Class 11 Physics · Chapter 10 NotesThermal Properties of Matter

Temperature is a relative measure of the hotness or coldness of a body; a body at a higher temperature is said to be hotter. Our sense of touch is unreliable and limited, so temperature is measured with a thermometer, which uses a property that changes measurably with temperature, such as the volume of mercury or alcohol in a liquid-in-glass thermometer. Heat, on the other hand, is the form of energy transferred between two systems, or between a system and its surroundings, because of a temperature difference. Heat flows from the hotter body to the colder one until both reach the same temperature. The SI unit of heat is the joule (J) and the SI unit of temperature is the kelvin (K); degree Celsius (°C) is also commonly used.

• Heatenergy transferred due to a temperature difference; SI unit joule (J)
• Temperaturemeasure of hotness or coldness; SI unit kelvin (K)
• Two fixed reference points are needed to define a temperature scale
• Ice point and steam point of water are the freezing and boiling points at standard pressure
• Fahrenheit scaleice point 32 °F, steam point 212 °F, with 180 equal intervals
• Celsius scaleice point 0 °C, steam point 100 °C, with 100 equal intervals
• Conversion(t_F - 32)/180 = t_C/100

A gas thermometer gives the same reading regardless of which gas is used, provided the gas is at low density, because all low-density gases show the same expansion behaviour. For a fixed quantity of gas, Boyle's law states that PV is constant at constant temperature, and Charles' law states that V/T is constant at constant pressure. Combining them gives PV/T = constant, the ideal-gas law. In its general form the ideal-gas equation is PV = µRT, where µ is the number of moles and R is the universal gas constant, R = 8.31 J mol⁻¹ K⁻¹. If the pressure of a gas held at constant volume is plotted against temperature, the straight line, when extrapolated, meets the temperature axis at -273.15 °C. This lowest possible temperature is called absolute zero and is the zero of the Kelvin scale, so T = t_C + 273.15.

• Boyle's lawPV = constant at constant temperature
• Charles' lawV/T = constant at constant pressure
• Ideal-gas equationPV = µRT
• Universal gas constant R = 8.31 J mol⁻¹ K⁻¹
• Absolute zero = -273.15 °C = 0 K
• T = t_C + 273.15; the kelvin and degree Celsius have the same unit size

Most substances expand on heating and contract on cooling. The increase in the dimensions of a body due to a rise in temperature is called thermal expansion. For a long rod, the fractional change in length is proportional to the temperature change: ∆l/l = α_l ∆T, where α_l is the coefficient of linear expansion. For a sheet, the fractional change in area is ∆A/A = α_A ∆T, with α_A = 2α_l. For a volume, ∆V/V = α_v ∆T, and for an isotropic solid α_v = 3α_l. Typical values of α_l are of the order of 10⁻⁵ K⁻¹, so metals expand more than glass; copper expands about five times more than glass for the same temperature rise. If expansion is prevented by rigid supports, a thermal stress is set up in the body. Water is unusual: it contracts on heating between 0 °C and 4 °C, so it has maximum density at 4 °C. This is why lakes and ponds freeze at the top first, protecting aquatic life below.

• Linear expansion∆l/l = α_l ∆T
• Area expansion∆A/A = α_A ∆T, where α_A = 2α_l
• Volume expansion∆V/V = α_v ∆T, where α_v = 3α_l for an isotropic solid
• For an ideal gas at constant pressure, α_v = 1/T
• Water has maximum density at 4 °C and shows anomalous expansion between 0 °C and 4 °C
• Thermal stress arises when a body is prevented from expanding or contracting

The heat needed to warm a substance depends on its mass, the rise in temperature and the nature of the substance. The heat capacity S of a body is S = ∆Q/∆T, the heat required to raise its temperature by one unit. The specific heat capacity is the heat required per unit mass per unit temperature change: s = (1/m)(∆Q/∆T), with SI unit J kg⁻¹ K⁻¹. For a substance measured in moles, the molar specific heat capacity is C = (1/µ)(∆Q/∆T), with SI unit J mol⁻¹ K⁻¹; for gases it is defined at constant pressure (C_p) or constant volume (C_v). Water has a very high specific heat capacity, about 4186 J kg⁻¹ K⁻¹, which is why it is used as a coolant in radiators and in hot water bags. Calorimetry is the measurement of heat. In an isolated system, heat lost by the hotter part equals heat gained by the colder part, and this principle is used with a calorimeter to find unknown specific heats.

