Thermal Properties of Matter: NEET notes

1. Temperature, heat and thermometer scales

NCERT §10.1, §10.2, §10.3

• Temperature says how hot or cold a body is, in numbers. Touch alone is a poor guide: skin can judge only roughly, so a measuring device is needed.
• A glass of iced water warms up on a hot day and a cup of hot tea cools down on the same table. In both cases energy moves from the hotter body to the colder one.
• Heat is the energy that passes between two systems, or between a system and its surroundings, because their temperatures differ. Its SI unit is the joule (J).
• The SI unit of temperature is the kelvin (K); the degree Celsius (°C) is the everyday unit. Heating a body can raise its temperature, make it expand or change its state.
• A thermometer uses some property of a material that changes with temperature. Liquid-in-glass thermometers use the volume of mercury or alcohol, which changes nearly linearly with temperature over a wide range.
• A standard scale needs two fixed reference points. Every material changes size with temperature, so the fixed points are tied to events that always recur at one temperature: pure water freezing (ice point) and boiling (steam point) under standard pressure.
• On the Fahrenheit scale the ice and steam points are 32 °F and 212 °F, with 180 equal divisions between them. On the Celsius scale they are 0 °C and 100 °C, with 100 divisions.
• A graph of t_F against t_C is a straight line, which gives (t_F − 32)/180 = t_C/100, or t_F = (9/5)t_C + 32.
• A change of 1 °C equals a change of 1.8 °F. Body temperature 37 °C is (9/5)(37) + 32 = 98.6 °F; −40 °C and −40 °F are the same temperature.

2. Ideal-gas equation and absolute temperature

NCERT §10.4

• Liquid-in-glass thermometers made with different liquids agree at the fixed points but can disagree in between, because the liquids expand differently. A gas thermometer reads the same whichever gas it holds, since all gases at low density behave alike.
• Boyle's law (Robert Boyle, 1627–1691): at fixed temperature, PV = constant for a given amount of gas at low density.
• Charles' law (Jacques Charles, 1747–1823): at fixed pressure, V/T = constant.
• The two combine into the ideal-gas equation PV = μRT. Here μ counts moles of gas, and R = 8.31 J mol⁻¹ K⁻¹ is the universal gas constant.
• A constant-volume gas thermometer uses the pressure of a fixed volume of gas: P ∝ T. Real gases liquefy at low temperature, but the straight P–t lines extended backwards all reach P = 0 at one temperature.
• That temperature, −273.15 °C, is absolute zero. It is the basis of the Kelvin scale, named after Lord Kelvin, on which the triple point of water is 273.16 K.
• A kelvin and a degree Celsius are the same size, so a temperature difference has the same value in both. Only the zero differs: T = t_C + 273.15.
• So 0 °C = 273.15 K and 100 °C = 373.15 K; in rough work the 0.15 is often dropped.

3. Thermal expansion

NCERT §10.5

• Most substances expand when heated and contract when cooled; the rise in size is thermal expansion. A tight metal lid loosens under hot water, mercury climbs a thermometer, and a partly blown balloon in warm water swells.
• Linear expansion: a rod of length l grows by Δl when its temperature rises by ΔT, with Δl/l = α_l ΔT. α_l is the coefficient of linear expansion, a property of the material.
• α_l in units of 10⁻⁵ K⁻¹, smallest first: lead 0.29, pyrex glass 0.32, iron 1.2, gold 1.4, copper 1.7, brass 1.8, silver 1.9, aluminium 2.5. Metals expand more than glass: copper about five times pyrex.
• Area expansion: a flat sheet's area grows by Δa/a = 2α_l ΔT, so the coefficient of area expansion is 2α_l.
• Volume expansion: ΔV/V = α_V ΔT, with α_V the coefficient of volume expansion. It is not strictly a constant: it depends on temperature and levels off only at high temperature, as the curve for copper shows.
• α_V in K⁻¹: aluminium 7 × 10⁻⁵, brass 6 × 10⁻⁵, iron 3.55 × 10⁻⁵, glass (ordinary) 2.5 × 10⁻⁵, pyrex 1 × 10⁻⁵, hard rubber 2.4 × 10⁻⁴, invar 2 × 10⁻⁶, paraffin 58.8 × 10⁻⁵, mercury 18.2 × 10⁻⁵, water 20.7 × 10⁻⁵, ethanol 110 × 10⁻⁵.
• For an isotropic solid α_V = 3α_l: a cube of side l heated by ΔT becomes (l + Δl)³ ≈ l³ + 3l²Δl, so ΔV/V = 3Δl/l = 3α_l ΔT.
• Gases expand far more than solids or liquids. For an ideal gas at constant pressure PΔV = μRΔT, which gives α_V = 1/T: about 3.7 × 10⁻³ K⁻¹ at 0 °C, falling as T rises, and about 3300 × 10⁻⁶ K⁻¹ near room temperature, much larger than for any solid or liquid.
• A thin plate expands like a magnified photograph: a hole in it grows too, because every length in the plate grows in the same ratio.

