Artificial diamonds are made by subjecting graphite to high pressure of $$2$$×$$1010$$ 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 $$=$$ $$3500$$ kgm−$$3$$ and its bulk modulus $$=$$ $$6$$ x $$1011$$ Nm−$$2$$.

Question

Artificial diamonds are  made by subjecting graphite to high pressure of $$2$$×$$1010$$      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 $$=$$ $$3500$$ kgm−$$3$$     and its bulk modulus $$=$$ $$6$$ x $$1011$$ Nm−$$2$$.

Infinity Learn · Accepted Answer

Given B $$=$$ $$6$$×$$1011$$ Nm−$$2Mass$$ $$=$$ $$210$$ gmVolume,$$V=massdensity=210$$×$$10-33500=0.06$$×$$10-3m3Bulk$$ modulus , $$B=$$Δ$$P($$−Δ$$VV)=($$Δ$$P)V$$−ΔVΔ$$V=($$Δ$$P)VB=2$$×$$10100.06$$×$$10-36$$×$$1011=2$$×$$10-6m3=2cm3original$$ $$volume=V+$$Δ$$V=60+2=62cm3$$

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