Heat Energy and Temperature Measurement

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Heat is internal energy in transit between bodies at different temperatures, while temperature measures the average kinetic energy of molecules. The two are not interchangeable: a swimming pool and a cup of tea at 80 °C hold very different quantities of heat despite identical temperatures.

Key formulas to memorise:

Q = mcΔθ — heat supplied = mass × specific heat capacity × temperature change (Q in J, c in J kg⁻¹ K⁻¹).
Q = ml — heat for a phase change (l = specific latent heat in J kg⁻¹).
T (K) = θ (°C) + 273 — SI unit conversion.
α, β = 2α, γ = 3α — linear, areal, cubical expansivities of solids.

High-yield pointers: (1) Mercury thermometers work from −39 °C to 357 °C; alcohol extends down to −115 °C. (2) The Celsius scale is fixed by the ice point (0 °C) and steam point (100 °C). (3) Radiation needs no medium, unlike conduction and convection.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Definitions and the Heat–Temperature Distinction

Heat is energy transferred spontaneously from a hotter body to a cooler one until thermal equilibrium is reached. Temperature is a scalar quantity indicating how hot or cold a body is, proportional to the mean kinetic energy of its molecules. Two bodies in contact exchange heat until their temperatures equalise, but the amount of heat each holds depends on mass and material.

Temperature Scales and Thermometric Properties

The Celsius scale uses two fixed points: the ice point (0 °C, pure melting ice at 1 atm) and the steam point (100 °C, boiling water at 1 atm). The Kelvin scale is the absolute thermodynamic scale, where 0 K is the lowest attainable temperature. Conversion: T = θ + 273.

A thermometric property is any physical quantity that changes predictably with temperature — e.g., the length of a mercury column, the resistance of a platinum wire, or the pressure of a gas at constant volume. The sealed liquid-in-glass thermometer exploits the linear expansion of mercury or coloured alcohol inside a glass bulb and stem.

Specific Heat Capacity and Latent Heat

Specific heat capacity c is the heat required to raise 1 kg of a substance by 1 K:

$$Q = mc\Delta\theta$$

Water has an unusually high c = 4200 J kg⁻¹ K⁻¹, which is why it moderates climate.

Latent heat is heat absorbed or released during a phase change at constant temperature: Q = ml, where l is either the latent heat of fusion (melting/solidifying) or vaporisation (boiling/condensing). During boiling, temperature stays at 100 °C even though energy continues to flow in.

Heat Transfer Modes

Conduction — energy passes through solids via molecular vibration and free-electron drift; metals conduct well.
Convection — energy carried by bulk movement of fluid molecules; only in liquids and gases.
Radiation — energy transferred as electromagnetic waves; requires no medium (the Sun warms Earth through vacuum).

Thermal Expansion of Solids

For a rod of original length L₀, the change in length is ΔL = αL₀Δθ, where α is the linear expansivity (K⁻¹). Areal and cubical expansivities are β = 2α and γ = 3α respectively. For liquids, the real expansivity equals the apparent expansivity (measured in a container) plus the cubical expansivity of the container material.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases in Heat Measurement

The equation Q = mcΔθ assumes no phase change occurs during the heating interval. If a substance crosses a melting or boiling point, the heat for the temperature rise and the latent heat must be added separately. In calorimetry, the heat lost by a hot body equals the heat gained by a cooler one plus the heat absorbed by the calorimeter (mc_calΔθ).

Common Mistakes to Avoid

Treating heat and temperature as synonymous — they have different units (J vs K).
Applying °C directly in gas-law calculations where K is required.
Forgetting that temperature stays constant during melting/boiling; the thermometer reads 100 °C the entire time water boils at 1 atm.
Confusing apparent and real expansivities of liquids: real γ_liquid = apparent γ_liquid + γ_container.
Assuming radiation needs air — infrared rays travel through vacuum.

Connection to Adjacent Topics

Heat energy ties directly to specific heat capacity, latent heat, and thermal expansion — NECO typically tests 1–2 calculation questions (4–8 marks each) drawn from these, plus a theory question on transfer modes. The relationship β = 2α and γ = 3α is regularly examined, as are unit conversions between Celsius and Kelvin.

Practice Prompts

A 2 kg block of aluminium (c = 900 J kg⁻¹ K⁻¹) is heated from 25 °C to 95 °C. Calculate the heat gained.
A brass rod of length 1.50 m is heated from 30 °C to 130 °C. Given α = 1.9 × 10⁻⁵ K⁻¹, find the increase in length and the new surface area of a square face.

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Heat Energy and Temperature Measurement