Thermal Expansion

Thermal expansion refers to the increase in size or volume of a substance when heat is applied.

Advantages of Expansion

1. It is useful in riveting two metal plates together.
2. It is applied in the construction of automatic fire alarms.
3. It is used in bimetallic strips in electric irons.

Disadvantages of Expansion

1. It can deform bridge structures.
2. Thick glass may crack due to uneven expansion.
3. It can cause railway tracks to buckle.
4. It affects the oscillation of pendulum clocks and the balance wheel of watches.

Linear Expansivity (α)

Linear expansivity is the fractional increase in length per unit length per degree rise in temperature.

It is given by:

\[ \alpha = \frac{\text{Increase in length}}{\text{Original length} \times \text{Change in temperature}} \]

Mathematically:

\[ \alpha = \frac{l_2 - l_1}{l_1 (\theta_2 - \theta_1)} \]

Area Expansivity (β)

Area expansivity is the fractional increase in area per unit area per degree rise in temperature.

It is given by:

\[ \beta = \frac{\text{Increase in area}}{\text{Original area} \times \text{Change in temperature}} \]

Since area expansivity is twice the linear expansivity:

\[ \beta = 2\alpha \]

Mathematically:

\[ \beta = \frac{A_2 - A_1}{A_1 (\theta_2 - \theta_1)} \]

Volume or Cubical Expansivity (γ)

Volume expansivity is the fractional increase in volume per unit volume per degree rise in temperature.

It is given by:

\[ \gamma = \frac{\text{Increase in volume}}{\text{Original volume} \times \text{Change in temperature}} \]

Since volume expansivity is three times the linear expansivity:

\[ \gamma = 3\alpha \]

Mathematically:

\[ \gamma = \frac{V_2 - V_1}{V_1 (\theta_2 - \theta_1)} \]

Where:

• \(A_1\) = Original area or area at initial temperature \(\theta_1\).
• \(A_2\) = Final area or area at final temperature \(\theta_2\).
• \(\Delta A\) = Change in area or increase in area, given by \(A_2 - A_1\).
• \(V_1\) = Original volume or volume at initial temperature \(\theta_1\).
• \(V_2\) = Final volume or volume at final temperature \(\theta_2\).
• \(\Delta V\) = Change in volume or increase in volume, given by \(V_2 - V_1\).

Both area and volume expansivity are measured in \(\text{K}^{-1}\).

Real and Apparent Expansivities

Apparent Cubic Expansivity (\(\gamma_a\))

The apparent cubic expansivity of a liquid is the increase in volume per unit volume per degree rise in temperature, without considering the expansion of the container.

It is given by:

\[ \gamma_a = \frac{\text{apparent increase in volume}}{\text{original volume} \times \text{rise in temperature}} \]

Alternatively, it can be expressed in terms of mass:

\[ \gamma_a = \frac{\text{mass of liquid expelled}}{\text{mass of liquid remaining} \times \text{rise in temperature}} \]

Or in terms of volume:

\[ \gamma_a = \frac{\text{volume of liquid expelled}}{\text{volume of liquid remaining} \times \text{rise in temperature}} \]

Real or Absolute Cubic Expansivity (\(\gamma_r\))

The real cubic expansivity (\(\gamma_r\)) of a liquid is the actual increase in volume per unit volume per degree rise in temperature, considering the expansion of the container.

It is given by:

\[ \gamma_r = \gamma_a + \gamma_c \]

Where:

• \(\gamma_r\) = Real cubic expansivity of the liquid.
• \(\gamma_a\) = Apparent cubic expansivity of the liquid.
• \(\gamma_c\) = Cubic expansivity of the container or vessel.