Question

Find the stress developed inside a tooth cavity filled with copper when hot tea at temperature of ${57}^{o}C$ is drunk. (Take temperature of tooth to be ${37}^{o}C,\alpha =1.7\times {10}^{-5}{/}^{o}C$ and bulk modulus for copper $=140\times {10}^{9}N{m}^{-2}$ )

• A. $1.43\times {10}^{8}N{m}^{-2}$
• B. $4.13\times {10}^{8}N{m}^{-2}$
• C. $2.12\times {10}^{4}N{m}^{-2}$
• D. $3.12\times {10}^{4}N{m}^{-2}$

Answer 1

The correct option is A $1.43\times {10}^{8}N{m}^{-2}$

Volumetric strain in tooth cavity $=\frac{\Delta V}{V}$
Let $\gamma$ be the coefficient of volume expansion with the change in temperature $\Delta T$ .
Change in volume is
$\Delta V=\gamma V\Delta Tor\frac{\Delta V}{V}=\gamma \Delta T$
Thermal stress in tooth cavity
$=\beta \times volumetricstrain=\beta \gamma \Delta T$
$=\beta \times 3\alpha \Delta T$ $(\because \gamma =3\alpha )$
$=140\times {10}^9\times 3\times 1.7\times {10}^{-5}\times (57-37)$
$=1.43\times {10}^{8}N{m}^{-2}$