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=1.7xx10^(-5)//""^(@)C, bulk modulus for copper =140xx10^(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=1.7xx10^(-5)//""^(@)C, bulk modulus for copper =140xx10^(9)N//m^(2).
Answer» SOLUTION :Increase in temperature `DeltaT=57-37=20^(@)C` or 20 K Coefficient of linear expansion of CAVITY, `alpha=1.7xx10^(-5)" "^(@)C^(-1)` Bulk modulus of cavity `K=140xx10^(9)" N/m"^(2)` Coefficient volume expansion of copper, `gamma=3alpha` `=3xx1.7xx10^(-5)` `=5.1xx10^(-5)" "^(@)C^(-1)` Suppose the original volume is V and the increase in volume is `DeltaV` DUE to increase in temperature `DeltaT`. We know that, `DeltaV=gammaVDeltaT` `:.(DeltaV)/(V)=gammaDeltaT` THERMAL stress = Bulk modulus `xx` volume strain `=Kxx(DeltaV)/(V)` `=KxxgammaDeltaT` `=140xx10^(9)xx5.1xx10^(-5)xx20` `=1.428xx10^(8)" N/m"^(2)` ATMOSPHERIC pressure is `P=1.01xx10^(5)" N/m"^(2)`