4. Anomalous expansion of water and thermal stress

NCERT §10.5

• Water does not follow the usual rule between 0 °C and 4 °C: it contracts on heating in this range. From 4 °C upwards it expands on heating like other liquids.
• So water has its largest density at 4 °C. Its volume is least there and the density falls on either side.
• Consequence for lakes and ponds in winter: water cooled at the surface sinks until the whole body reaches 4 °C. Colder water then stays on top, and the lake freezes from the surface downwards.
• The ice layer and the cold water above the depths act as insulators, so the water at the bottom stays near 4 °C and water life survives the winter. If water behaved normally, lakes would freeze from the bottom up.
• Thermal stress: a rod whose ends are held fixed cannot expand when heated, so its supports compress it. The compressive strain equals the expansion that was prevented, αΔT.
• Stress = Y × strain = YαΔT. For a steel rail 5 m long and 40 cm² in section, warmed by 10 °C with α = 1.2 × 10⁻⁵ K⁻¹ and Y = 2 × 10¹¹ N m⁻²: strain 1.2 × 10⁻⁴, stress 2.4 × 10⁷ N m⁻², force 2.4 × 10⁷ × 40 × 10⁻⁴ ≈ 10⁵ N. This is why rails and bridges have expansion gaps.
• A blacksmith fixes an iron ring on the wooden rim of a horse-cart wheel. At 27 °C the ring's diameter is 5.231 m and the rim's is 5.243 m; with α = 1.20 × 10⁻⁵ K⁻¹ the ring must be heated to about 218 °C. It fits hot and grips the rim tightly as it cools.
• Working for the ring: ΔL = 5.243 − 5.231 = 0.012 m = α L ΔT, so ΔT = 0.012/(1.20 × 10⁻⁵ × 5.231) ≈ 191.2 K, and T = 27 + 191.2 ≈ 218 °C.

5. Specific heat capacity

NCERT §10.6

• Heating water on a steady burner: raising it by 40 °C takes about twice as long as raising the same water by 20 °C, and a 20 °C rise for double the mass also takes twice as long. Mustard oil of the same mass heats faster than water.
• So the heat needed depends on the mass, the temperature rise and the substance. The heat capacity S = ΔQ/ΔT is the heat needed to raise a body's temperature by one unit.
• Specific heat capacity s = (1/m)(ΔQ/ΔT), in J kg⁻¹ K⁻¹: the heat per unit mass per unit temperature rise. It depends on the substance and its temperature, not on the amount.
• Specific heat capacity in J kg⁻¹ K⁻¹: aluminium 900.0, carbon 506.5, copper 386.4, lead 127.7, silver 236.1, tungsten 134.4, water 4186.0, ice 2060, glass 840, iron 450, kerosene 2118, edible oil 1965, mercury 140.
• Molar specific heat capacity C = (1/μ)(ΔQ/ΔT), in J mol⁻¹ K⁻¹, uses moles instead of mass.
• For a gas, the conditions under which heat is added matter. C_p is measured at constant pressure and C_v at constant volume; C_p is larger.
• Molar values (J mol⁻¹ K⁻¹), C_p / C_v: He 20.8 / 12.5, H₂ 28.8 / 20.4, N₂ 29.1 / 20.8, O₂ 29.4 / 21.1, CO₂ 37.0 / 28.5.
• Water has the highest specific heat among these substances. That is why it is used as the coolant in car radiators and in hot-water bags.
• Because of water's large s, the sea warms and cools slowly compared with land. Coastal climates stay mild, while deserts heat up quickly by day and cool quickly at night.

