Question

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 $37{}^{o}C$, ${\alpha }_{Cu}=1.7\times {10}^{-5}{}^{o}C$ and bulk modulus for copper $B_{Cu}=140\times {10}^{9}N/m^2$.

• A. $42\times {10}^{6}N/m^2$
• B. $22\times {10}^{6}N/m^2$
• C. $36\times {10}^{6}N/m^2$
• D. $18\times {10}^{6}N/m^2$

Answer 1

Answer: (A)

Given, change in temperature, $△T=57-37=20{}^{o}C$

Coefficient of cubical expansion of copper,

${\gamma }_{Cu}=3{\alpha }_{Cu}=5.1\times {10}^{-5}{}^{o}C$

Let initial volume of the cavity be V and its volume increases by ∆V due to increase in temperature.

$\Delta V=\gamma V\Delta T\Rightarrow \frac{\Delta V}{V}=\gamma \Delta T$

Thermal stress produced = B × Volumetric strain = $B\times \frac{\Delta V}{V}=B\times \gamma \Delta T=140\times {10}^9\times (5.1\times {10}^{-5}\times 20)=1.43\times {10}^{8}N/m^2$

None of the options is correct.