Ncert Exercises & Solutions

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at a temperature of 57 °C is drunk. You can take body (tooth) temperature to be 37 °C and $α = 1.7 \times 10^{- 5}$ /°C Bulk modulus for copper = 140 $\times 10^{9} N / m^{2}$

Hint: Stress in the tooth is developed due to the expansion of the tooth.

Step 1: Find the strain produced in the tooth.

Given, the decrease in temperature,

$(∆ t) = 57 - 37 = 20 ° C$

Coefficient of linear expansion,

$(α) = 1.7 \times 10^{- 5} / ° C$

Bulk modulus for copper, (B)

$= 140 \times 10^{9} N / m^{2}$

Coefficient of cubical expansion, (

$γ$ )

$= 3 α = 5.1 \times 10^{- 5} / ° C$

Let the initial volume of the cavity be V and its volume increases by

$∆ V$ due to an increase in temperature.

$∴ ∆ V = γ V ∆ t$

$\Rightarrow \frac{∆ V}{V} = γ ∆ t$

Step 2: Find the stress developed.

Thermal stress produced = B x Volumetric strain

$= B \times \frac{∆ V}{V} = B \times γ ∆ t$

$= 140 \times 10^{9} \times (5.1 \times 10^{- 5} \times 20)$

$= 1.428 \times 10^{8} N / m^{2}$

This is about

$10^{3}$ times of atmospheric pressure.

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