Thermal Properties of Matter — NEET Notes

Temperature and heat — defining the difference

Temperature is a measure of the hotness of a body — an intensive property that tells you nothing about how much matter is involved. A drop of water at 100 °C and a swimming pool at 100 °C are equally hot, but they hold wildly different amounts of thermal energy. Our skin gives us a crude sense of temperature, but the range is narrow and unreliable: a metal handrail at 25 °C feels far colder than a wooden one at the same temperature because the metal conducts heat away from us faster. For science, we need a sharper instrument and a sharper definition.

Heat, by contrast, is the form of energy transferred between two systems (or between a system and its surroundings) because of a temperature difference. A glass of ice-cold water left on a hot summer table eventually warms up; a cup of tea on the same table cools down. In both cases, the body and its surroundings come into thermal equilibrium — they reach the same temperature. The SI unit of heat energy transferred is the joule (J); the SI unit of temperature is the kelvin (K), with degree Celsius (°C) in common use. The CGS unit of heat — the calorie — is still encountered in NEET problems: 1 cal = 4.186 J is the heat needed to raise 1 g of water by 1 °C.

Measurement of temperature & the three scales

A thermometer exploits some material property that varies smoothly with temperature — mercury or alcohol's volume, the pressure of a confined gas, the electrical resistance of a platinum wire. To assign numbers, we need two fixed points: the temperatures at which a chosen physical phenomenon recurs reproducibly. The standard choices are the ice point (water freezing) and the steam point (water boiling), both at standard atmospheric pressure. Three temperature scales partition the interval between these fixed points differently — Fahrenheit, Celsius and Kelvin.

Ideal-gas equation & absolute temperature

Liquid-in-glass thermometers using mercury, alcohol, or any other fluid disagree slightly at temperatures other than the fixed points, because their expansion properties differ. Gas thermometers, however, agree closely with each other at low densities — every dilute gas expands the same way. This universal behaviour points to a deeper law. Holding mass constant, the three state variables of a gas — pressure P, volume V and temperature T — obey two empirical laws: Boyle's law (PV = constant at fixed T) and Charles's law (V/T = constant at fixed P). Combining them gives the ideal-gas equation:

PV = μRT

Ideal gas law — R = 8.31 J mol⁻¹ K⁻¹

where μ is the number of moles and R = 8.31 J mol⁻¹ K⁻¹ is the universal gas constant. At constant volume, P ∝ T — the basis of the constant-volume gas thermometer, the most accurate of all thermometric devices. A plot of pressure versus Celsius temperature for any dilute gas is a straight line; extrapolating that line back to P = 0 gives the same intercept regardless of which gas you use: −273.15 °C. This is absolute zero, the floor of physical temperature. The Kelvin scale takes absolute zero as 0 K, and because the step size matches Celsius:

T (K) = t (°C) + 273.15

Kelvin–Celsius bridge — same step, different origin

The Kelvin scale is mandatory in any equation that contains temperature multiplied by something else — including PV = μRT and the Stefan-Boltzmann law. Use Celsius in those equations and your answer will be off by orders of magnitude. NEET problems sometimes give Celsius numbers and check whether you remember to convert.

Thermal expansion — α, β and γ

Most substances expand on heating and contract on cooling. NCERT introduces three coefficients — one for each dimension being measured. For a long rod, the fractional change in length is proportional to the temperature change: Δℓ/ℓ = α ΔT, where α is the coefficient of linear expansion. For a thin sheet, the fractional change in area is ΔA/A = β ΔT (areal expansivity). For a solid block or a liquid, the fractional change in volume is ΔV/V = γ ΔT (cubical expansivity). For an isotropic solid — one that expands equally in all directions — these three are not independent.

If a rod is rigidly clamped at both ends and then heated, it cannot expand. Instead it develops a thermal stress equal to YαΔT, where Y is the Young's modulus. For a 5-metre steel rail prevented from expanding when heated by 10 °C, the thermal stress works out to 2.4 × 10⁷ N m⁻²; two such rails can buckle each other in summer if the expansion joints between them are insufficient. This is why railway tracks have small gaps and why long bridges sit on roller bearings.

