Heat and Temperature

Heat and Temperature

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Heat is energy in transit between bodies at different temperatures; it flows spontaneously from the hotter body to the cooler one until thermal equilibrium is reached. Temperature is a scalar that indicates the average kinetic energy of a body’s particles — it is not the same as heat. Two governing equations cover almost every NABTEB calculation:

• Q = mcΔθ — heat gained/lost by a mass m (kg) when its temperature changes by Δθ (K or °C, same interval), where c is specific heat capacity (J kg⁻¹ K⁻¹).
• Q = mL — heat absorbed/released during a change of phase at constant temperature; L is latent heat (J kg⁻¹), either of fusion (melting) or vaporisation (boiling).

For scale conversion use K = °C + 273, and °C/100 = (F − 32)/180. Three modes carry heat: conduction, convection, radiation. In NABTEB objectives, the most-tested traps are confusing heat with temperature and using °C where a difference must be in K.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Definitions that examiners test

Heat (Q) is measured in joules (J) because it is a form of energy — the kinetic energy of randomly moving molecules plus the potential energy of their intermolecular forces (together called internal energy, U). Temperature (T) is the intensive property that fixes the direction of heat flow: if T_A > T_B, net heat flows A → B. Two bodies in contact reach thermal equilibrium when their temperatures equalise.

Calorimetry equations

• Specific heat capacity c = energy to raise 1 kg of a substance by 1 K; SI unit J kg⁻¹ K⁻¹. Water’s value is 4200 J kg⁻¹ K⁻¹ — used as the reference in method-of-mixtures problems.
• Heat capacity C = mc = Q/Δθ (J K⁻¹) for the whole body.
• Latent heat L applies at constant temperature during melting (latent heat of fusion, L_f) or boiling (latent heat of vaporisation, L_v).

Temperature scales

The Kelvin scale is absolute: 0 K = −273 °C = absolute zero, the temperature at which molecular translational motion is minimal. Interval relationships: a 1 K change equals a 1 °C change, while a Fahrenheit degree is only 5/9 of a Celsius degree. Conversion: K = °C + 273; °F = (9/5)°C + 32.

Heat transfer modes

Mode	Medium	Carrier
Conduction	Solids (best in metals)	Vibrating lattice ions + free electrons
Convection	Fluids	Bulk movement of fluid masses
Radiation	Vacuum or any	Electromagnetic (infra-red) waves

NABTEB question patterns

Expect short-theory: “Differentiate between heat and temperature” (3 marks); objectives on reading thermometers or identifying transfer mode in a diagram; calculation items using Q = mcΔθ or Q = mL; and conversion of clinical thermometer readings among °C, °F and K.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Worked example (method of mixtures)

A copper block of mass 0.5 kg at 200 °C is dropped into 0.4 kg of water at 25 °C in an aluminium calorimeter of mass 0.2 kg (c_Al = 900 J kg⁻¹ K⁻¹, c_cu = 400 J kg⁻¹ K⁻¹, c_water = 4200 J kg⁻¹ K⁻¹). Assuming no heat loss, find the final temperature θ.

Heat lost by copper = 0.5 × 400 × (200 − θ) = 80 000 − 400θ. Heat gained by water = 0.4 × 4200 × (θ − 25) = 1680θ − 42 000. Heat gained by calorimeter = 0.2 × 900 × (θ − 25) = 180θ − 4500.

Setting lost = gained: 80 000 − 400θ = 1860θ − 46 500 → 126 500 = 2260θ → θ ≈ 56 °C.

Common mistakes examiners exploit

1. Using Δθ in °C as if it differs from K — for intervals they are numerically equal, but absolute zero is 0 K, not 0 °C.
2. Applying latent heat of fusion instead of vaporisation (or vice versa) when steam condenses and then cools — steam first releases mL_v, then cools with mcΔθ.
3. Treating heat as something “contained” inside a body. Heat is energy in transit; once the transfer ends, the energy resides as internal energy.
4. Confusing linear expansivity α (length change, ΔL = αL₀Δθ) with cubic expansivity γ ≈ 3α.
5. For Joule’s electrical method: equating electrical energy to heat requires Q = I²Rt = VIt, with a correction factor for heat lost to the surroundings.

Adjacent-topic links

Calorimetry feeds directly into specific latent heat experiments and Joule’s electrical heating (linking to electric circuits). Linear expansivity links to bimetallic strips and thermometry. Radiation leads to black-body emission curves and the greenhouse effect, both frequent in current NABTEB General Physics.

Practice prompts

1. A 2 kW immersion heater runs for 5 minutes inside a 1.5 kg aluminium kettle containing 0.8 kg of water, both initially at 20 °C. Use Q = I²Rt = mcΔθ to find the final temperature of the water (assume 10% heat loss; c_Al = 900 J kg⁻¹ K⁻¹).
2. Explain, with reference to molecular behaviour, why a swimming pool at 25 °C contains far more internal energy than a cup of water at 95 °C, even though the cup is “hotter”.

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