6. Calorimetry

NCERT §10.7

• A system is isolated when it exchanges no heat with its surroundings. When bodies at different temperatures are placed in contact inside such a system, heat flows from the hot ones to the cold ones until they share one temperature.
• Principle of calorimetry: in an isolated system, heat lost by the hot bodies = heat gained by the cold bodies.
• A calorimeter is the device for measuring heat. It is a metal vessel with a stirrer of the same metal, usually copper or aluminium, placed inside a wooden jacket with glass wool between them to keep heat from escaping.
• A thermometer passes through the lid into the liquid. The metal vessel itself takes part in the heat exchange, so its heat must be counted as well as the liquid's.
• Heat changes are found from Q = m s ΔT for each body. For mixtures the unknown is usually a specific heat or the final temperature.
• Worked example: an aluminium sphere of 0.047 kg at 100 °C is dropped into a copper calorimeter of 0.14 kg holding 0.25 kg of water at 20 °C; the final temperature is 23 °C.
• Heat gained by water and calorimeter = (0.25 × 4.18 × 10³ + 0.14 × 0.386 × 10³) × 3 = 3297.1 J. Heat lost by the sphere = 0.047 × s_Al × 77. Equating gives s_Al ≈ 911 J kg⁻¹ K⁻¹ = 0.911 kJ kg⁻¹ K⁻¹.
• Losses to the surroundings make a real measurement less exact, which is why the insulation, lid and quick readings matter.

7. Change of state

NCERT §10.8

• Matter exists as solid, liquid or gas. A change from one to another is a change of state, and it happens by exchanging heat with the surroundings.
• Melting (fusion) turns a solid into a liquid; freezing is the reverse. While ice melts the temperature stays fixed until all of it has melted: solid and liquid coexist in thermal equilibrium.
• The melting point is the temperature at which the solid and liquid are in thermal equilibrium. It is a property of the substance and depends on pressure; at standard atmospheric pressure it is the normal melting point.
• Regelation: a wire with a 5 kg block hanging from each end sinks through a slab of ice. The pressure under the wire lowers the melting point so ice melts there, and the water freezes again above the wire; the slab stays in one piece.
• Skating works because the pressure under the skate melts a thin layer of snow or ice, and that water acts as a lubricant.
• Vaporisation turns a liquid into vapour. While water boils, liquid and vapour coexist and the temperature stays fixed until all the liquid has changed; that temperature is the boiling point.
• The boiling point rises with pressure. In a flask of water taken off the flame and closed, pouring cold water on the flask lowers the vapour pressure inside, and the water boils again at a lower temperature.
• On hills the air pressure is lower, so water boils below 100 °C and food takes longer to cook. A pressure cooker raises the pressure, so water boils above 100 °C and food cooks faster. The normal boiling point is the value at standard atmospheric pressure.
• Sublimation is a direct change from solid to vapour without melting; the reverse is also called sublimation. Dry ice (solid CO₂) and iodine sublime.
• On a pressure–temperature (phase) diagram the sublimation, fusion and vaporisation curves separate the solid, liquid and vapour regions. They meet at the triple point, where all three phases coexist; for water it is 273.16 K at about 611 Pa (roughly 0.006 atm).