Anomalous expansion of water deserves special mention. Between 0 °C and 4 °C, water contracts on heating — opposite to the general rule. Its density therefore peaks at 4 °C. In a freezing lake, water at the surface cools, becomes denser, and sinks; warmer water rises and takes its place. Once the surface cools below 4 °C, however, further cooling makes the surface water less dense, not more. It stays at the top and eventually freezes. The ice layer insulates the warmer water below, allowing fish and aquatic plants to survive the winter. NEET likes this story for assertion-reason questions.

Specific heat capacity & molar heat capacity

If you heat a kettle of water and an identical kettle of mustard oil over the same flame, the oil reaches a higher temperature faster. Equal masses of different substances require different amounts of heat to undergo the same temperature change. NCERT formalises the observation in three steps. Heat capacity S of a body is the heat required to change its temperature by one unit: S = ΔQ/ΔT. It is a property of the body — a bigger body has a bigger S. Specific heat capacity s of a substance is the heat needed per unit mass per unit temperature change: s = ΔQ / (m ΔT). It is a property of the material. Molar heat capacity C uses moles instead of kilograms: C = ΔQ / (μ ΔT). For gases, two molar specific heats matter — Cₚ (at constant pressure) and Cᵥ (at constant volume) — which differ by R for an ideal gas (Mayer's relation, covered in the Thermodynamics chapter).

The high specific heat capacity of water has macroscopic consequences. Coastal cities have milder summers and winters than inland cities at the same latitude, because the sea absorbs and releases heat slowly while land warms and cools quickly. The same property makes water the universal coolant in automobile engines and the working fluid in thermal power station heat exchangers. Solids, by contrast, have much lower specific heats — aluminium 900, copper 386, iron 470, lead 128 J kg⁻¹ K⁻¹ — which is why a small mass of metal heats up rapidly on a hot plate. The unit of all of these is J kg⁻¹ K⁻¹.

Calorimetry — the principle of heat balance

A calorimeter is a thermally insulated vessel — typically copper or aluminium with a stirrer of the same metal, jacketed in glass wool or felt — that lets you measure heat exchanges without losing energy to the surroundings. Calorimetry is the art of writing one equation in one unknown by exploiting a single principle: in an isolated system, the heat lost by hot bodies equals the heat gained by cold bodies.

A worked NCERT example uses this principle to find the specific heat of aluminium. A 47-gram aluminium sphere at 100 °C is dropped into a copper calorimeter (140 g) containing 250 g of water at 20 °C; the final temperature is 23 °C. Writing heat lost = heat gained and solving gives s_Al ≈ 911 J kg⁻¹ K⁻¹ — close to the tabulated value of 900. Calorimetry questions in NEET almost always follow this template; the trick is to remember whether a phase change has occurred along the way, and to use the right specific heat in each temperature range (e.g., s_ice ≠ s_water).

Change of state & latent heat

When you heat ice steadily on a burner, its temperature rises until it hits 0 °C and then stops rising even though heat keeps flowing in. All the supplied energy goes into breaking the bonds that hold the solid lattice together, not into raising temperature. Once every ice molecule has been freed, the temperature begins climbing again — until it reaches 100 °C, where it stalls again while the water vaporises. The plateaux on the temperature-versus-heat curve are the signatures of change of state.

The latent heat L of a substance is the heat absorbed (or released) per unit mass during a phase change at constant temperature: Q = mL. Two values matter for NEET: the latent heat of fusion L_f, for solid ↔ liquid transitions, and the latent heat of vaporisation L_v, for liquid ↔ gas transitions. For water, these values are striking.

Two related concepts close out this section. Melting and boiling points depend on pressure. Higher pressure raises the boiling point — which is why a pressure cooker cooks faster — and lowers the freezing point slightly for water (rare; most substances behave oppositely). At high altitudes, atmospheric pressure is reduced and water boils below 100 °C; cooking takes longer. Sublimation is direct transition from solid to vapour without an intervening liquid phase — dry ice (solid CO₂) and iodine sublime under standard conditions. The unique pressure-temperature point at which all three phases of a substance coexist is the triple point; for water it is 273.16 K and 6.11 × 10⁻³ atm.

