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)`.

Calculate the stress developed inside a tooth cavity filled with coppe

1.	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» 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`

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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)`.

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