Chapter 10: Thermal Properties of Matter | Summary

Temperature is measured using a thermometer, which exploits physical properties of materials that change with temperature. The most commonly used property is the variation of volume of a liquid with temperature, as in liquid-in-glass thermometers using mercury or alcohol. Thermometers are calibrated using two fixed reference points: the ice point (freezing point of water) and the steam point (boiling point of water) at standard pressure.

The Celsius scale assigns 0°C and 100°C to the ice and steam points respectively, while the Fahrenheit scale assigns 32°F and 212°F. The two scales are related by the equation: (tF – 32)/180 = tC/100. On the Fahrenheit scale there are 180 equal intervals between the two fixed points, and on the Celsius scale there are 100.

Gas thermometers give consistent readings regardless of the gas used because all gases at low densities exhibit the same expansion behaviour. Combining Boyle's Law (PV = constant at constant T) and Charles' Law (V/T = constant at constant P), the ideal gas equation is derived: PV = μRT, where μ is the number of moles and R = 8.31 J mol⁻¹ K⁻¹ is the universal gas constant.

Extrapolating the pressure-temperature graph for an ideal gas to zero pressure gives the absolute minimum temperature of –273.15°C, called absolute zero, which forms the basis of the Kelvin scale. The Kelvin and Celsius scales have the same unit size but different origins: T = tC + 273.15. At absolute zero (0 K), every substance has the least possible molecular activity.

Most substances expand on heating and contract on cooling. The increase in dimensions of a body due to an increase in temperature is called thermal expansion. There are three types: linear expansion (change in length), area expansion (change in area), and volume expansion (change in volume). The coefficients are defined as: αl = (Δl/l)/ΔT, αA = (ΔA/A)/ΔT = 2αl, and αV = (ΔV/V)/ΔT = 3αl.

Water exhibits anomalous expansion: it contracts on heating between 0°C and 4°C and expands below 4°C, giving water its maximum density at 4°C. This is why lakes and ponds freeze at the top first, preserving aquatic life. Gases expand much more than solids and liquids; for an ideal gas, αV = 1/T. When thermal expansion of a rod is prevented, thermal stress is developed in the rod, which can be large enough to bend steel rails.

The quantity of heat required to warm a substance depends on its mass, the change in temperature, and the nature of the substance. The heat capacity S of a substance is defined as S = ΔQ/ΔT. The specific heat capacity s is defined as s = ΔQ/(mΔT), with SI unit J kg⁻¹ K⁻¹. It represents the heat required per unit mass per unit temperature change and depends on the nature of the substance and its temperature.

The molar specific heat capacity C = ΔQ/(μΔT) is used when amount is specified in moles, with SI unit J mol⁻¹ K⁻¹. For gases, Cp (at constant pressure) and Cv (at constant volume) are distinguished. Water has the highest specific heat capacity (4186 J kg⁻¹ K⁻¹) among common substances, making it an excellent coolant in automobile radiators and a heat-retaining medium in hot water bags.

Calorimetry is the measurement of heat. In an isolated system, heat lost by a hotter body equals heat gained by a cooler body. A calorimeter is a device for heat measurement, consisting of a metallic vessel (copper or aluminium) inside a wooden jacket with heat-insulating material like glass wool, minimising heat exchange with surroundings.

The principle of calorimetry — heat lost equals heat gained — is used to determine specific heat capacities of substances experimentally. A known mass of a substance at a known temperature is placed in a calorimeter containing water at a different known temperature, and the final equilibrium temperature is measured to calculate the unknown specific heat.

Matter exists in three states: solid, liquid, and gas. A transition between these states is a change of state. The solid-to-liquid change is melting (fusion); liquid-to-solid is freezing; liquid-to-gas is vaporisation; gas-to-liquid is condensation; and solid-to-vapour directly is sublimation (e.g., dry ice, iodine). During any change of state, the temperature remains constant even though heat is being continuously added or removed.

The melting point is the temperature at which solid and liquid coexist in equilibrium; boiling point is where liquid and vapour coexist. Both depend on pressure: boiling point increases with pressure (pressure cooker) and decreases at high altitudes. The triple point is where all three phases coexist simultaneously; for water it is 273.16 K and 6.11×10⁻³ Pa. The phenomenon of regelation (refreezing after pressure-induced melting) explains ice-skating.