Heat transfer — three modes

Once a temperature difference exists, heat finds three different physical routes to flow from hot to cold. NCERT and NIOS together cover all three at the level NEET tests: conduction through a stationary medium, convection by bulk motion of a fluid, and radiation through electromagnetic waves needing no medium at all.

Conduction obeys Fourier's law: the heat current H (joules per second, i.e. watts) through a slab of cross-section A and thickness L, with its two faces at temperatures T₁ and T₂, is H = KA(T₁ − T₂)/L. K is a material constant called thermal conductivity. Good conductors of heat — silver, copper, aluminium — also tend to be good electrical conductors, because both depend on the mobility of conduction electrons. Insulators contain trapped air pockets (felt, foam, wool, ice on a roof) because air's K is exceptionally low. Composite rods are a favourite NEET problem: rods in series have an equivalent K analogous to resistors in series, while rods in parallel give K_eq = (K₁ + K₂)/2 if they have equal cross-sections.

Convection involves bulk motion of a fluid. When a fluid is heated from below, the lower layer expands, becomes less dense, and rises by buoyancy; the cooler, denser fluid above sinks to take its place — and the cycle continues. Convection therefore needs gravity (or some other body force) and a fluid medium. NCERT lists familiar consequences: sea breezes (during the day, land warms faster than sea; air rises over land; cooler air flows in from the sea), land breezes (at night, the reverse), and trade winds (a global convection current modified by Earth's rotation). Forced convection — a pump pushing the fluid — drives radiators, blood circulation, and refrigerators.

Stefan-Boltzmann law and Wien's displacement law

Every body emits electromagnetic radiation by virtue of its temperature — a red-hot iron poker, the filament of a bulb, even your own skin (which radiates roughly 60–70 W of mostly infrared light at body temperature). A perfect emitter and absorber is called a black body. The total power radiated per unit area of a black body, integrated over all wavelengths, depends only on its absolute temperature, and the dependence is breathtakingly steep — proportional to T to the fourth power. This is the Stefan-Boltzmann law.

The wavelength at which a black body radiates most strongly is governed by Wien's displacement law: λ_m T = b, where Wien's constant b = 2.9 × 10⁻³ m K. As temperature rises, the peak wavelength shifts toward shorter (bluer) values. A piece of iron heated in a forge glows first dull red, then orange, then yellow, then white as its temperature climbs — exactly what Wien's law predicts. Astronomers use the same relation to estimate the surface temperatures of stars from the colour of their light. The Sun's spectrum peaks near 480 nm, corresponding to a surface temperature of about 6000 K. NEET 2016 and 2018 both leaned on Wien's law + Stefan's law combined.

Thermos flask design uses all three modes simultaneously — and works by defeating them. The double-walled glass vessel has a vacuum between the walls (no conduction or convection), silvered inner and outer surfaces (no radiation — radiation is reflected back), and a cork support (no leakage through the supports). This is why a thermos keeps coffee hot for hours.

Newton's law of cooling

Stefan's law (H ∝ T⁴) is exact but inconvenient for everyday cups of coffee. When the body's temperature T is only slightly above the surroundings T_s, the radiated heat loss reduces to a much simpler form: linearly proportional to the temperature difference. This is Newton's law of cooling.

−dT/dt = k (T − T_s)

Newton's law of cooling — valid for small (T − T_s)

The rate of cooling is proportional to the excess temperature. The minus sign expresses that T decreases. Solving the differential equation gives an exponential approach to T_s: T(t) − T_s = (T₀ − T_s) e^−kt. For NEET problems, NCERT presents the law in its convenient average form: if a body cools from T₁ to T₂ in time Δt in surroundings T_s, then (T₁ − T₂)/Δt = k [(T₁ + T₂)/2 − T_s]. This is the form used in the NEET 2021 cup-of-coffee problem: a cup cools from 90 °C to 80 °C in time t in a 20 °C room; the time taken to cool from 80 °C to 60 °C (still at 20 °C) is 13t/5. Two applications of the average formula and one division reach the answer.