Board exam focus — Thermal Properties of Matter (CBSE & HBSE)

This chapter studies how matter responds to heat: the distinction between temperature and heat, thermal expansion of solids/liquids/gases, specific and latent heat through calorimetry, changes of state, and the three modes of heat transfer (conduction, convection, radiation) together with Newton's law of cooling, the Stefan-Boltzmann law and Wien's displacement law. Both CBSE and HBSE expect conceptual clarity plus numerical fluency.

Temperature, Heat and Thermal Expansion

Temperature vs Heat

Temperature is a measure of the degree of hotness or coldness of a body; it determines the direction of net heat flow between two bodies in contact. Heat (Q) is the energy that flows because of a temperature difference. Heat is energy in transit, measured in joules (or calories).

Trap: A bigger body at lower temperature can contain more internal energy than a small body at higher temperature. Temperature is intensive; heat/internal energy is extensive.

Temperature Scales

The Celsius and Fahrenheit scales are related by:

$$\frac{C}{100}=\frac{F-32}{180}=\frac{K-273.15}{100}$$

Thermal Expansion

Most substances expand on heating. Three coefficients describe this:

• Linear: $\Delta L = \alpha L_0 \Delta T$
• Areal (superficial): $\Delta A = \beta A_0 \Delta T$
• Cubical (volume): $\Delta V = \gamma V_0 \Delta T$

For an isotropic solid the coefficients are related as $\beta = 2\alpha$ and $\gamma = 3\alpha$, so $\alpha : \beta : \gamma = 1 : 2 : 3$.

Anomalous expansion of water: between 0°C and 4°C water contracts on heating; it has maximum density at 4°C. This lets aquatic life survive under frozen lakes.

Thermal Stress

If a rod is rigidly clamped so it cannot expand, a thermal stress develops:

$$\text{Stress} = Y \alpha \Delta T$$

where $Y$ is Young's modulus. This is why gaps are left between railway tracks and in bridges.

Specific Heat, Calorimetry and Latent Heat

Specific Heat Capacity

The specific heat capacity $s$ of a substance is the heat required to raise the temperature of unit mass by 1 K:

$$Q = m\,s\,\Delta T$$

For a given body, heat capacity $= ms$. The molar specific heat is $C = M s$ (heat per mole). Water has an unusually high specific heat ($4186\ \text{J kg}^{-1}\text{K}^{-1}$), which moderates climate.

Calorimetry — Principle of Mixtures

When bodies at different temperatures are mixed in an isolated system:

$$\text{Heat lost by hot body} = \text{Heat gained by cold body}$$

Trap: Always check whether a change of state occurs during mixing. If ice is added to water, part of the heat may go into melting (latent heat) before temperature rises.

Change of State and Latent Heat

During melting or boiling, temperature stays constant while heat is absorbed. The heat per unit mass for the phase change is the latent heat $L$:

$$Q = mL$$

• Melting point decreases with pressure for ice (regelation).
• Boiling point increases with pressure (pressure cookers).

A temperature vs heat graph shows flat plateaus at melting and boiling points — useful for many board MCQs.

Heat Transfer and Cooling Laws

Modes of Heat Transfer

Conduction

The steady-state rate of heat flow through a slab is:

$$\frac{dQ}{dt} = \frac{K A (T_1 - T_2)}{L}$$

where $K$ is thermal conductivity, $A$ area, $L$ thickness. The quantity $L/(KA)$ is the thermal resistance. Conductors in series add resistances; in parallel they add conductances.

Radiation Laws

Stefan-Boltzmann law: The energy radiated per unit area per second by a black body is

$$E = \sigma T^4$$

with $\sigma = 5.67 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$. For a body of emissivity $e$, $E = e\sigma T^4$. Net power radiated to surroundings at $T_0$:

$$P = e\sigma A (T^4 - T_0^4)$$

Wien's displacement law: The wavelength of maximum emission shifts with temperature:

$$\lambda_m T = b, \quad b = 2.9 \times 10^{-3}\ \text{m K}$$

Newton's Law of Cooling

For small temperature differences, the rate of cooling is proportional to the excess temperature over surroundings:

$$-\frac{dT}{dt} = k(T - T_0)$$

Trap: Newton's law of cooling is a special, approximate case of the Stefan-Boltzmann law valid only for small temperature differences and forced convection.

Frequently asked questions

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Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Thermal Properties of Matter.