Question

Find the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57^{\circ }C$ is drunk. You can take body (tooth) temperature to be $37^{\circ }C$ and $a=1.7\times 10^{-5}{}^{\circ }{C}^{-1}$, Bulk modulus for copper $B=140\times 10^{9}N\cdot M^{-2}$

• A. $1.4\times 10^{8}N\cdot m^{-2}$
• B. $1.9\times 10^{8}N\cdot m^{-2}$
• C. $2.0\times 10^{8}N\cdot m^{-2}$
• D. $3.4\times 10^{7}N\cdot m^{-2}$

Answer 1

Answer: (A)

Temperature of hot tea, $t_2=57^{\circ }C$
Normal temperature of tooth, $t_1=37^{\circ }C$
$\alpha =1.7\times 10^{-5}{C}^{-1}$
Bulk modulus, $B=140\times 10^{9}N{m}^{-2}$
Thermal stress in tooth cavity
$=$ Bulk modulus $\times$ Volumetric strain
$=B\times \frac{\Delta V}{V}=B\times \gamma \cdot \Delta t$
$[\because \Delta V=V\gamma \Delta t]$
$=B\times 3\alpha \times \Delta t[\because \gamma =3\alpha ]$
$=3B\alpha \Delta t=3B\alpha \left(t_2-t_1\right)$
$=3\times 140\times 10^9\times 1.7\times 10^{-5}(57-37)$
$=1.4\times 10^{8}N{m}^{-2}$