← All printables Chapter 01 · Thermodynamics · 2 sheets · read the chapter →
Vedatom Physics
FORMULA CARD · PHYSICS.VEDATOM.COM
Chapter 01 · Part III · Thermodynamics
Revised on ____________________
Chapter 01 · Thermal Properties of Matter

Expansion, calorimetry, and the three ways heat travels

2 sheets
2 diagrams
26 results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

Temperature and expansion

THE HOLE EXPANDS TOO
I.Scales  C5 = F − 329 = K − 273.155
II.Linear  ΔL = L0 α ΔT
III.Areal and volume  β = 2α , γ = 3α isotropic solids
IV.A cavity  expands exactly as the solid would
V.Thermal stress  σ = Y α ΔT clamped ends — no length in it
VI.Apparent expansion  γapp = γliquid − 3αvessel what the level actually shows
VII.Pendulum clock  ΔTdayT = 12 α ΔT loses time when heated
VIII.Water  densest at 4 °C expands on freezing
II

Heat and calorimetry

FIND THE PHASE CHANGE FIRST
I.Sensible heat  Q = m c ΔT
II.Latent heat  Q = m L temperature does not move
III.Mixtures  Qlost = Qgained in an isolated calorimeter
IV.Water equivalent  W = mc cc of the calorimeter itself
V.Molar heat capacity  C = M c
VI.If the heat runs out  the mixture sits at the transition temperature
Theat added Q0°100°meltingboilinglatent L_flatent L_v
III

Conduction

RESISTANCES, EXACTLY LIKE A CIRCUIT
I.Fourier's law  H = k A ΔTL steady state
II.Thermal resistance  R = Lk A
III.In series  R = R1 + R2 same H through each slab
IV.In parallel  1R = 1R1 + 1R2 same ΔT across each
V.Junction temperature  T = T1/R1 + T2/R21/R1 + 1/R2
VI.Growth of ice  t ∝ y² doubling the sheet takes four times as long
R1R2T1T2H = (T₁−T₂)/(R₁+R₂)series · R = L/kA
IV

Radiation

THE FOURTH POWER, IN KELVIN
I.Stefan–Boltzmann  P = σ ε A T4
II.Net exchange  P = σ ε A (T4 − T04)
III.Wien's law  λm T = b hotter means bluer
IV.Kirchhoff  a good absorber is a good emitter e = a at every wavelength
V.Newton's cooling  dTdt = − k (T − Ts) small excess only
VI.Its solution  T = Ts + (T0 − Ts) e−kt
Water, c
4186 J kg−1 K−1
Ice, Lf
3.34×105 J kg−1
Steam, Lv
22.6×105 J kg−1
Stefan, σ
5.67×10−8
Wien, b
2.9×10−3 m K
Steel, α
1.2×10−5 K−1
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Celsius in a formula with a standalone T. p V = n R T, σT4 and λmT = b all need kelvin.
2Omitting latent heat in a mixing problem. Check whether the heat available finishes the phase change.
3Reading the rise in liquid level as the real expansion. It is apparent — add back 3α of the vessel.
4Thinking a heated plate's hole shrinks. Every dimension scales by (1 + αΔT), the cavity included.