InterviewSolution
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InterviewSolution
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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)`.A. `1.43 xx 10^(8) Nm^(-2)`B. `4.13 xx 10^(8) Nm^(-2)`C. `2.12 xx 10^(4) Nm^(-2)`D. `3.12 xx 10^(4) Nm^(-2)` |
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Answer» Correct Answer - A Volumetric strain in tooth cavity `= (V)/(V)` Let `gamma` be the coefficient of volume expansion with change in temperature `DeltaT .^(@)C`. Change in volume is `DeltaV = gammaVDeltaT` or `(DeltaV)/(V) = gammaDeltaT` Thermal stress in tooth cavity `= beta xx "volumetric strain" = beta xx gamma DeltaT` `= beta xx 3alpha DeltaT` `= 140 xx 10^(9) xx 3 xx 1.7 xx 10^(-5) xx (57^(@)C - 37^(@)C)` ` = 1.43 xx 10^(8) N m^(-2)`. |
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