Calculate the stress developed inside a tooth cavity filled with copper when hot tea at a temperature of $57\,^{\circ}C$ is drunk. You can take the body (tooth) temperature to be $37\,^{\circ}C$ and $\alpha = 1.7 \times 10^{-5}/^{\circ}C$,bulk modulus for copper $= 140 \times 10^9\, N/m^2$.
(N/A) Increase in temperature $\Delta T = 57 - 37 = 20\,^{\circ}C$ or $20\,K$.
Coefficient of linear expansion of copper,$\alpha = 1.7 \times 10^{-5}\,^{\circ}C^{-1}$.
Bulk modulus of copper,$K = 140 \times 10^9\,N/m^2$.
Coefficient of volume expansion of copper,$\gamma = 3\alpha = 3 \times 1.7 \times 10^{-5} = 5.1 \times 10^{-5}\,^{\circ}C^{-1}$.
Thermal stress is given by the formula: $\text{Stress} = K \times \text{volumetric strain} = K \times \frac{\Delta V}{V}$.
Since $\frac{\Delta V}{V} = \gamma \Delta T$,the stress is $\text{Stress} = K \gamma \Delta T$.
Substituting the values: $\text{Stress} = (140 \times 10^9) \times (5.1 \times 10^{-5}) \times 20$.
$\text{Stress} = 140 \times 5.1 \times 20 \times 10^4 = 14280 \times 10^4 = 1.428 \times 10^8\,N/m^2$.
Coefficient of linear expansion of copper,$\alpha = 1.7 \times 10^{-5}\,^{\circ}C^{-1}$.
Bulk modulus of copper,$K = 140 \times 10^9\,N/m^2$.
Coefficient of volume expansion of copper,$\gamma = 3\alpha = 3 \times 1.7 \times 10^{-5} = 5.1 \times 10^{-5}\,^{\circ}C^{-1}$.
Thermal stress is given by the formula: $\text{Stress} = K \times \text{volumetric strain} = K \times \frac{\Delta V}{V}$.
Since $\frac{\Delta V}{V} = \gamma \Delta T$,the stress is $\text{Stress} = K \gamma \Delta T$.
Substituting the values: $\text{Stress} = (140 \times 10^9) \times (5.1 \times 10^{-5}) \times 20$.
$\text{Stress} = 140 \times 5.1 \times 20 \times 10^4 = 14280 \times 10^4 = 1.428 \times 10^8\,N/m^2$.
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