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Shweta Parmar
Shweta Parmar
Asked: 3 years ago2022-11-08T20:11:31+05:30 2022-11-08T20:11:31+05:30In: General Awareness

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. `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)`

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. `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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  1. c246b
    2022-10-29T20:50:23+05:30Added an answer about 3 years ago

    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.

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Roma Darpan Gaba
Roma Darpan Gaba
Asked: 3 years ago2022-11-05T17:18:36+05:30 2022-11-05T17:18:36+05:30In: General Awareness

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)`

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)`
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  1. cf466
    2022-11-08T03:47:44+05:30Added an answer about 3 years ago

    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)`.

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Hari Singh Kothari
Hari Singh Kothari
Asked: 3 years ago2022-11-03T08:16:40+05:30 2022-11-03T08:16:40+05:30In: General Awareness

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)`.

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)`.
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  1. 498d5
    2022-11-05T23:01:42+05:30Added an answer about 3 years ago

    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`

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Riddhi Amin
Riddhi Amin
Asked: 3 years ago2022-11-01T00:49:37+05:30 2022-11-01T00:49:37+05:30In: General Awareness

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)`.

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)`.
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  1. 67a7f
    2022-10-30T10:51:47+05:30Added an answer about 3 years ago

    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.

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