Temperature

A-Level Physics 9702 · Topic 14 revision notes · A2

Thermal equilibrium, the thermodynamic (kelvin) scale, practical thermometers, and the energy needed to heat a substance or change its state.

9 definitions to learn word for word, 7 equations in their own column, 8 diagrams and graphs. Read it, cover it, test yourself.

Definitions (mark-scheme wording)EquationsExam traps

14.1Thermal equilibrium

Thermal equilibrium: the state in which two regions are at the same temperature, so there is no net transfer of thermal energy between them.
Temperature: a measure of the average random kinetic energy of the particles; it determines the direction of net thermal energy transfer.

Net thermal energy flows from a region of higher temperature to a region of lower temperature.
Energy still passes both ways at equilibrium; the net transfer is zero.
Temperature, not energy stored, sets the direction of flow: a hot spark is hotter than a warm bath.
Two objects each in equilibrium with a third are in equilibrium with each other: the basis of a thermometer.

Net energy flows from hot to cold until both reach the same temperature.

Temperature-time: the hot object cools, the cold one warms, both level off at the equilibrium temperature.

Equal temperature means equilibrium, not equal internal energy: a bath and a cup at 40 °C are in equilibrium.
At equilibrium energy transfer has not stopped; the net transfer is zero.

Thermodynamic (kelvin) scale: a temperature scale that does not depend on the property of any particular substance.
Absolute zero: the temperature at which a substance has minimum internal energy (0 K).
Kelvin: the SI unit of thermodynamic temperature; a temperature change of 1 K equals a change of 1 °C.

Any physical property that varies with temperature can be used to measure it.
Examples: density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m.f. of a thermocouple.
Scales based on different properties agree only at the calibration points, since the properties do not vary linearly.
The kelvin scale is absolute: no substance-dependent calibration; its zero is absolute zero.
Gas thermometer: p against θ extrapolates to p = 0 at -273.15 °C = 0 K.
A temperature difference has the same numerical value in K and °C.

Celsius and kelvin scales: the same size of degree, zero shifted by 273.

Constant-volume gas thermometer: extrapolating p to zero locates absolute zero at -273 °C.

Every gas-law and kinetic-theory formula needs kelvin; never substitute °C for T.
Absolute zero is minimum internal energy, not "all motion stops" in the mark scheme wording.

Specific heat capacity (c): the energy required per unit mass to raise the temperature by one kelvin (or one degree Celsius).
Heat capacity: the energy required to raise the temperature of an object by one kelvin.

Electrical method: heater of known power in a lagged block (or liquid); measure V, I, t and the temperature rise.
Energy supplied = VIt (or read a joulemeter); then c = VIt / mΔθ.
Plot θ against t: gradient = P / mc, so c = P / (m × gradient).
Heat loss to the surroundings makes the measured c too large; lag, and start below room temperature and end the same amount above.
Continuous-flow method: repeat at two flow rates with the same Δθ to cancel the heat loss.
Water has a high c (4200 J kg^-1 K^-1): it heats and cools slowly.

Electrical method: a heater and thermometer in a lagged metal block; energy from a joulemeter (or V, I and t).

θ-t graph for a constant heater power: the steady gradient gives c.

Use the temperature change Δθ, not the final temperature.
Heat losses make the energy supplied larger than the energy gained, so c comes out too high, not too low.

Specific latent heat of fusion: the energy required per unit mass to change a substance from solid to liquid without a change of temperature.
Specific latent heat of vaporisation: the energy required per unit mass to change a substance from liquid to gas without a change of temperature.

During a change of state the temperature is constant: energy increases the potential energy of the molecules, not their kinetic energy.
L_v is much larger than L_f: molecules must be completely separated and the gas must do work pushing back the atmosphere.
Measuring L_v: boil liquid with a heater of power P on a balance; L = PΔt / Δm.
Measuring L_f: heater in a funnel of ice, collect melt water; a control funnel with no heater corrects for melting by the room.
Repeat at two powers and subtract to cancel heat losses: (P₁ - P₂)t = (m₁ - m₂)L.

Heating curve at constant power: sloping parts use mcΔθ; flat plateaus (state changes) use mL.

Measuring L_f: the control funnel measures ice melted by the room alone.

On a plateau energy is supplied but the temperature does not rise: use E = mL, never mcΔθ.
Subtract the control mass before calculating L_f.