8. Latent heat

NCERT §10.8.1

• During a change of state, heat goes in (or out) but the temperature does not change. The heat per unit mass needed for the change is the latent heat L, so Q = mL. Its SI unit is J kg⁻¹, and it depends on pressure.
• L_f, the latent heat of fusion, applies to solid ↔ liquid; L_v, the latent heat of vaporisation, applies to liquid ↔ gas. The same amount of heat is released when the change runs the other way.
• For water at standard pressure: L_f = 3.33 × 10⁵ J kg⁻¹ and L_v = 22.6 × 10⁵ J kg⁻¹. Melting 1 kg of ice at 0 °C takes 3.33 × 10⁵ J; turning 1 kg of water at 100 °C into steam takes 22.6 × 10⁵ J.
• Steam at 100 °C scalds more badly than water at 100 °C: as it condenses on skin it gives up its latent heat of vaporisation as well.
• Melting point, L_f, boiling point, L_v (L in 10⁵ J kg⁻¹): ethanol −114 °C, 1.0, 78 °C, 8.5; gold 1063 °C, 0.645, 2660 °C, 15.8; lead 328 °C, 0.25, 1744 °C, 8.67; mercury −39 °C, 0.12, 357 °C, 2.7; nitrogen −210 °C, 0.26, −196 °C, 2.0; oxygen −219 °C, 0.14, −183 °C, 2.1; water 0 °C, 3.33, 100 °C, 22.6.
• A temperature–heat graph for heating ice to steam has sloping parts (temperature rising, Q = msΔT) and flat parts (state changing, Q = mL). The slope of a sloping part is 1/(ms), so ice rises faster than water for the same heat.
• Worked example: a 0.15 kg block of ice at 0 °C goes into 0.30 kg of water at 50 °C; the mixture settles at 6.7 °C. Heat lost by water = 0.30 × 4186 × 43.3 = 54376.14 J; heat to warm the melted ice = 0.15 × 4186 × 6.7 = 4206.93 J; so 0.15 L_f = 50169.21 J and L_f ≈ 3.34 × 10⁵ J kg⁻¹.
• Worked example: turning a 3 kg ice block that starts at −12 °C into steam at 100 °C, with s_ice = 2100 J kg⁻¹ K⁻¹, s_water = 4186 J kg⁻¹ K⁻¹, L_f = 3.35 × 10⁵ J kg⁻¹, L_steam = 2.256 × 10⁶ J kg⁻¹. Warm ice 75600 J, melt 1005000 J, warm water 1255800 J, boil 6768000 J; total 9104400 J ≈ 9.1 × 10⁶ J.
• In that example boiling alone takes about three-quarters of the total heat, far more than warming the water from 0 °C to 100 °C.

9. Conduction

NCERT §10.9, §10.9.1

• Heat moves in three ways: conduction, convection and radiation. Conduction passes heat between neighbouring parts of a body through molecular collisions, with no flow of matter; it is the usual way heat moves in solids.
• A bar of length L and cross-section A with its ends held at T_C and T_D (T_C > T_D) reaches a steady state in which the temperature falls uniformly along it. The heat current is then H = KA(T_C − T_D)/L.
• K is the thermal conductivity, in W m⁻¹ K⁻¹ (J s⁻¹ m⁻¹ K⁻¹). A large K means a good conductor.
• K in W m⁻¹ K⁻¹. Metals, lowest first: mercury 8.3, lead 34.7, steel 50.2, brass 109, aluminium 205, copper 385, silver 406. Non-metals: felt and glass wool 0.04, wood 0.12, insulating brick 0.15, body fat 0.20, concrete, glass and water 0.8, ice 1.6. Gases: argon 0.016, air 0.024, hydrogen 0.14.
• Everyday uses: some cooking pots have copper-coated bottoms to spread heat evenly; plastic foam insulates because it traps pockets of air; a concrete roof gets very hot in summer, so a layer of earth or foam insulation keeps rooms cooler. In nuclear reactors elaborate heat-transfer systems carry away the heat that fission produces.
• Worked example: a steel rod 15.0 cm long (K = 50.2) and a copper rod 10.0 cm long (K = 385) are joined end to end, sides insulated, the steel end at 300 °C and the copper end at 0 °C; the steel rod has twice the copper's cross-section. In steady state the same heat current crosses both, which gives the junction temperature T = 44.4 °C.
• Working: 50.2 × 2A × (300 − T)/0.15 = 385 × A × (T − 0)/0.10, i.e. 669.3(300 − T) = 3850 T, so T = 200800/4519.3 ≈ 44.4 °C.
• Worked example: an iron rod (K = 79) and a brass rod (K = 109), each 0.1 m long and 0.02 m² in area, are joined end to end with the free ends at 373 K and 273 K. The junction settles at T₀ = (K₁T₁ + K₂T₂)/(K₁ + K₂) = 315 K.
• The pair behaves like a single rod of double length with K′ = 2K₁K₂/(K₁ + K₂) = 91.6 W m⁻¹ K⁻¹, and the heat current through it is H = 916.1 W.

