Thermal Properties of Matter

2.1 Core concepts

• Temperature is a relative measure of the hotness or coldness of a body; heat is the form of energy transferred between two systems (or a system and its surroundings) by virtue of a temperature difference. SI unit of heat is the joule (J); SI unit of temperature is the kelvin (K), with degree Celsius (°C) as a common unit (NCERT §10.2, p. 203).
• Thermometers exploit a physical property that varies with temperature; common liquid-in-glass thermometers use mercury or alcohol whose volume varies linearly with temperature. Calibration uses two fixed points: the ice point and the steam point of water (NCERT §10.3, p. 203).
• On the Fahrenheit scale the ice and steam points are 32 °F and 212 °F (180 equal intervals); on Celsius they are 0 °C and 100 °C (100 intervals). The conversion is (tF − 32)/180 = tC/100 (NCERT §10.3, Eq. 10.1, p. 203).
• A constant-volume gas thermometer uses P ∝ T and gives the same reading regardless of which low-density gas is used; extrapolating P–T lines for different gases meets the T-axis at the same point, −273.15 °C, which is taken as absolute zero (0 K) on the Kelvin scale (NCERT §10.4, pp. 203–204).
• Boyle's law (PV = constant, T fixed) and Charles' law (V/T = constant, P fixed) combine into the ideal-gas equation PV = µRT, where µ is the number of moles and R = 8.31 J mol⁻¹ K⁻¹ is the universal gas constant (NCERT §10.4, Eq. 10.2, p. 204).
• Kelvin and Celsius scales have the same unit size but different origins: T = tC + 273.15 (NCERT §10.4, Eq. 10.3, p. 204).
• Most substances expand on heating and contract on cooling. For a long rod: ∆l/l = αl ∆T, where αl is the coefficient of linear expansion (a material constant) (NCERT §10.5, Eq. 10.4, p. 205).
• For a rectangular sheet, the coefficient of area expansion equals 2αl (the (αl ∆T)² term being negligible); for a cube, the coefficient of volume expansion αv = 3αl (NCERT §10.5, Eqs. 10.7–10.9, pp. 207–208).
• Liquids and gases are described by ∆V/V = αv ∆T. Gases expand much more than solids/liquids; for an ideal gas at constant pressure αv = 1/T, so at 0 °C, αv ≈ 3.7 × 10⁻³ K⁻¹ (NCERT §10.5, Eq. 10.6, p. 206).
• Water shows anomalous behaviour: between 0 °C and 4 °C it contracts on heating, so water has its maximum density at 4 °C. This makes lakes freeze at the top first, preserving aquatic life (NCERT §10.5, pp. 206–207).
• If thermal expansion of a rod is prevented by rigid supports, a compressive thermal stress is set up; for a steel rail with αl = 1.2 × 10⁻⁵ K⁻¹ and ∆T = 10 °C, the strain is 1.2 × 10⁻⁴ and thermal stress is 2.4 × 10⁷ N m⁻² (NCERT §10.5, p. 207).
• Heat capacity S = ∆Q/∆T; specific heat capacity s = (1/m)(∆Q/∆T) is the heat needed to change unit mass by one unit of temperature. SI unit: J kg⁻¹ K⁻¹ (NCERT §10.6, Eqs. 10.10–10.11, p. 208).
• Water has an unusually high specific heat capacity of 4186 J kg⁻¹ K⁻¹ — the highest in Table 10.3 — which is why water is used as a coolant in radiators and as a heater in hot-water bags, and why sea breezes have a cooling effect (NCERT §10.6, Table 10.3, p. 209).
• Molar specific heat capacity C = (1/µ)(∆Q/∆T); for gases one distinguishes Cp (constant pressure) and Cv (constant volume) (NCERT §10.6, Eq. 10.12, pp. 208–209).
• Calorimetry: in an isolated system, heat lost by the hotter body equals heat gained by the colder body. A calorimeter is a metallic vessel (copper/aluminium) kept inside an insulating jacket (NCERT §10.7, pp. 209–210).
• During a change of state (melting/fusion, freezing, vaporisation, condensation, sublimation) temperature remains constant; both phases coexist in thermal equilibrium. The temperature at which solid–liquid coexist is the melting point; liquid–vapour coexist at the boiling point (NCERT §10.8, pp. 210–212).
• Latent heat L = Q/m is the heat per unit mass required for a change of state at constant T and P. SI unit: J kg⁻¹. For water Lf = 3.33 × 10⁵ J kg⁻¹ and Lv = 22.6 × 10⁵ J kg⁻¹ — so steam at 100 °C carries 22.6 × 10⁵ J kg⁻¹ more energy than water at 100 °C, explaining why steam burns are more serious (NCERT §10.8.1, Eq. 10.13, Table 10.5, p. 213).
• Boiling point increases with pressure (pressure cooker) and decreases with reduced pressure (cooking is difficult on hills); regelation (refreezing under pressure) makes skating possible (NCERT §10.8, pp. 211–212).
• Three modes of heat transfer: conduction, convection, radiation (NCERT §10.9, p. 214).
