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 $$109$$ $$N/m2$$

Question

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 $$109$$ $$N/m2$$

Infinity Learn · Accepted Answer

Given, decrease in $$temperature($$∆$$t)$$ $$=$$ $$57-37$$ $$=$$ $$200CCoefficient$$ of cubical expansion of copperγCu $$=$$ $$3$$αCu $$=$$ $$5.1$$×$$10-5/0CLet$$ 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.

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 $α_{Cu}$ = $1.7 \times 10^{- 5} /^{0} C$ bulk modulus for copper $B_{Cu}$ = 140 x $10^{9} N / m^{2}$

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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

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Ready to Test Your Skills?

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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 $α_{Cu}$ = $1.7 \times 10^{- 5} /^{0} C$ bulk modulus for copper $B_{Cu}$ = 140 x $10^{9} N / m^{2}$