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Water freezes at 0°C = 32°F and boils at 100°C = 212°F. There are 180 Fahrenheit divisions and 100 Celsius divisions between the two fixed points.

Absolute zero = −273.15°C = 0 K. The Kelvin scale has the same unit size as Celsius. Ice melts at 273.15 K = 0°C; water boils at 373.15 K = 100°C.

R is the universal gas constant = 8.31 J mol⁻¹ K⁻¹. This combines Boyle's Law (PV = const at constant T) and Charles' Law (V/T = const at constant P).

α_l is the fractional change in length per unit change in temperature. SI unit: K⁻¹. Relationship: α_V = 3α_l for isotropic solids.

For a cube of side l expanding in all directions: ΔV = (l+Δl)³ − l³ ≈ 3l²·Δl = 3Vα_l·ΔT. Similarly, coefficient of area expansion α_A = 2α_l.

Water contracts on heating from 0°C to 4°C (anomalous behaviour). Maximum density = 1000 kg/m³ occurs at 4°C. This causes lakes to freeze from the top, preserving aquatic life.

SI unit of specific heat capacity: J kg⁻¹ K⁻¹. Water has the highest specific heat capacity ≈ 4186 J kg⁻¹ K⁻¹. This makes it an excellent coolant in radiators and hot water bags.

During a phase change, heat supplied is used to break intermolecular bonds (phase change), NOT to raise temperature. Both phases coexist in thermal equilibrium at the phase change temperature.

3.33 × 10⁵ J is needed to melt 1 kg ice at 0°C. The much larger L_v = 22.6 × 10⁵ J/kg explains why steam burns are more severe than boiling water burns.

In an isolated system, heat lost by hot body = heat gained by cold body. This is conservation of energy applied to thermal systems. The total heat content remains constant when no heat escapes to surroundings.

K = thermal conductivity (SI unit: W m⁻¹ K⁻¹ or J s⁻¹ m⁻¹ K⁻¹). Metals have high K (silver: 406, copper: 385), insulators have low K (glass wool: 0.04). Heat current H is analogous to electric current.

Conduction (molecular vibration transfer) and convection (bulk fluid motion) both need a material medium. Radiation is electromagnetic waves — it travels through vacuum (e.g., Sun's heat reaching Earth).

For a body with emissivity e: H = AeσT⁴. The net heat loss from a body at T surrounded by T_s is: H = Aeσ(T⁴ − T_s⁴). e = 1 for perfect blackbody.

Higher temperature → shorter wavelength of peak emission. This explains why hot iron glows dull red → reddish yellow → white hot as temperature rises. Used to estimate stellar surface temperatures.

Valid for small temperature differences only. T₂ = body temperature, T₁ = surrounding temperature. Mathematically: T₂(t) = T₁ + C′e^(−Kt), an exponential decay curve.

A pressure cooker increases internal pressure → raises boiling point above 100°C → food cooks at higher temperature → faster cooking. At high altitudes, lower atmospheric pressure lowers the boiling point → cooking is slower.

Sublimation: solid → vapour directly, without passing through liquid phase. Examples: dry ice (solid CO₂), iodine, naphthalene. During sublimation, solid and vapour coexist in thermal equilibrium.

Convection involves bulk motion of fluid — hot fluid rises (less dense), cool fluid sinks. Requires gravity (natural convection) or pump (forced convection). Examples: sea breeze, trade winds, human circulatory system.

Skate blades exert high pressure → ice melts below melting point → water acts as lubricant. When pressure is removed, water refreezes. This is regelation. Ice has an anomalous property: its melting point decreases with increasing pressure.

Diatomic gases (H₂, N₂, O₂) have higher C_v (~20.8) because they have additional rotational degrees of freedom. Polyatomic gases have even higher values.

Absolute zero = −273.15°C = 0 K. At this temperature, an ideal gas would have zero volume/pressure (extrapolated). It is the temperature of minimum molecular activity — no substance can be cooled below this.

When expansion is prevented, the rod experiences compressive strain α_l·ΔT. The resulting thermal stress = Y × strain = Yα_lΔT. This can be enormous in railway tracks — hence expansion gaps are provided.

Water has the highest specific heat capacity (4186 J/kg·K) among common substances. This is why: coastal climates are mild, water is used as coolant in car radiators, and the sea breeze effect occurs at beaches.

Triple point of water = 273.16 K at 6.11 × 10⁻³ Pa. At this unique P-T combination, all three phases (solid, liquid, vapour) coexist. It is preferred over melting/boiling points as a fixed point because it is unique and reproducible.

All are correct applications: white clothes reflect solar radiation in summer (less absorption). Blackened utensil bottoms absorb maximum heat from fire. Dark clothes absorb more solar radiation in winter for warmth. Good absorbers are also good emitters (Kirchhoff's Law).

The tape has expanded, so each scale division is now slightly larger than 1 cm, making the actual rod slightly longer than 63.0 cm.

NCERT value: s_Al = 900 J/kg·K. Our calculated value is close, small difference due to heat losses.

This matches the standard value: L_f(water) = 3.33 × 10⁵ J/kg.

A force of ~10⁵ N (10 tonnes!) can easily bend two rails. This is why railway tracks have expansion gaps.

In steady state, heat current through both rods must be equal:

Using exact NCERT values: T = 44.4°C. Heat flows faster through copper (high K), so junction temperature is closer to the cold end.

About 1.46 kg of ice can be melted by the copper block. In reality the final temperature of the system may be above 0°C depending on relative amounts.

Temperature rises by about 103°C. Starting at room temperature (~27°C), the block would reach ~130°C — hot enough to cause burns!

Since density ρ = m/V and mass is constant:

Density decreases by about 1.47% for a 30°C rise. This is why hot glycerine is less dense and rises in convection currents.