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Question

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57 oC is drunk. You can take body (tooth) temperature to be 37oC , αCu =1.7×105/oC 
and bulk modulus for copperBCu =140×109 N/m2.
  1. 42×106 N/m2
  2. 22×106 N/m2
  3. 36×106 N/m2
  4. 18×106 N/m2


Solution

The correct option is A 42×106 N/m2
Given, change in temperature,
t=5737=20 oC
Coefficient of cubical expansion of copper,
γCu=3αCu=5.1×105/oC
Let initial volume of the cavity be V and its volume increases by ΔV due to increase in temperature.
ΔV=γVΔtΔVV=γΔtThermal stress produced = B×Volumetric strain= B×ΔVV=B×γΔt=140×109×(1.5×105×20)=42×106 N/m2This is about 103 times of atmospheric pressure.

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