Question

A tooth cavity is filled with a copper having coefficient of linear expansion `1.7 xx 10^(-5) .^(@)C^(-1)` and bulk modules `1.4 xx 10^(11) Nm^(-2)`. The temperature of the tooth `3.^(@)C`. Calculate the thermal stress developed inside the tooth cavity when hot milk at temperature of `60 .^(@)C` is drunk.

Answer 1

Here, `alpha = 1.7 xx 10^(-5) .^(@)C_(1)`
`B = 1.4 xx 10^(11) Nm^(-2)`,
`Delta T = 60 - 35 = 25 .^(@) C`
Thermal stress `= B gamma Delta T = (3 alpha) Delta T`
`=(1.4 xx 10^(11)) xx (3 xx 1.7 xx 10^(-5)) xx 25`
`=1.78 xx 10^(8) Nm^(-2)`.