Thermal Properties Of Matter Notes

Introduction

The thermal properties of matter encompass a wide range of phenomena related to temperature, heat, and their effects on different materials. Understanding these properties is crucial for various applications, from everyday life to advanced scientific research. This study note document covers the essential thermal properties of matter as outlined in the NEET Physics syllabus, breaking down complex ideas into digestible sections.

Temperature and Heat

Temperature

Temperature is a measure of the average kinetic energy of the particles in a substance. It is a scalar quantity and can be measured using various scales:

• Celsius (°C)
• Fahrenheit (°F)
• Kelvin (K)

The Kelvin scale is the SI unit for temperature, where $0 , \text{K}$ (absolute zero) is the point at which particles have minimal thermal motion.

$$ T(K) = T(°C) + 273.15 $$

Heat

Heat is a form of energy transfer between bodies or systems due to a temperature difference. It is measured in joules (J) in the SI system.

• Specific Heat Capacity (c): The amount of heat required to raise the temperature of 1 kg of a substance by 1°C or 1 K. $$ Q = mc\Delta T $$ Where:
  • $Q$ is the heat added or removed (in joules)
  • $m$ is the mass (in kg)
  • $c$ is the specific heat capacity (in J/kg·K)
  • $\Delta T$ is the change in temperature (in K or °C)

Thermal Expansion

Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature.

Linear Expansion

For solids, the change in length ($\Delta L$) is proportional to the original length ($L$) and the change in temperature ($\Delta T$):

$$ \Delta L = \alpha L \Delta T $$

Where $\alpha$ is the coefficient of linear expansion.

Area Expansion

The change in area ($\Delta A$) is given by:

$$ \Delta A = 2\alpha A \Delta T $$

Volume Expansion

The change in volume ($\Delta V$) is:

$$ \Delta V = \beta V \Delta T $$

Where $\beta$ is the coefficient of volume expansion, and $\beta \approx 3\alpha$ for most solids.

Modes of Heat Transfer

Heat can be transferred in three primary ways: conduction, convection, and radiation.

Conduction

Conduction is the transfer of heat through a material without the movement of the material itself. It occurs mainly in solids.

• Fourier's Law of Heat Conduction: $$ Q = -kA \frac{dT}{dx} $$ Where:
  • $Q$ is the heat transfer per unit time (in watts)
  • $k$ is the thermal conductivity (in W/m·K)
  • $A$ is the cross-sectional area (in m²)
  • $\frac{dT}{dx}$ is the temperature gradient (in K/m)

Convection

Convection is the transfer of heat by the physical movement of fluid (liquid or gas).

• Natural Convection: Driven by buoyancy forces due to density differences.
• Forced Convection: Driven by external means, like fans or pumps.

Radiation

Radiation is the transfer of heat through electromagnetic waves, without the need for a medium.

• Stefan-Boltzmann Law: $$ P = \sigma A T^4 $$ Where:
  • $P$ is the power radiated (in watts)
  • $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} , \text{W/m}^2\text{K}^4$)
  • $A$ is the surface area (in m²)
  • $T$ is the absolute temperature (in K)

Thermal Properties of Gases

Ideal Gas Law

The behavior of gases can be described by the ideal gas law:

$$ PV = nRT $$

Where:

• $P$ is the pressure (in Pa)
• $V$ is the volume (in m³)
• $n$ is the number of moles
• $R$ is the universal gas constant ($8.314 , \text{J/mol·K}$)
• $T$ is the temperature (in K)

Specific Heat Capacities of Gases

• At constant volume ($C_V$): $$ Q = nC_V \Delta T $$
• At constant pressure ($C_P$): $$ Q = nC_P \Delta T $$

For an ideal gas, the relationship between $C_P$ and $C_V$ is given by:

$$ C_P - C_V = R $$

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes.

Principle of Calorimetry

The principle of calorimetry is based on the conservation of energy:

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

Conclusion

Understanding the thermal properties of matter is essential for solving problems related to heat and temperature changes in various materials. Mastery of these concepts will provide a solid foundation for tackling related questions in the NEET exam.