• Conduction: in steady state, H = KA(TC − TD)/L, where K is thermal conductivity (SI unit J s⁻¹ m⁻¹ K⁻¹ = W m⁻¹ K⁻¹). Metals have large K (silver 406, copper 385); gases are poor conductors (air 0.024) (NCERT §10.9.1, Eq. 10.14, Table 10.6, pp. 214–215).
• Convection is heat transfer by bulk motion of matter and is possible only in fluids; it can be natural (gravity-driven, e.g., sea breeze, trade winds) or forced (pumps, heart, automobile cooling) (NCERT §10.9.2, pp. 217–218).
• Radiation requires no medium; energy is carried by electromagnetic waves at speed 3 × 10⁸ m s⁻¹. Stefan-Boltzmann law for a perfect radiator: H = AσT⁴ with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; for a real body H = AeσT⁴ where e is emissivity (e = 1 for perfect radiator). For a body at T with surroundings at Ts, net loss is H = eσA(T⁴ − Ts⁴) (NCERT §10.9.3, Eqs. 10.16–10.18, pp. 218–219).
• Blackbody radiation has a continuous spectrum. Wien's displacement law: λmT = constant = 2.9 × 10⁻³ m K. This explains why heated iron turns dull red → reddish yellow → white-hot, and lets us estimate Sun's surface temperature ≈ 6060 K from λm = 4753 Å (NCERT §10.9.4, Eq. 10.15, pp. 218–219).
• A Dewar flask reduces all three modes: silvered walls reflect radiation, evacuated space cuts conduction and convection (NCERT §10.9.3, p. 218).
• Newton's law of cooling: for small temperature differences, −dQ/dt = k(T2 − T1). Integrating gives loge(T2 − T1) = −Kt + c, so a plot of loge(T2 − T1) against t is a straight line with negative slope (NCERT §10.10, Eqs. 10.19–10.23, pp. 220–221).
• Triple point of water, the unique combination of pressure (4.58 mm Hg) and temperature (273.16 K) at which all three phases of water — ice, water and vapour — coexist in thermal equilibrium, is the modern SI defining point of the kelvin (NCERT §10.4, p. 204; Points to Ponder, p. 222).
• Anomalous expansion of water has profound ecological significance: as a lake cools, the densest (4 °C) water sinks while colder (less dense) water floats on top, eventually freezing into an insulating ice cap that protects fish and other aquatic life in the comparatively warmer (≈4 °C) water below (NCERT §10.5, p. 206–207).
• Mayer's relation Cp − Cv = R for an ideal gas follows from the first law plus the ideal-gas equation: the extra Cp − Cv accounts for the work done by the gas during a constant-pressure expansion. Cp and Cv are introduced individually here; their algebraic relation is fully developed in the next NCERT chapter (NCERT §10.6, p. 208–209).
• Black-body is an idealised body that absorbs (and re-emits) all incident radiation. Stefan-Boltzmann emission H = AσT⁴ refers to a perfect black-body (e = 1); for real bodies the emissivity e (0 < e < 1) multiplies the law. Wien's displacement λ_m T = b (b ≈ 2.9 × 10⁻³ m K) tracks the peak of the spectrum (NCERT §10.9.3–10.9.4, p. 218–219).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 10.1 (p. 203): Straight-line plot of Fahrenheit tF versus Celsius tC — basis of conversion equation (tF − 32)/180 = tC/100.
• Fig. 10.2 and 10.3 (p. 204): P–T lines for low-density gases at constant volume; all extrapolations meet at absolute zero (−273.15 °C).
• Fig. 10.4 (p. 204): Side-by-side comparison of Kelvin, Celsius and Fahrenheit scales.
• Fig. 10.5 (p. 205): Linear, area and volume expansion sketches with the relations ∆l/l = αl ∆T, ∆A/A = 2αl ∆T, ∆V/V = 3αl ∆T.
• Fig. 10.7 (p. 206): Volume and density of water versus temperature, showing the dip in volume (peak in density) at 4 °C — anomalous expansion of water.
• Fig. 10.9 (p. 211): Temperature vs time when ice is heated steadily — flat plateaus at 0 °C (melting) and 100 °C (boiling) where latent heat is absorbed.
• Fig. 10.12 (p. 213): Temperature vs heat for water at 1 atm, showing slopes (specific heats of ice, water, steam) and flat segments of length Lf and Lv.
• Fig. 10.14 (p. 215): Steady-state conduction along an insulated bar between reservoirs at TC and TD.
• Fig. 10.17 (p. 217): Convection cycles — day-time sea breeze (warm air rises over land) and reversed night-time circulation.
• Fig. 10.18 (p. 218): Blackbody emission curves at different temperatures — λm shifts to shorter wavelengths as T rises (Wien's law).
• Fig. 10.19 (p. 220): Cooling curve T2 − T1 versus t — exponential decay (Newton's law of cooling).
• Fig. 10.20 (p. 220): Verification of Newton's law of cooling — straight-line plot of loge(T2 − T1) versus t with negative slope.

