question_answer 46)

                  Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of \[{{57}^{o}}C\] is drunk. You can take body (tooth) temperature to be \[{{37}^{o}}C\] and \[\alpha =\,1.7\,\times \,{{10}^{-5}}{{/}^{0}}C,\,\] bulk modulus for copper \[=140\times {{10}^{9}}\,N/{{m}^{2}}\].                

Answer:

                  Thermal stress = K × strain                 \[=\,K\,\frac{\Delta V}{V}\]                 Now \[\gamma =\,\frac{\Delta V}{V\Delta T}\] or \[\frac{\Delta V}{V}=\,\gamma \Delta T\]                 \[\therefore \] Thermal stress \[=K\,\gamma \,\,\Delta \,T\]                 \[=3K\,\alpha \,\Delta T\]                     \[(\therefore \,\,\gamma \,=\,3\alpha )\]                 \[=3\times \,140\,\times \,{{10}^{9}}\,\times \,1.7\,\times \,{{10}^{-5}}\,\times \,20\]                 \[=1.428\,\times \,{{10}^{8}}\,N{{m}^{-2}}\]