Q. 24

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57o C is drunk. You can take body (tooth) temperature to be 37o C and α = 1.7× 10-5 /o C, bulk modulus for copper = 140 × 10 9 N/m2.

Answer :

Given,

Coefficient of linear expansion, α = 1.7× 10-5 /°C


Therefore, Coefficient of volumetric expansion(𝛾)


𝛾 = 3α = 1.7× 10-5 /°C = 5.1× 10-5 /°C


Bulk modulus, B= 140 × 10 9 N/m2.


Body temperature, T1 = 37°C


Temperature of tea, T2 = 57 °C


Temperature difference, ΔT = 57 - 37 = 20 °C


We know,




Now, stress,




Atmospheric pressure is 105 N/m2.


So, the stress is about 103 times atmospheric pressure.


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