Thermal Properties of Matter

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Thermal Properties — Key Facts

Heat and Temperature:

Heat (Q) is energy transferred due to temperature difference. $$Q = mc\Delta T$$ (sensible heat) $$Q = mL$$ (latent heat, no temperature change)

where c = specific heat capacity, L = latent heat.

Ideal Gas Equation: $$PV = nRT$$

where n = number of moles, R = 8.314 J/(mol·K), T = temperature in Kelvin.

For air at STP: P = 1 atm = 1.01 × 10⁵ Pa, T = 273 K

Heat Transfer:

Conduction: $H = \frac{dQ}{dt} = -kA\frac{dT}{dx}$

• k = thermal conductivity (W/m·K)
• Metals have high k; insulators have low k
• Copper: ~400 W/m·K; Air: ~0.02 W/m·K

Convection: Heat transfer by fluid motion (natural or forced)

Radiation: $P = \varepsilon\sigma AT^4$ (Stefan-Boltzmann law)

• σ = 5.67 × 10⁻⁸ W/m²K⁴
• ε = emissivity (0 to 1)

⚡ JEE Exam Tip: During phase change, temperature remains constant. All the heat goes into changing the phase (latent heat). This is why sweating cools you — liquid sweat absorbs heat to vaporise.

---

🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding…

Thermal Expansion:

Type	Formula
Linear	ΔL = αLΔT
Area	ΔA = 2αAΔT
Volume	ΔV = 3αVΔT

where α = coefficient of linear expansion.

Bimetallic Strip: Two metals with different α bonded together. When heated, the one with higher α expands more, causing the strip to bend. Used in thermostats.

Newton’s Law of Cooling: $$\frac{dT}{dt} = -k(T - T_{surr})$$

Solution: $T - T_{surr} = (T_0 - T_{surr})e^{-kt}$

Rate of cooling is proportional to temperature difference.

⚡ JEE Exam Tip: For Newton’s law problems, the time to cool from T₁ to T₂ depends on the average temperature during that interval. Use logarithmic relation: $\ln\frac{T_1 - T_{surr}}{T_2 - T_{surr}} = kt$.

---

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Black Body Radiation:

Perfect black body: absorbs all radiation (ε = 1), emits maximum radiation at any temperature.

Wien’s Displacement Law: $$\lambda_{max} T = b = 2.898 \times 10^{-3} \text{ m·K}$$

As temperature increases, λ_max decreases (shifts toward blue).

Kirchhoff’s Law: Emissivity = Absorptivity at every wavelength and temperature.

Heat Conduction Through Composite Wall:

For slabs in series (areas A, thicknesses L₁, L₂…, thermal conductivities k₁, k₂…): $$H = \frac{\Delta T}{\frac{L_1}{k_1A} + \frac{L_2}{k_2A} + …} = \frac{\Delta T}{R_1 + R_2 + …}$$

where R_i = L_i/(k_iA) = thermal resistance.

Critical Radius of Insulation:

For cylindrical wire: $r_c = \frac{k}{h_{cond}}$

• If r_insulation < r_c: adding insulation increases heat loss
• If r_insulation > r_c: adding insulation decreases heat loss

Entropy:

$$\Delta S \geq \frac{Q}{T} \quad \text{(for any process)}$$

For reversible process: $\Delta S = \oint \frac{dQ_{rev}}{T} = 0$

For irreversible process: $\Delta S > 0$

Carnot Cycle:

Maximum efficiency of any heat engine operating between T_hot and T_cold: $$\eta = 1 - \frac{T_c}{T_h}$$

For refrigerator (COP = cooling effect/work input): $$COP = \frac{T_c}{T_h - T_c}$$

Latent Heat Values:

Substance	Melting Point (°C)	L_f (kJ/kg)	Boiling Point (°C)	L_v (kJ/kg)
Water	0	334	100	2260
Ice (CO₂)	-78.5*	-	-78.5*	571
Oxygen	-219	13	-183	213

*Sublimation

⚡ JEE Advanced 2023 Analysis: Questions on Newton’s law of cooling, combined heat transfer, and entropy calculations appeared in recent papers. For entropy, remember it is a state function — the change depends only on initial and final states, not the path.

---

Content adapted based on your selected roadmap duration. Switch tiers using the pill selector above.