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Class XI · Chapter 10

Thermal Properties of Matter

Why a thermometer works, why bridges have expansion joints, why ice stays at 0°C while it melts, and the three genuinely different ways heat actually moves.

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1Temperature and Heat

These two words are often used interchangeably in everyday speech, but they mean genuinely different things in physics. Temperature is a measure of the average kinetic energy of a substance's particles — how "hot" something is, in a precise sense. Heat is energy that flows from a hotter object to a cooler one because of that temperature difference. A cup of tea has a temperature; heat is what flows out of it as it cools on the table.

2Measuring Temperature and Temperature Scales

Thermometers work by using some measurable property that changes predictably with temperature — mercury's expansion, a metal strip's bending, or an electrical resistance change.

Converting Between Scales
F = (9/5)C + 32, K = C + 273.15
The Kelvin scale is the SI standard, and it's the only one where zero has real physical meaning — absolute zero, the coldest temperature theoretically possible, where particle motion is at an absolute minimum.

3Ideal Gas Equation and Absolute Temperature

Ideal Gas Equation
PV = nRT
n = number of moles, R = universal gas constant. This single equation is where the Kelvin scale's absolute zero originally came from — extrapolating pressure-vs-temperature data for a gas at constant volume, the pressure would theoretically reach zero at exactly −273.15°C.

4Thermal Expansion

Nearly all materials expand when heated, as increased thermal motion pushes atoms slightly farther apart on average.

Linear Expansion
ΔL = α L ΔT
α = coefficient of linear expansion, specific to each material.
Area and Volume Expansion
ΔA = β A ΔT (β ≈ 2α), ΔV = γ V ΔT (γ ≈ 3α)
This is precisely why bridges and railway tracks include small expansion gaps — without them, thermal expansion on a hot day would buckle the structure with nowhere to go.

5Specific Heat Capacity

Heat and Specific Heat Capacity
Q = m c ΔT
c = specific heat capacity — the heat needed to raise 1 kg of a substance by 1°C (or 1 K). Water has an unusually high specific heat capacity, which is exactly why coastal climates stay milder than inland ones: large bodies of water absorb or release huge amounts of heat with relatively small temperature swings.

6Calorimetry

Principle of Calorimetry In an isolated system with no heat lost to the surroundings, heat lost by hotter objects exactly equals heat gained by cooler ones — a direct application of energy conservation.

This principle is what lets you predict a final equilibrium temperature when substances at different temperatures are mixed, without needing to track the detailed process moment by moment.

7Change of State and Latent Heat

Heat a solid enough, and it eventually melts; heat a liquid enough, and it boils. During these phase transitions, temperature stays completely constant even as heat continues flowing in — that energy is going into breaking intermolecular bonds, not increasing kinetic energy (and therefore temperature).

Latent Heat
Q = m L
L = latent heat (of fusion, for melting; of vaporisation, for boiling) — the energy per unit mass needed for the phase change alone, with no temperature change involved. This is exactly why ice at 0°C stays at 0°C throughout melting, and why steam at 100°C can cause far worse burns than boiling water at the same temperature — steam carries substantially more energy, released as latent heat on contact with skin.

8Heat Transfer

Heat moves from hot to cold by three genuinely distinct mechanisms:

Conduction
H = K A (T₁ − T₂) / L
K = thermal conductivity. Heat passed directly through a material via particle collisions, with no bulk motion of the material itself — a metal spoon in hot soup heating up at the handle end.
  • Convection: heat carried by the actual bulk movement of a fluid (liquid or gas) — warm air rising, driving weather patterns and boiling water's circulating currents.
  • Radiation: heat transferred as electromagnetic waves, needing no medium at all — this is how the Sun's warmth reaches Earth across the vacuum of space.
Stefan-Boltzmann Law (Radiation)
E = σ T⁴
Energy radiated per unit area per unit time by an ideal (black body) radiator, σ = Stefan's constant. The steep fourth-power dependence means even modest temperature increases dramatically boost radiated energy.

9Newton's Law of Cooling

Newton's Law of Cooling
dT/dt = −k (T − Ts)
Ts = surrounding temperature. For a small temperature difference, the rate of cooling is proportional to that difference — a hot object cools quickly at first, then more slowly as it approaches room temperature, tapering off rather than cooling at a constant rate.

Formula Summary

Celsius to Kelvin
K = C + 273.15
Ideal Gas Equation
PV = nRT
Linear Expansion
ΔL = αLΔT
Heat (Temperature Change)
Q = mcΔT
Latent Heat
Q = mL
Conduction
H = KA(T₁−T₂)/L
Radiation
E = σT⁴
Newton's Cooling Law
dT/dt = −k(T−Tₛ)

Solved Examples

Example 1 · Linear Thermal Expansion

A steel rod of length 2 m at 20°C is heated to 100°C. Find the increase in length. (αsteel = 1.2×10⁻⁵ /°C)

Solution: ΔL = αLΔT = 1.2×10⁻⁵ × 2 × (100 − 20) = 1.2×10⁻⁵ × 2 × 80 ≈ 1.92×10⁻³ m ≈ 1.92 mm.

Example 2 · Calorimetry

200 g of water at 80°C is mixed with 300 g of water at 20°C. Find the final equilibrium temperature, assuming no heat loss to the surroundings.

Solution: Heat lost by hot water = heat gained by cold water: 200(80 − Tf) = 300(Tf − 20).

16000 − 200Tf = 300Tf − 6000 → 22000 = 500Tf → Tf = 44°C.

Quick Check

1. The SI unit of temperature is:
Celsius
Fahrenheit
✓ Kelvin (correct)
Joule
2. During a change of state (like melting ice), the temperature of the substance:
Rises steadily
Falls steadily
✓ Remains constant (correct)
Oscillates
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Mechanical Properties of Fluids

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Thermodynamics

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