Thermal Properties of Matter
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Direct answer
Adding heat to a body either raises its temperature, Q = msΔT, or changes its state at constant temperature, Q = mL — and calorimetry is bookkeeping between the two. The chapter then carries that heat onward by conduction (H = kA ΔT/L), convection and radiation (Stefan's T^4 law, Wien's displacement, Newton's cooling). Water's anomalous behaviour between 0 °C and 4 °C and the huge latent heats of ice and steam supply the textbook-specific numbers NEET-UG loves.
What you must remember
- T(K) = T(°C) + 273.15; the ideal-gas volume coefficient is 1/273.15 per °C — the origin of absolute zero.
- Linear expansion ΔL = α L ΔT, with area coefficient β ≈ 2α and volume coefficient γ ≈ 3α; every linear dimension of a body scales, so a hole in a plate grows on heating exactly as the plate does.
- Water is anomalous: densest at 4 °C, so lakes freeze from the top down and aquatic life survives under the insulating ice.
- Specific heat of water 4186 J kg^-1 K^-1 (1 cal g^-1 °C^-1) — unusually high, which is why water is the coolant of choice and the moderate climate of coastal regions.
- Latent heat of fusion of ice 3.335 × 10^5 J/kg (80 cal/g); latent heat of vaporisation of water 2.26 × 10^6 J/kg (540 cal/g) — the reason steam scalds far worse than boiling water.
- Conduction: H = kA(T1 - T2)/L; metals conduct best (copper's k is hundreds of W m^-1 K^-1).
- Newton's law of cooling: dT/dt = -k(T - T_s), reliable for small excess temperature.
- Stefan's law: P = σA(T^4 - T_s^4) with σ = 5.67 × 10^-8 W m^-2 K^-4, kelvins mandatory; Wien: λ_m T = 2.9 × 10^-3 m K — hotter stars look bluer.
A worked calorimetry walk
Pass 10 g of steam at 100 °C into 100 g of water at 20 °C and find the final temperature. The steam first condenses, releasing 0.01 × 2.26 × 10^6 = 22,600 J, then the condensed water cools from 100 °C to T, giving up 0.01 × 4186 × (100 - T). The cold water absorbs 0.1 × 4186 × (T - 20). Equating heat lost to heat gained: 22,600 + 41.86(100 - T) = 418.6(T - 20), which solves to T ≈ 76 °C. Notice the structure, because it repeats in every mixture problem: each body contributes a latent term for each phase change plus a sensible term for each temperature leg, and the ledger must balance. The dominant lesson is numerical — a mere 10 g of steam brought as much energy as roughly 56 g of boiling water would have, because the latent term dwarfs the sensible term. That asymmetry is why burns are catalogued by steam rather than water, and why the exam keeps asking for final states rather than final temperatures: always check whether the steam runs out (or the ice fully melts) before assuming a single-phase answer.
Where students slip
Plugging Celsius into Stefan's law is the classic fatal error — T^4 means kelvins raised to the fourth, and a 100 °C body is 373 K, not 100 units hot. Second, heating-curve plateaus: while ice melts or water boils, temperature sits flat and all heat goes latent; sketching the curve before computing prevents assuming a straight-line temperature rise through a phase change. Third, the anomalous-expansion direction: from 0 °C to 4 °C water contracts on heating, so a "what happens between 0 and 4" option stating uniform expansion is wrong. Fourth, in expansion problems, a metal ring's hole enlarges on heating — students who reason that metal expands "into the hole" tick the wrong box. Newton's law of cooling, finally, is a small-excess approximation; using it for a red-hot body in cold air overstates its reach.
Frequently asked questions
Why do steam burns injure more than boiling-water burns?
Steam carries the latent heat of vaporisation, 2.26 × 10^6 J/kg, released on the skin during condensation in addition to the heat a boiling liquid transfers.
What is the anomalous expansion of water?
Between 0 °C and 4 °C water contracts on warming, reaching maximum density at 4 °C; this keeps deep lakes liquid in winter under an ice lid.
State Wien's displacement law.
The wavelength of maximum emission satisfies λ_m T = 2.9 × 10^-3 m K: hotter bodies radiate at shorter wavelengths, hence blue-white versus red stars.
Why is water used as a coolant in engines and industry?
Its specific heat, 4186 J kg^-1 K^-1, is among the highest of common liquids, so each kilogram absorbs a large heat for a modest temperature rise.
Does a hole in a metal plate become larger or smaller on heating?
Larger — every linear dimension, including gaps, scales with αΔT; a heated washer fits its bolt more loosely, not more tightly.