Problems on Linear, Area, and Cubic Expansivity

Note: ( β = 2α , γ = 3α)

Remember

Area Expansivity formula: A₂ = A₁ +  β A₁( θ₂ – θ₁)

Cubic Expansivity formula: \( \scriptsize V_2 = V_1 \: + \: \gamma V_1(\theta_2 \: – \: \theta_1)\)

Therefore, Area and cubical expansivity can also be written as 

A₂ = A₁ + A₁2α ( θ₂ –  θ₁)

or

A₂ = A₁(1 + 2α( θ₂ –  θ₁))

V₂ = V₁ + V₁3α ( θ₂ –  θ₁)

or

V₂ = V₁(1 + 3α( θ₂ –  θ₁))

Example 10.6.1:

If the cubic expansivity of brass between 27°C and 1000°C is 5.7 × 10^-5 K^-1, what is its linear expansivity?

Solution