Latent heat is the heat per unit mass transferred during a change of state without any change in temperature: L = Q/m, with SI unit J kg⁻¹. The latent heat of fusion (Lf) applies to the solid-liquid transition and the latent heat of vaporisation (Lv) applies to the liquid-gas transition. For water, Lf = 3.33×10⁵ J kg⁻¹ and Lv = 22.6×10⁵ J kg⁻¹.

The large latent heat of vaporisation of water (about 6.8 times its latent heat of fusion) explains why steam burns are more dangerous than boiling water burns at the same temperature. The value of L also depends on pressure. The slopes of the temperature-heat graph differ in different phase regions, indicating that specific heats of solid, liquid, and vapour states are not equal.

There are three modes of heat transfer: conduction, convection, and radiation. Conduction occurs through molecular collisions in adjacent parts of a body without bulk motion of matter; it is most effective in metals. The rate of heat flow is H = KA(TC – TD)/L, where K is the thermal conductivity (SI unit: W m⁻¹ K⁻¹). Metals have high K values; insulators like wood and glass wool have very low values.

Convection is heat transfer by actual bulk movement of matter and is possible only in fluids. Natural convection (driven by gravity and buoyancy) explains sea breezes and trade winds. Forced convection is used in home heating systems and the human circulatory system. Radiation requires no medium and transfers heat by electromagnetic waves at the speed of light (3×10⁸ m s⁻¹), enabling heat transfer across vacuum, as from the Sun to Earth.

A blackbody absorbs and emits radiant energy most efficiently. Thermal radiation has a continuous spectrum of wavelengths; the wavelength of maximum emission λm is related to absolute temperature by Wien's Displacement Law: λmT = 2.9×10⁻³ m K. As temperature increases, λm shifts to shorter wavelengths, explaining why a heated iron turns from red to yellow to white.

The Stefan-Boltzmann law states that the energy emitted per unit time by a perfect radiator is H = AσT⁴, where σ = 5.67×10⁻⁸ W m⁻² K⁻⁴. For a body with emissivity e, H = AeσT⁴, and the net rate of heat loss when surroundings are at temperature Ts is H = eσA(T⁴ – Ts⁴). Emissivity e = 1 for a perfect blackbody. A Dewar flask minimises heat transfer by combining silvered walls (to reduce radiation), vacuum (to reduce conduction and convection), and insulating support.

Newton's Law of Cooling states that the rate of heat loss of a body is directly proportional to the excess temperature of the body over its surroundings: –dQ/dt = k(T2 – T1), where k depends on the area and nature of the surface. This law is valid only for small temperature differences. Integrating gives: T2 = T1 + C′e⁻Kt, showing an exponential decay of the excess temperature with time.

A graph of log(T2 – T1) versus time gives a straight line with negative slope, which is used to verify Newton's law experimentally. Initially the rate of cooling is higher and decreases as the body cools toward the surrounding temperature. The law applies as a valid approximation for heat loss through room walls, radiator-to-room transfer, and cooling of beverages on a table.

Chapter 10 establishes the foundational understanding of how matter interacts with heat. The key takeaways are: temperature drives heat transfer; thermal expansion (linear, area, and volume) is quantified by characteristic coefficients; specific heat capacity and latent heat govern how substances absorb and release energy during temperature changes and phase transitions respectively; and the three modes of heat transfer — conduction, convection, and radiation — each operate through distinct mechanisms governed by precise mathematical laws including Fourier's law, Stefan-Boltzmann law, Wien's law, and Newton's law of cooling.

From the examination perspective, this chapter is extremely important for CBSE Class 11 and forms a strong foundation for thermodynamics in Class 12. Students must be comfortable with unit conversions between temperature scales, applying the ideal gas equation, solving calorimetry problems using heat lost equals heat gained, calculating latent heat and thermal expansion, applying Newton's law of cooling, and interpreting blackbody radiation concepts. Numericals from this chapter appear regularly in board exams as well as in competitive entrance examinations like JEE and NEET.