Thermal properties of matter

Thermal Properties of Matter

Heat

• Definition: Heat is a form of energy that produces sensations of hotness or coldness.

• Units:

  • SI Unit: Joule (J)

  • CGS Unit: Caloric

  • Conversion: 1 Caloric = 4.1865 Joules.

  • 1 calorie is defined as the heat energy required to raise the temperature by 1°C of one gram of water.

Thermometers and Temperature Measurement

• Thermometer: A device used to measure temperature.

• Thermometric Scales: The range between two fixed temperature points is divided into equal divisions, forming a thermometric scale.

  • Each division is called 1 degree.

Key Reference Points:

• Celsius: 0°C (Freezing point of water) to 100°C (Boiling point of water)

• Fahrenheit: 32°F (Freezing point of water) to 212°F (Boiling point of water)

• Kelvin: 273K (Freezing point of water) to 373K (Boiling point of water)

Temperature Conversion Formulas

• From Celsius to Fahrenheit:
  $T<em>F = (T</em>C × rac{9}{5}) + 32$
  where:

  • $T_C$ = temperature in Celsius

  • $T_F$ = temperature in Fahrenheit

• From Fahrenheit to Celsius:
  $T<em>C = (T</em>F - 32) × rac{5}{9}$

• From Celsius to Kelvin:
  $T<em>K = T</em>C + 273$

• From Kelvin to Celsius:
  $T<em>C = T</em>K - 273$

• From Fahrenheit to Kelvin:
  $T<em>K = (T</em>F - 32) × rac{5}{9} + 273$

• From Kelvin to Fahrenheit:
  $T<em>F = (T</em>K - 273) × rac{9}{5} + 32$

Absolute Zero

• Definition: The lowest temperature at which a gas is supposed to have zero pressure and the entire motion of the molecules stops.

• Absolute zero in various units:

  • In Kelvin: 0K

  • In Celsius: -273.15°C

  • In Fahrenheit: -459.69°F

Thermal Expansion

• Definition: The increase in dimensions of a body when it is heated.

Types of Thermal Expansion:

1. Linear Expansion

   • Formula:
     $rac{ riangle l}{l_0} = \beta imes riangle T$
     where:

   • $riangle l$ = change in length

   • $l_0$ = original length

   • $\beta$ = coefficient of linear expansion

   • $riangle T$ = change in temperature

   • Linear Expansion is defined as the increase in length per unit original length per degree rise in temperature.

   • SI unit: $K^{-1}$ or $°C^{-1}$.

2. Superficial/Areal Expansion

   • Formula:
     $rac{ riangle A}{A_0} = \beta' imes riangle T$
     where:

   • $riangle A$ = change in area

   • $A_0$ = original area

   • $\beta'$ = coefficient of superficial or areal expansion.

   • Coefficient of areal expansion is defined as the increase in area per unit area per degree rise in temperature.

   • SI unit: $K^{-1}$ or $°C^{-1}$.

3. Cubical/Volumetric Expansion

   • Formula:
     $rac{ riangle V}{V_0} = \beta'' imes riangle T$
     where:

   • $riangle V$ = change in volume

   • $V_0$ = original volume

   • $\beta''$ = coefficient of cubical expansion.

   • Coefficient of cubical expansion is defined as the increase in volume per unit original volume per degree rise in temperature.

   • SI unit: $K^{-1}$ or $°C^{-1}$.

4. Relation Between Linear and Cubical Expansion

   • Formula:
     $riangle V = 3\beta l_0 riangle T$
     This shows that volumetric expansion is three times the linear expansion for the same temperature change.

Anomalous Behavior of Water

• Density of water varies with temperature and is maximum at 4°C.

Heat Transfer

• Definition: The transfer of thermal energy from one system to another or within a system due to temperature difference.

Types of Heat Transfer

1. Conduction

   • The transfer of heat through materials without any movement of the material itself.

   • Fourier's law of heat conduction:
     $Q = k rac{A (T<em>1 - T</em>2)}{d}$
     where:

   • $k$ = thermal conductivity of the material

   • $A$ = cross-sectional area

   • $T<em>1$ and $T</em>2$ = temperatures at two ends

   • $d$ = distance between the two ends.

2. Convection

   • The process of heat transfer through the movement of fluids (liquids or gases).

   • Example: Sea breeze and land breeze phenomena.

3. Radiation

   • Heat transfer through electromagnetic waves without requiring any medium.

   • Example: Thermal radiation emitted by bodies based on their temperature.

Latent Heat

• Definition: The hidden heat required to change the state of matter without changing its temperature.

• Classification:

  1. Latent Heat of Fusion (L_f): Heat required to change a substance from solid to liquid or vice versa.

  2. **Latent Heat of