Area Expansivity

When substances are heated, there is an increase in length, breadth and height, hence area and volume also increases.

An increase in area of a solid when heated is called area or superficial expansivity.

Therefore;

Area Expansivity = β

 \(\scriptsize β = \normalsize \frac {A_2 \: – \: A_1}{A_1 \: \times \: (\theta_2 \: – \: \theta_1)}\) 

A₂ = New area

A₁ = Initial/Original area

θ₂ = New temperature

θ₁ = Original temperature

From the equation

A₂ – A₁ =  β A₁( θ₂ –  θ₁)

A₂ = A₁ +  β A₁( θ₂ – θ₁)

or

A₂ = A₁ (1 +  β(θ₂ – θ₁))

Area expansivity = 2 * Linear expansivity

β = 2α ( Proof of The Relationship between Linear Expansivity and Area Expansivity)

The S.I unit is per kelvin \( \scriptsize K^{-1} \) or per degree Celsius \( \scriptsize ^{०} C^{-1} \)

Example 10.3.1:

Calculate the area expansivity of a metal plate whose area at 36°C is 0.25 m² and 1.15 m² at 56.2 °C.

Solution

Values given:

Area expansivity β = ?, A₁ = 0.25m² , A₂ = 1.15m² , θ₁ = 36°C, θ₂ = 56.2°C

Formula for area expansivity β

 ⇒ \(\scriptsize β = \normalsize \frac {1.15\: – \: 0.25}{0.25 \: \times \: (56.2 \: – \: 36)}\) 

 ⇒ \(\scriptsize β = \normalsize \frac {0.9}{0.25 \: \times \: 20.2}\) 

⇒ \(\scriptsize β = \normalsize \frac {0.9}{5.05}\) 

⇒ \(\scriptsize β = 0.178 K^{-1}\)