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. `42 xx 10^(6) N//m^(2)`B. `22 xx 10^(6) N//m^(2)`C. `36 xx 10^(6) N//m^(2)`D. `18 xx 10^(6) N//m^(2)` |
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Answer» Correct Answer - A Given , decrease in temperature `(Delta t) = 57-37 = 20^(@)C` Coefficient of cubical expansion of copper `gamma_(Cu) = 3 alpha_(Cu) = 5.1xx10^(-5)//^(@)C` Let initial volume of the cavity be `V` and its volume increases by `Delta V` due to increase in temperature `:. Delta V = gamma V Delta t` `rArr (Delta V)/(V) = gamma Delta t` Thermal stress produced = `B xx` Volumetric strain `=B xx (Delta V)/(V) = B xx gamma Delta t` `=140xx10^(9)xx(1.5xx10^(-5)xx20) = 42 xx 10^(6)N//m^(2)` This is about `10^(3)` times of atmospheric pressure. |
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