Intuition The one core ideaTemperature is the single number that two touching objects share once heat has stopped flowing between them. Everything else on the parent page — thermometers, scales, absolute zero — is just machinery for measuring and labelling that shared number.
This page is the toolbox. Before you read the parent note, you must be able to read every symbol it writes without pausing. Below, each symbol gets three things: what it means in plain words , the picture it stands for , and why the topic cannot proceed without it . They are ordered so each one leans only on the ones before it.
Definition Heat (the word, before any letter)Heat is energy that moves because one thing is hotter than another. It is energy in transit — like water flowing through a pipe, not water sitting in a tank. See Heat and Internal Energy for the full story; here we only need the picture of flow .
Look at the first figure. Two blocks touch. Wavy red arrows show energy leaking from the hot block into the cold block. The arrows shrink over time. When they vanish, flow has stopped.
That "arrows vanish" moment is the whole reason temperature exists. Hold that image — every symbol below decorates it.
A system is just "the object we chose to watch" — one block, one cup of water, one balloon of gas. Everything else is the surroundings .
Picture: draw a dotted box around the thing you care about. Inside = system. Outside = surroundings.
Definition Macroscopic propertyA macroscopic property is something you can measure about the whole system without looking at individual atoms: its pressure , its volume , its length , its colour, its electrical resistance.
Why the topic needs it: "their properties stop changing" in the parent note means these numbers stop changing. Without a measurable property, "nothing changes" would be a feeling, not physics.
Each of these is a letter that stands for one number you could read off a gauge.
P V L
P pressure : how hard a gas pushes outward on its container walls, in pascals (Pa P V volume : how much space the system fills, in m 3 L length : e.g. the height of a mercury thread in a glass tube. Picture: a red line climbing a ruler.
Each is a candidate thermometric property : a number that reliably shifts when hotness shifts. The parent note calls the general one X
Intuition Why give them a single stand-in nameX any property that tracks hotness and build a thermometer from it" without repeating the argument for length, then pressure, then resistance. So it writes one general symbol X X = P X = L
This is the star of the topic, so it gets its own figure.
T t C t F
t C Celsius scale (°C): ice melts at 0 100 t F Fahrenheit scale (°F): ice at 32 212 T Kelvin (absolute) scale (K): ice at 273.15
Picture: three thermometers side by side, same physical bath, three different numbers painted on the glass (see figure). The mercury is at the same height — only the printed numbers differ.
Intuition Why the topic bothers with three scalesA scale is just where you put the zero and how big one step is . Celsius zeroes at ice; Kelvin zeroes at the absolute coldest. Because they measure the same physical thing , converting between them is pure arithmetic — that is what the parent's conversion formulas do.
t t Here it does not. On this topic t C t F temperatures on named scales; capital T
0 tr C F tiny label that says "which particular value." It never changes what the main letter means.
P 0 T tr P tr X tr at the triple point ("tr") — the single anchor point of the Kelvin scale, at 273.16 K t C t F on the Celsius / Fahrenheit scale .
Δ Δ T final value minus initial value of T Picture: two dots on the thermometer; Δ Why the topic needs it: converting a reading and converting a change use different rules — the origin shift (+ 32 + 273.15 Δ
The parent writes T ( X ) = a X + b
a b T X
a slope : how many kelvin T X b intercept : the value of T X = 0
Two unknowns (a b two known points to draw exactly one line. That is precisely why the parent uses two fixed points (ice + steam).
α P = P 0 ( 1 + α t C ) α ≈ 273.15 1 ° C − 1 how big a fraction of its ice-point pressure a gas gains per degree Celsius .
Picture: the slope of the pressure-vs-Celsius line, written as a fraction of the starting pressure. Follow that line backwards until P 0 − 273.15 ° C Ideal Gas Law hiding in disguise.)
∝ T ∝ X X T through the origin (b = 0 Picture: the special line from the last figure that passes through ( 0 , 0 ) T = T tr X / X tr
Definition "same temperature"= thermal equilibrium , we write that they have equal T Zeroth Law of Thermodynamics is what guarantees this "equals" behaves like real equality (if A = C B = C A = B
Heat as energy in transit
Thermal equilibrium: flow stops
System and its macro properties P V L
Zeroth Law makes equals real
Temperature: one shared number T
Two fixed points ice and steam
Scales tC tF T and conversions
Worked example Reading the same bath on three scalesA bath sits at t C = 25 ° C t F = 5 9 ( 25 ) + 32 = 45 + 32 = 77 ° F T = 25 + 273.15 = 298.15 K Why: the mercury height is one physical fact; each scale just prints a different number for it. Same physical thing, three labels — that is section 3 in action.
Cover the right-hand side and say each answer out loud before revealing.
What does Δ T T The change (final minus initial); T Δ T
In T = a X + b a b a b T X = 0
Why do you need exactly two fixed points for a linear scale? Two unknowns (a , b
What is a thermometric property X Any measurable macroscopic property that varies smoothly and reproducibly with hotness — length, pressure, resistance, gas volume.
What does ∝ It passes through the origin, so the intercept b = 0 X T
Why is t C On this topic t temperature ; capital T
What does the subscript "tr" mean? "Triple point of water" — the single anchor of the Kelvin scale at 273.16 K
What physical event defines thermal equilibrium? Net heat flow between the two touching systems has stopped and their macroscopic properties no longer change.
What does α P = P 0 ( 1 + α t C ) The fractional rise in gas pressure per degree Celsius; extrapolating its line to P = 0