• Heat capacityS = ∆Q/∆T
• Specific heat capacitys = (1/m)(∆Q/∆T), SI unit J kg⁻¹ K⁻¹
• Molar specific heat capacityC = (1/µ)(∆Q/∆T), SI unit J mol⁻¹ K⁻¹
• For gasesC_p at constant pressure and C_v at constant volume
• Specific heat capacity of water = 4186 J kg⁻¹ K⁻¹
• Principle of calorimetryheat lost = heat gained (no heat escapes to surroundings)

Matter normally exists as solid, liquid or gas, and a transition between these states is called a change of state. When ice is heated, its temperature rises until it reaches the melting point, then stays constant while the ice melts; both solid and liquid coexist in thermal equilibrium. The temperature at which this happens is the melting point, and its value at standard atmospheric pressure is the normal melting point. Similarly, a liquid boils at its boiling point, where liquid and vapour coexist, and the normal boiling point is the value at standard atmospheric pressure. Boiling point rises with increasing pressure and falls with decreasing pressure, which is why cooking is difficult on hills and faster in a pressure cooker. Some substances change directly from solid to vapour, which is called sublimation. The heat transferred per unit mass during a change of state is the latent heat, Q = mL. For melting or freezing it is the latent heat of fusion (L_f), and for boiling or condensation it is the latent heat of vaporisation (L_v). For water, L_f = 3.33 × 10⁵ J kg⁻¹ and L_v = 22.6 × 10⁵ J kg⁻¹.

• Melting pointtemperature where solid and liquid coexist in thermal equilibrium
• Boiling pointtemperature where liquid and vapour coexist in thermal equilibrium
• Latent heatQ = mL, SI unit J kg⁻¹
• Latent heat of fusion L_fsolid to liquid change at the same temperature
• Latent heat of vaporisation L_vliquid to vapour change at the same temperature
• Sublimationdirect change from solid to vapour, as in dry ice and iodine
• Triple point of water273.16 K at a pressure of 6.11 × 10⁻³ Pa

Heat can be transferred in three distinct ways. Conduction occurs between adjacent parts of a body at different temperatures, without any flow of matter. For a bar of length L and uniform cross-section A whose ends are at temperatures T_C and T_D, the steady rate of heat flow is H = KA(T_C - T_D)/L, where K is the thermal conductivity of the material, measured in J s⁻¹ m⁻¹ K⁻¹ or W m⁻¹ K⁻¹. Metals have large K and are good conductors; wood, glass wool and air have small K and are good insulators. Convection transfers heat by the actual motion of matter and occurs only in fluids; it may be natural, driven by buoyancy, or forced, as when a pump or the heart circulates a fluid. Radiation needs no medium: all bodies emit thermal radiation by virtue of their temperature, and this is how the earth receives heat from the Sun through space.

• ConductionH = KA(T_C - T_D)/L, with K the thermal conductivity
• SI unit of KJ s⁻¹ m⁻¹ K⁻¹ or W m⁻¹ K⁻¹
• Convectionheat transfer by bulk motion of a fluid; natural or forced
• Radiationtransfer of energy by electromagnetic waves; needs no medium
• Black bodies absorb and emit radiant energy better than lighter-coloured bodies
• A Dewar flask reduces heat loss by using silvered walls, vacuum and an insulating support

Thermal radiation from a body has a continuous spectrum of wavelengths, and the energy emitted varies with wavelength. The wavelength λ_m at which the emitted energy is maximum decreases as the temperature rises, according to Wien's displacement law, λ_m T = constant, where the constant is 2.9 × 10⁻³ m K. For a perfect radiator, the energy emitted per unit time is H = AσT⁴, the Stefan-Boltzmann law, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. For a real body, H = AeσT⁴, where e is the dimensionless emissivity. A body also receives radiation from its surroundings, so the net rate of loss is H = eσA(T⁴ - T_s⁴). Newton's law of cooling states that the rate of loss of heat of a body is directly proportional to the difference in temperature between the body and its surroundings: dQ/dt = -k(T₂ - T₁). It holds for small temperature differences, and leads to log_e(T₂ - T₁) = -Kt + c.

• Wien's displacement lawλ_m T = constant = 2.9 × 10⁻³ m K
• Stefan-Boltzmann lawH = AσT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
• For a real bodyH = AeσT⁴, where e is the emissivity
• Net lossH = eσA(T⁴ - T_s⁴)
• Newton's law of coolingdQ/dt = -k(T₂ - T₁), valid for small temperature differences
• Cooling equationlog_e(T₂ - T₁) = -Kt + c