14. Temperature
- Syllabus
- 9702–2028–2029
- Section
- 14
- Level
- A2
Exam analysis
14.1 Thermal equilibrium
- Syllabus
- 9702–2028–2029
- Topic
- 14.1
- Level
- A2
Thermal energy transfers spontaneously from higher temperature to lower temperature
When two regions have different temperatures, thermal energy is transferred from the hotter region to the colder until equilibrium is reached.
Temperature indicates the direction of net thermal transfer; the mechanism may be conduction, convection or radiation.
A hot metal block in cooler water loses thermal energy while the water gains it, even if the block contains less total energy.
Heat is energy in transfer, not a substance stored in an object, and transfer direction is not set simply by which object has more energy.
Thermal equilibrium means regions have equal temperature and no net heat transfer
Two systems are in thermal equilibrium when their temperatures are equal, so there is no net transfer of thermal energy between them in contact.
Microscopic exchanges may still occur, but they balance on average. Thermal equilibrium is not the same as identical internal energy.
A thermometer left long enough in a liquid reaches the liquid’s temperature and is then in thermal equilibrium with it.
Equal temperature does not mean equal mass, energy content or particle number.
14.2 Temperature scales
- Syllabus
- 9702–2028–2029
- Topic
- 14.2
- Level
- A2
Calibrate a temperature-dependent physical property as a thermometer
A physical property that changes with temperature can be used as a thermometric property: calibrate measured property values against known temperatures, then infer an unknown temperature from its measured value after thermal equilibrium is reached.
| Official thermometric property | Typical instrument/condition |
|---|---|
| density of a liquid | density-based liquid thermometer; property must give a unique reading |
| volume of a gas at constant pressure | constant-pressure gas thermometer |
| resistance of a metal | metal/platinum resistance thermometer |
| e.m.f. of a thermocouple | thermocouple junction pair |
| Useful characteristic | Why it matters |
|---|---|
| monotonic, ideally near-linear | one property value maps unambiguously to temperature |
| reproducible and stable | calibration remains valid |
| sensitive over required range | small temperature changes are resolvable |
| low thermal mass / fast response when needed | reaches equilibrium without strongly disturbing or lagging the object |
A thermocouple's small sensing junction suits rapidly changing temperature. A bulky gas thermometer can be accurate for calibration but responds slowly and may disturb a small object. Water density is unsuitable over ranges where its variation is non-monotonic or one density corresponds to more than one temperature.
Do not replace the official liquid-density example with liquid volume, and do not omit 'constant pressure' for gas volume or 'metal' for resistance. Variation alone is insufficient without calibration, unique response and an appropriate range/time response.
Thermodynamic temperature is defined independently of any particular thermometric substance
The thermodynamic temperature scale is based on universal physical principles rather than a chosen material property; the kelvin is the SI unit.
A practical thermometer is calibrated to approximate this scale, but its raw property may be nonlinear or limited in range.
A gas, resistance and radiation thermometer can agree after calibration even though their measured properties differ.
The Celsius scale and a material’s expansion are convenient representations, not the fundamental definition of temperature.
Convert between kelvin and Celsius using T(K)=θ(°C)+273.15
Thermodynamic temperature T in kelvin relates to Celsius temperature θ by T=θ+273.15.
Kelvin is an absolute scale with the same degree size as Celsius but a different zero. Use kelvin in gas and thermodynamic equations unless instructed otherwise.
25 °C is 298.15 K; 0 °C is 273.15 K, not 0 K.
A temperature difference of 1 °C equals 1 K, but an absolute temperature of 1 °C is not 1 K.
Absolute zero is 0 K, the lower limit of the thermodynamic temperature scale
Absolute zero is zero kelvin, the lowest limit of thermodynamic temperature; it corresponds to −273.15 °C.
It is a limiting state, not simply “no motion” in every quantum description. Use it as the zero of the absolute scale.
Cooling from 300 K to 150 K halves the absolute temperature even though Celsius readings do not behave as a ratio scale.
Negative Celsius temperatures can be physically valid, but temperatures below 0 K are not reached in the ordinary thermodynamic scale.
14.3 Specific heat capacity and specific latent heat
- Syllabus
- 9702–2028–2029
- Topic
- 14.3
- Level
- A2
Specific heat capacity links energy to mass and temperature change
Specific heat capacity c is the thermal energy required per unit mass to produce unit temperature change in a substance.
Q=mcΔT,c=Q/(mΔT),unitJkg−1K−1
Heating 2.0 kg of water by 5.0 K with c = 4200 J kg⁻¹ K⁻¹ requires Q = (2.0)(4200)(5.0) = 4.2 × 10⁴ J. A change of 5.0 °C is also 5.0 K.
In a perfectly insulated system, energy lost equals energy gained. If 0.54 kg of material P (c=390 J kg⁻¹ K⁻¹) and 0.37 kg of Q (c=910 J kg⁻¹ K⁻¹) both warm by ΔT after receiving 24 kJ, then 24000=[(0.54)(390)+(0.37)(910)]ΔT, giving ΔT=43.8 K.
| Step | Check |
|---|---|
| define system | include substance, container and heater parts only when their heat capacities matter |
| assign each ΔT | final minus initial for that body; use magnitude in an energy-gained/lost ledger |
| conserve energy | total lost + supplied = total gained for the stated insulation model |
Use temperature difference, not absolute temperature. High c means more energy per kilogram per kelvin; it does not guarantee a higher final temperature. Account for losses or apparatus heat capacity unless the problem says they are negligible.
Specific latent heat changes state at constant temperature
Specific latent heat L is the thermal energy required per unit mass to change state at constant temperature.
Q=mL,L=Q/m,unitJkg−1
| Quantity | State change on energy input | Microscopic change |
|---|---|---|
| specific latent heat of fusion L_f | solid → liquid at melting point | particles loosen from fixed arrangement; separation changes modestly |
| specific latent heat of vaporisation L_v | liquid → gas at boiling point | particles separate much more and work is done against intermolecular attraction/ambient pressure |
For a substance, L_v is usually greater than L_f because vaporisation produces a much larger increase in particle separation and intermolecular potential energy and involves more work. During either phase change, average kinetic energy and therefore temperature remain constant.
To melt ice of mass m at 0 °C and then warm the resulting water to θ, total energy gained is Q = mL_f + mc_waterθ. In an insulated ice-water mixture, set this plus any other gains equal to the warm water's mcΔT loss before solving for L_f or final temperature.
Do not use mcΔT during a constant-temperature state change or use mL while temperature changes within one phase. Fusion and vaporisation have different L values, and the newly formed phase may require a separate mcΔT term afterward.