Thermal Properties of Matter Class 11 Physics Quick Recall (Short Notes 2026-27)

Thermal Properties and Calorimetry Visual

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Thermal Expansion: ΔL = α L ΔT. Relation: β = 2α; γ = 3α.

Calorimetry: Heat gained = Heat lost. Specific heat Q = mcΔT. Latent heat Q = mL.

Conduction: Heat current H = KA(T1 - T2)/L.

Stefan's Law: Power P = σ A T⁴.

Newton's Law of Cooling: Rate of cooling dθ/dt ∝ (θ - θ_s). 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

Heat is a fundamental form of energy that drives the physical and chemical processes of our universe. From the expansion of railway tracks in summer to the cooling of a cup of tea, the "Thermal Properties of Matter" govern how substances respond to changes in temperature. This chapter transitions from the macro-mechanics of forces to the micro-mechanics of molecular vibrations and energy transfer. In this "Comprehensive" guide, we provide exhaustive derivations for the relationship between thermal expansion coefficients, a rigorous mathematical analysis of Newton’s Law of Cooling, and the foundational principles of Calorimetry—essential for top-tier competitive exams like JEE and NEET.

1. Temperature and Heat

Temperature: A measure of the average kinetic energy of molecules.
Heat: Energy in transit due to a temperature difference.
Triple Point of Water: The unique temperature (273.16 K) and pressure where water exists in all three phases in equilibrium.

2. Thermal Expansion: Concepts and Derivations

Most substances expand when heated. We define three coefficients of expansion:

Linear (α): ΔL = L α ΔT.
Areal (β): ΔA = A β ΔT.
Volume (γ): ΔV = V γ ΔT.

Derivation: Relation between α, β, and γ

I. Relation between α and β:

Consider a square of side L. A = L².
A' = (L + ΔL)² = L² + 2LΔL + (ΔL)².
Ignoring the small term (ΔL)²: A' ≈ L² + 2L(LαΔT) = L²(1 + 2αΔT).
Comparing with A' = L²(1 + βΔT):
- β = 2α. (Proven)

II. Relation between α and γ:

Consider a cube of side L. V = L³.
V' = (L + ΔL)³ = L³ + 3L²ΔL + ... (ignoring higher-order terms).
V' ≈ L³ + 3L²(LαΔT) = L³(1 + 3αΔT).
Comparing with V' = L³(1 + γΔT):
- γ = 3α. (Proven) Conclusion: α : β : γ = 1 : 2 : 3.

3. Calorimetry: The Science of Mixing

Principle: Heat Lost by Hot Body = Heat Gained by Cold Body.

Specific Heat (s): Q = msΔT.
Molar Specific Heat (C): Q = nCΔT.
Latent Heat (L): Q = mL (Energy required for phase change at constant temperature).

4. Heat Transfer: Conduction, Convection, Radiation

Conduction: Heat flow through solids. dQ/dt = KA (T1-T2) / d.
Convection: Heat flow via fluid movement.
Radiation: Heat flow via electromagnetic waves. (Prevents need for a medium).

5. Derivation: Newton’s Law of Cooling

Statement: The rate of loss of heat of a body is directly proportional to the difference in temperature between the body and its surroundings.

Derivation:

-dQ/dt = k(T - Ts).
Since Q = msT, then dQ = ms dT.
-ms (dT/dt) = k(T - Ts).
dT / (T - Ts) = - (k/ms) dt.
Integrating both sides:
- ln(T - Ts) = -Kt + C.
Taking antilog:
- (T - Ts) = (T₀ - Ts) e⁻ᴷᵗ. (Proven) Result: The temperature of a body decays exponentially over time toward the surrounding temperature.

6. Stefan-Boltzmann and Wien’s Laws

Stefan’s Law: Radiant energy E = σ A T⁴.
Wien’s Displacement Law: λ_max T = b (Constant). As temperature increases, the peak wavelength shifts toward shorter (bluer) values.

Comprehensive Exam Strategy (Q&A)

Q1: Why is the anomalous expansion of water crucial for aquatic life? Answer: Water has maximum density at 4°C. In winter, as surface water cools toward 4°C, it sinks, bringing oxygen down. Once the surface hits 0°C and freezes, the ice (being less dense) floats and acts as an insulator, keeping the bottom water at 4°C and allowing fish to survive.

Q2: Which reflects more heat—a black body or a shiny polished surface? Answer: A shiny polished surface. A perfect black body is a perfect absorber (absorptivity = 1), whereas a polished surface reflects most of the incident radiation.

Q3: State the condition under which Newton's Law of Cooling is valid. Answer: It is valid only for small temperature differences between the body and the surroundings (typically ΔT < 30°C) and when heat loss occurs primarily via natural convection.

Related Revision Notes

Conclusion

Thermal properties define the limits of sustainability and efficiency in our world. By mastering the mathematical relationships between expansion, cooling, and radiation, you gain the ability to predict how materials will behave in extreme environments. Master the derivation of Newton’s Law of Cooling and the coefficients of expansion—these are the core thermal principles that power everything from thermometers to heat shields. Stay cool, keep your internal energy balanced, and never reach thermal equilibrium!

Reference: NIST: Thermodynamics and Thermal Properties