Lesson 13 of 13 · 19 min
Chapter review
Must-know facts
21 facts
- 1Heat is energy moving because of a temperature difference; unit joule.
- 2Ice and steam points: 0 °C / 100 °C and 32 °F / 212 °F; t_F = (9/5)t_C + 32.
- 3PV = μRT with R = 8.31 J mol⁻¹ K⁻¹; absolute zero is −273.15 °C.
- 4T = t_C + 273.15; a kelvin and a degree Celsius are the same size.
- 5Δl/l = α_l ΔT; area coefficient 2α_l; α_V = 3α_l.
- 6For an ideal gas at constant pressure α_V = 1/T (3.7 × 10⁻³ K⁻¹ at 0 °C).
- 7Water contracts on heating from 0 °C to 4 °C; it is densest at 4 °C, so lakes freeze from the top.
- 8Thermal stress in a clamped rod = YαΔT.
- 9Q = msΔT; water's s = 4186 J kg⁻¹ K⁻¹, the largest in the table.
- 10C_p > C_v for a gas; molar heat capacity is per mole.
- 11Calorimetry: heat lost = heat gained in an isolated system.
- 12Temperature stays fixed during melting and boiling; Q = mL.
- 13Water: L_f = 3.33 × 10⁵ J kg⁻¹, L_v = 22.6 × 10⁵ J kg⁻¹.
- 14Higher pressure lowers ice's melting point (regelation) and raises water's boiling point (pressure cooker).
- 15Triple point of water: 273.16 K, where solid, liquid and vapour coexist.
- 16H = KAΔT/L; the same heat current crosses every rod in series.
- 17Convection needs a fluid; sea breeze by day, land breeze by night.
- 18Wien: λ_m T = 2.9 × 10⁻³ m K.
- 19Stefan: H = AeσT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴, T in kelvin.
- 20Good absorbers are good emitters; a thermos flask cuts all three modes of transfer.
- 21Newton's cooling: rate ∝ (T₂ − T₁); ln(T₂ − T₁) against t is a falling straight line.
Common traps
Where marks are lost
Converting a temperature difference with the +273 or +32 offset.
Taking water's maximum density at 0 °C.
Using α_l in place of α_V (or 2α_l for volume).
Assuming all the ice melts in a mixture problem.
Using Q = msΔT during melting or boiling.
Putting °C into Stefan's law.
Adding conductivities for rods in series.
Saying convection can happen in solids.
Thinking Wien's law gives a star's interior temperature.
Using the starting temperature in Newton's law over an interval.
Formulas
15 to know
Celsius and Fahrenheit
(t_F − 32)/180 = t_C/100; t_F = (9/5)t_C + 32
Equal at −40.
Kelvin
T = t_C + 273.15
Same unit size as °C.
Ideal-gas equation
PV = μRT
R = 8.31 J mol⁻¹ K⁻¹.
Linear expansion
Δl/l = α_l ΔT
Area: 2α_l; volume: α_V = 3α_l.
Volume expansion
ΔV/V = α_V ΔT
Ideal gas at constant P: α_V = 1/T.
Thermal stress
stress = Y α ΔT; F = Y A α ΔT
Rod held between fixed ends.
Heat capacity
S = ΔQ/ΔT; s = (1/m) ΔQ/ΔT; C = (1/μ) ΔQ/ΔT
J K⁻¹, J kg⁻¹ K⁻¹, J mol⁻¹ K⁻¹.
Heat for a temperature change
Q = m s ΔT
No change of state.
Calorimetry
heat lost = heat gained
Isolated system.
Latent heat
Q = m L
Water: L_f = 3.33 × 10⁵, L_v = 22.6 × 10⁵ J kg⁻¹.
Conduction
H = K A (T_C − T_D)/L
Steady state.
Rods in series
K′ = 2K₁K₂/(K₁ + K₂) (equal lengths)
Same heat current through each rod.
Wien's displacement law
λ_m T = 2.9 × 10⁻³ m K
Hotter body, shorter peak wavelength.
Stefan–Boltzmann law
H = A e σ T⁴; net H = e σ A (T⁴ − T_s⁴)
σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; T in kelvin.
Newton's law of cooling
−dQ/dt = k(T₂ − T₁); T₂ = T₁ + C′e^(−Kt)
K = k/(ms); small temperature differences.
Key terms
16 terms
- Heat
- Energy transferred between bodies because of a temperature difference.
- Temperature
- A number that measures how hot or cold a body is.
- Absolute zero
- −273.15 °C, the zero of the Kelvin scale, found by extending gas-thermometer lines to P = 0.
- Coefficient of linear expansion
- Fractional increase in length per kelvin rise, α_l = Δl/(l ΔT).
- Anomalous expansion
- Water's contraction on heating between 0 °C and 4 °C.
- Thermal stress
- Stress set up when a body is prevented from expanding or contracting.
- Specific heat capacity
- Heat needed per unit mass per unit temperature rise.
- Calorimeter
- An insulated metal vessel with stirrer used to measure heat exchanged.
- Regelation
- Melting under pressure and refreezing when the pressure is removed.
- Sublimation
- Direct change between solid and vapour without passing through the liquid state.
- Triple point
- The one temperature and pressure at which solid, liquid and vapour coexist.
- Latent heat
- Heat per unit mass absorbed or released during a change of state at constant temperature.
- Thermal conductivity
- K in H = KAΔT/L; how readily a material conducts heat.
- Convection
- Heat transfer by the bulk movement of a fluid.
- Emissivity
- The fraction of a perfect radiator's emission that a surface emits, between 0 and 1.
- Blackbody
- An ideal body that absorbs all radiation falling on it and emits the maximum possible radiation at its temperature.