie that makes it simple
  2. 2 The period that depends on the swing, computed exactly
  3. 3 The three ways of coming to rest
  4. 4 The length nobody has to measure
  5. 5 Held up by a force that averages to nothing
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7 essays · mechanics The same 120 N force at 3 different arms. 3 spanners of different lengths, each with the same 120 newton force applied at its end. The torque printed under each is the force times its own moment arm, so it rises with the length while the force does not change.

Rotation

  1. 1 The same push, further out, and why that is a different quantity
  2. 2 The mass, and where it sits, which is what decides the race
  3. 3 The axis that will not hold
  4. 4 The quantity that survives a change of shape
  5. 5 The push that comes out sideways
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7 essays · mechanics Harmonics on a fixed string. Standing-wave patterns on a string clamped at both ends, at n = 1, 2, 3, 4. Only whole numbers of half-wavelengths fit, which is why the allowed frequencies are discrete.

Standing waves

  1. 1 Only some notes fit, and that is where discreteness comes from
  2. 2 The box that allows only some energies
  3. 3 The drum that has no harmonics
  4. 4 How many ways there are to vibrate
  5. 5 The count that cannot be cheated
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7 essays · waves The straight line between two plates. A layer of water 10 mm deep with its top plate drawn along at 1 m/s. In the steady state the velocity is a straight line from zero at the fixed surface to the plate's speed at the moving one, and the stress needed to keep it going is μ times that slope: 0.100 Pa. The fluid at each wall is at rest with respect to it, which is an experimental fact rather than a consequence of anything above.

Viscosity

  1. 1 Momentum going sideways
  2. 2 The fourth power in a pipe
  3. 3 The thickness that goes both ways
  4. 4 The shear that only reaches so far
  5. 5 The drift a sound leaves behind
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7 essays · fluids An f² law that is right in shape and out by 30× in size. Two absorption curves for air against frequency, both logarithmic, in decibels per kilometre. The lower one is the classical Stokes–Kirchhoff result computed from air's viscosity and thermal conductivity alone, and it goes as f^2.000 — exactly two, because the loss per cycle is fixed and the number of cycles per metre is proportional to the frequency. The upper one is the measured atmospheric absorption at 20 °C and 50 per cent humidity, which fits f^1.42 and is 30 times larger at 1 kHz and 211 times at 125 Hz. The excess is not a correction to viscosity: it is nitrogen and oxygen storing energy in vibration and giving it back late, at a rate the water vapour sets, and it is the mechanism that actually removes the treble from a distant sound.

Attenuation

  1. 1 The distance that takes the treble out
  2. 2 The answer that cannot come first
  3. 3 Where the loudness goes
  4. 4 The steps in an absorption curve
  5. 5 The ripple that counts the neighbours
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6 essays · waves Where the upward force comes from. A block submerged with its top 1.2 m down. The pressure on the bottom face (19.6 kPa) exceeds that on the top (11.8 kPa) by exactly the weight of a column of water as tall as the block, and the sideways pressures cancel in pairs. Nothing has been added to the physics of pressure to get buoyancy out of it.

Buoyancy

  1. 1 The weight of the water that is not there
  2. 2 Why a ship comes back upright
  3. 3 The depth past which it must sink
  4. 4 The block the water does not lift
  5. 5 The body that displaces two things
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6 essays · fluids Two sources 4 wavelengths apart. Circular wavefronts from two sources, with the lines along which they arrive in step drawn through the pattern. Those lines are where the path difference is a whole number of wavelengths.

Coherence

  1. 1 Why two lamps never interfere
  2. 2 How far a wave can remember
  3. 3 The fringe that measures a star
  4. 4 The grain that is in the light
  5. 5 The correlation that survives what the phase does not
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6 essays · optics

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