10. Convection

NCERT §10.9.2

• Convection carries heat by the actual movement of matter. It can happen only in fluids.
• Natural convection is driven by gravity: fluid heated from below expands, becomes less dense, and is pushed up by buoyancy; colder, denser fluid sinks to replace it. The circulation repeats and carries heat upward.
• Forced convection moves the fluid with a pump or fan. Examples: forced-air heating in homes, the human circulatory system with the heart as the pump, and the cooling system of a car engine.
• The body's blood circulation is forced convection that helps keep body temperature steady.
• Sea breeze by day: land heats faster than water, the air above land warms and rises, and cooler air from the sea moves in to take its place; the loop closes aloft.
• Land breeze at night: land loses heat faster, the water surface is now warmer, and the whole cycle reverses.
• Trade wind: steady surface wind blowing from the north-east towards the equator. Near the equator surface air is hot and rises, while polar air aloft is cool.
• Earth's rotation changes the simple loop. Air near the equator moves eastward at about 1600 km/h while air near the poles has almost no such speed, so the air descends at about 30° N rather than at the poles and returns to the equator.

11. Radiation and blackbody radiation

NCERT §10.9.3, §10.9.4

• Radiation needs no medium: heat from the sun crosses the vacuum of space. It travels as electromagnetic waves at 3 × 10⁸ m s⁻¹, and the part emitted because of a body's temperature is called thermal radiation.
• A body that absorbs well also emits well. Black surfaces absorb most of the radiation falling on them; white or shiny surfaces reflect most of it.
• White clothes keep us cooler in summer; dark clothes help in winter. Cooking pots are often blackened at the bottom so that they take in more heat from the fire.
• A thermos (Dewar) flask keeps liquids hot or cold with a double-walled glass vessel. The facing walls are silvered to reflect radiation, the gap between them is evacuated to stop conduction and convection, and the vessel rests on insulating supports such as cork.
• Every body emits radiation over a continuous range of wavelengths. For a blackbody at temperature T the intensity peaks at λ_m given by Wien's displacement law: λ_m T = 2.9 × 10⁻³ m K.
• So a hotter body peaks at a shorter wavelength: iron in a flame glows dull red, then reddish yellow, then white. The moon's peak near 14 μm gives a surface temperature of about 200 K; the sun's peak at 4753 Å gives about 6100 K for its surface, not its interior.
• Blackbody curves depend only on temperature, not on the size, shape or material of the body. Explaining them led to quantum physics.
• Stefan–Boltzmann law: a perfect radiator of area A at absolute temperature T emits H = AσT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. Real bodies emit H = AeσT⁴, where the emissivity e is between 0 and 1; lamp black comes close to e = 1, a tungsten filament has e ≈ 0.4.
• A body at T in surroundings at T_s also absorbs radiation, so the net loss is H = eσA(T⁴ − T_s⁴).
• A person with skin area 1.9 m², skin at 28 °C (301 K), room at 22 °C (295 K) and e = 0.97 loses H = 0.97 × 5.67 × 10⁻⁸ × 1.9 × (301⁴ − 295⁴) ≈ 66.4 W by radiation, more than half the 120 W the body produces at rest. Arctic clothing adds a thin shiny layer to reflect this radiation back.