2.4 Common confusions / NTA trap points

• Tc = T − 273.15, not −273.16. The triple point of water is defined as 273.16 K, but the offset between Celsius and Kelvin is 273.15 (NCERT §10.4, p. 204).
• αv = 3αl applies only to isotropic solids (and to liquids by definition of αv). For gases αv = 1/T at constant pressure and depends on T (NCERT §10.5, Eq. 10.6, p. 206).
• Anomalous expansion of water is between 0 °C and 4 °C (not "below 0 °C" or "below 4 °C for all temperatures") — maximum density is at 4 °C (NCERT §10.5, p. 206).
• Steam at 100 °C carries 22.6 × 10⁵ J kg⁻¹ more heat than water at 100 °C; that is why steam burns are more serious than burns from boiling water — a frequent assertion–reason trap (NCERT §10.8.1, p. 213).
• Stefan-Boltzmann law uses absolute (Kelvin) temperature, not Celsius, and net loss has (T⁴ − Ts⁴), not (T − Ts)⁴ (NCERT §10.9.3, Eq. 10.18, p. 219).
• Newton's law of cooling holds only for small differences in temperature between body and surroundings (NCERT §10.10, p. 220).
• Convection requires a fluid (and gravity for natural convection); conduction does not need bulk motion; radiation does not need any medium. Mixing these up is a classic NTA distractor (NCERT §10.9, pp. 214–218).
• Stress = Y × αl × ∆T for a clamped rod whose expansion is prevented — independent of the rod's length. Many students wrongly include L in the formula.
• Latent heat is absorbed at constant T, so heating curves for water show two horizontal plateaus (at 0 °C and 100 °C). Sloped segments give specific heat; plateau lengths give latent heat.
• Boiling vs evaporation: boiling is bulk vaporisation at the boiling point; evaporation occurs at any temperature from the surface, and is what drives sweat-based cooling.
• K (thermal conductivity) ≠ k (Newton's-law cooling constant); they have different units (W m⁻¹ K⁻¹ vs s⁻¹) and arise from unrelated phenomena. The same letter "k" causes confusion in problems.

2.5 Key formulas table