Question

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of `57^(@)C` is drunk. You can take body (tooth) temperature to be `37^(@)C` and `alpha_(Cu) = 1.7 xx 10^(-5)//^(@)C` bulk modulus for copper `B_(Cu) = 140 xx 10^(9) N//m^(2)`.

Answer 1

Volumetric strian in tooth cavity ` = Delta V//V` Let `gamma` be the coefficient of volume expansion with the change in temperature `Delta theta.^@C,` the cange in volume is `Delta V = gamma V Delta theta` or `(Delta V)/(V) = gamma Delta theta` Thermal stress in tooth cavity ` = B xx` volumetric strain `= B xx gamma Delta theta = B xx 3 alpha Delta theta (:. gamma = 3 alpha)`
`= (140 xx 10^9) xx (3xx1.7 xx 10^(-5)) xx 20 = 1.428 xx 10^8 N//m^2`