Question:
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57oC is drunk. You can take body temperature to be 37oC and α = 1.7 × 10-5oC, bulk modulus for copper = 140 × 109 N/m2.
Solution:
Decrease in temperature, ∆t = 57 – 37 = 20oC
Coefficient of linear expansion, α = 1.7 × 10-5oC
Bulk modulus for copper, B = 140 × 109 N/m2
Coefficient of cubical expansion, γ = 3α = 5.1 × 10-5oC
Increase in volume with increase in temperature is given as
$\Delta V=\gamma V \Delta t \Rightarrow \frac{\Delta V}{V}=\gamma \Delta t$
Thermal stress = B(γ∆t) = 1.428 × 108 N/m2