First slide

Elastic behaviour of solids

Question

Artificial diamonds are made by subjecting graphite to high pressure of $2 \times 10^{10}$ Pa at a high temperature. Assuming that natural diamonds were formed at such high pressure within the earth, what must have been the original volume of a diamond whose mass is 210 g? The density of diamond = 3500 $k g m^{- 3}$ and its bulk modulus = $6 x 1 0^{11} {Nm}^{- 2} .$

Difficult

A

60 $c m^{3}$
B

61 $c m^{3}$
C

62 $c m^{3}$
D

63 $c m^{3}$

Solution

Given B = $6 \times 10^{11} N m^{- 2}$
Mass = 210 gm
$V o l u m e, V = \frac{m a s s}{d e n s i t y} = \frac{210 \times 10^{- 3}}{3500} = 0.06 \times 10^{- 3} m^{3}$
Bulk modulus , $B = \frac{Δ P}{(\frac{- Δ V}{V})} = \frac{(Δ P) V}{- Δ V}$
$Δ V = \frac{(Δ P) V}{B} = \frac{2 \times 10^{10} (0.06 \times 10^{- 3})}{6 \times 10^{11}} = 2 \times 10^{- 6} m^{3} = 2 c m^{3}$
$o r i g i n a l v o l u m e = V + Δ V = 60 + 2 = 62 c m^{3}$

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