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.

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions