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)`
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Correct Answer – 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)`.
Volumetric strian in tooth cavity ` = Delta V//V` Let `gamma` be the coefficient of volume expansion with the change in temperature `Delta theta.^@C,` the cange in volume is `Delta V = gamma V Delta theta` or `(Delta V)/(V) = gamma Delta theta` Thermal stress in tooth cavity ` = B xx` volumetric strain `= B xx gamma Delta theta = B xx 3 alpha Delta theta (:. gamma = 3 alpha)`
`= (140 xx 10^9) xx (3xx1.7 xx 10^(-5)) xx 20 = 1.428 xx 10^8 N//m^2`
Given, decrease in temperature `(Delta t) = 57 – 37 = 20^(@)C`
Coefficient of linear expansion `(alpha) = 1.7 xx 10^(-5)//^(@)C`
Bulk modulus for copper (B) `= 140 xx 10^(9) N//m^(2)`
Coefficient of cubical expansion `(gamma) = 3 alpha = 5.1 xx 10^(-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`
`= 140 xx 10^(9) xx (5.1 xx 10^(-5) xx 20)`
`= 1, 428 xx 10^(8)N//m^(2)`
This is about `10^(3)` times of atmospheric pressure.
Correct Answer – A
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.