12. Newton's law of cooling

NCERT §10.10

• Hot milk left on a table cools until it reaches room temperature. Measuring water heated about 40 °C above the room every minute shows the cooling is fast at first and slows as the gap to room temperature shrinks.
• Newton's law of cooling: for small temperature differences, the rate at which a body loses heat is proportional to the difference between its temperature T₂ and that of its surroundings T₁: −dQ/dt = k(T₂ − T₁).
• k depends on the area and nature of the surface. With dQ = ms dT₂ for a body of mass m and specific heat s: dT₂/dt = −K(T₂ − T₁), where K = k/(ms).
• Integrating: ln(T₂ − T₁) = −Kt + c, or T₂ = T₁ + C′e^(−Kt). The excess temperature decays exponentially with time.
• So a graph of ln(T₂ − T₁) against t is a straight line with negative slope. This is checked with a copper calorimeter of hot water inside a double-walled vessel whose walls hold water at a steady T₁.
• The law covers the combined loss by conduction, convection and radiation when the temperature difference is small: a radiator warming a room, heat leaking through a wall, a cup of tea cooling.
• Worked example: food in a pan cools from 94 °C to 86 °C in 2 min in a room at 20 °C. Average 90 °C, excess 70 °C: 8/2 = 70K, so K = 4/70 per minute.
• Cooling from 71 °C to 69 °C: average 70 °C, excess 50 °C, so 2/t = 50K = 50 × 4/70, which gives t = 0.7 min = 42 s.
• A shortcut for such problems: (T_a − T_b)/t = K[(T_a + T_b)/2 − T_s], which uses the average temperature over the interval.

Must-know facts

1. Heat is energy moving because of a temperature difference; unit joule.
2. Ice and steam points: 0 °C / 100 °C and 32 °F / 212 °F; t_F = (9/5)t_C + 32.
3. PV = μRT with R = 8.31 J mol⁻¹ K⁻¹; absolute zero is −273.15 °C.
4. T = t_C + 273.15; a kelvin and a degree Celsius are the same size.
5. Δl/l = α_l ΔT; area coefficient 2α_l; α_V = 3α_l.
6. For an ideal gas at constant pressure α_V = 1/T (3.7 × 10⁻³ K⁻¹ at 0 °C).
7. Water contracts on heating from 0 °C to 4 °C; it is densest at 4 °C, so lakes freeze from the top.
8. Thermal stress in a clamped rod = YαΔT.
9. Q = msΔT; water's s = 4186 J kg⁻¹ K⁻¹, the largest in the table.
10. C_p > C_v for a gas; molar heat capacity is per mole.
11. Calorimetry: heat lost = heat gained in an isolated system.
12. Temperature stays fixed during melting and boiling; Q = mL.
13. Water: L_f = 3.33 × 10⁵ J kg⁻¹, L_v = 22.6 × 10⁵ J kg⁻¹.
14. Higher pressure lowers ice's melting point (regelation) and raises water's boiling point (pressure cooker).
15. Triple point of water: 273.16 K, where solid, liquid and vapour coexist.
16. H = KAΔT/L; the same heat current crosses every rod in series.
17. Convection needs a fluid; sea breeze by day, land breeze by night.
18. Wien: λ_m T = 2.9 × 10⁻³ m K.
19. Stefan: H = AeσT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴, T in kelvin.
20. Good absorbers are good emitters; a thermos flask cuts all three modes of transfer.
21. Newton's cooling: rate ∝ (T₂ − T₁); ln(T₂ − T₁) against t is a falling straight line.

Common traps

Formulas

Key terms

Heat

Energy transferred between bodies because of a temperature difference.

Temperature

A number that measures how hot or cold a body is.

Absolute zero

−273.15 °C, the zero of the Kelvin scale, found by extending gas-thermometer lines to P = 0.

Coefficient of linear expansion

Fractional increase in length per kelvin rise, α_l = Δl/(l ΔT).

Anomalous expansion

Water's contraction on heating between 0 °C and 4 °C.

Thermal stress

Stress set up when a body is prevented from expanding or contracting.

Specific heat capacity

Heat needed per unit mass per unit temperature rise.

Calorimeter

An insulated metal vessel with stirrer used to measure heat exchanged.

Regelation

Melting under pressure and refreezing when the pressure is removed.

Sublimation

Direct change between solid and vapour without passing through the liquid state.

Triple point

The one temperature and pressure at which solid, liquid and vapour coexist.

Latent heat

Heat per unit mass absorbed or released during a change of state at constant temperature.

Thermal conductivity

K in H = KAΔT/L; how readily a material conducts heat.

Convection

Heat transfer by the bulk movement of a fluid.

Emissivity

The fraction of a perfect radiator's emission that a surface emits, between 0 and 1.

Blackbody

An ideal body that absorbs all radiation falling on it and emits the maximum possible radiation at its temperature.