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)`.

Options

A. `42 xx 10^(6) N//m^(2)`
B. `22 xx 10^(6) N//m^(2)`
C. `36 xx 10^(6) N//m^(2)`
D. `18 xx 10^(6) N//m^(2)`

Answer

A

Explanation

Given , decrease in temperature
`(Delta t) = 57-37 = 20^(@)C`
Coefficient of cubical expansion of copper
`gamma_(Cu) = 3 alpha_(Cu) = 5.1xx10^(-5)//^(@)C`
Let initial volume of the cavity be `V` and its volume increases by `Delta V` due to increase in temperature
`:. Delta V = gamma V Delta t`
`rArr (Delta V)/(V) = gamma Delta t`
Thermal stress produced = `B xx` Volumetric strain
`=B xx (Delta V)/(V) = B xx gamma Delta t`
`=140xx10^(9)xx(1.5xx10^(-5)xx20) = 42 xx 10^(6)N//m^(2)`
This is about `10^(3)` times of atmospheric pressure.