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 αCu = 1.7×10-5/0C bulk modulus for copper BCu = 140 x 109 N/m2

Given, decrease in temperature(∆t) = 57-37 = 200CCoefficient of cubical expansion of copperγCu = 3αCu = 5.1×10-5/0CLet initial volume of the cavity be V and its volume increases by ∆V due to increase in temperature.∴ ∆V= γV∆t⇒∆VV = γ∆tThermal stress produced = B x Volumetric strain= B×∆VV = B ×γ∆t= 140 x 109 x (1.5 x 10-5 x 20) = 42 x106 N/m2This is about 103 times of atmospheric pressure.