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Calculate the stress developed inside a ...

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 `alpha_(Cu) = 1.7 xx 10^(-5)//^(@)C` bulk modulus for copper `B_(Cu) = 140 xx 10^(9) N//m^(2)`.

A

`1.43 xx 10^(8) Nm^(-2)`

B

`4.13 xx 10^(8) Nm^(-2)`

C

`2.12 xx 10^(4) Nm^(-2)`

D

`3.12 xx 10^(4) Nm^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Volumetric strain in tooth cavity `= (V)/(V)`
Let `gamma` be the coefficient of volume expansion with change in temperature `DeltaT .^(@)C`.
Change in volume is
`DeltaV = gammaVDeltaT` or `(DeltaV)/(V) = gammaDeltaT`
Thermal stress in tooth cavity
`= beta xx "volumetric strain" = beta xx gamma DeltaT`
`= beta xx 3alpha DeltaT`
`= 140 xx 10^(9) xx 3 xx 1.7 xx 10^(-5) xx (57^(@)C - 37^(@)C)`
` = 1.43 xx 10^(8) N m^(-2)`.
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