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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.

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a

60cm3

b

61cm3

c

62cm3

d

63cm3

answer is C.

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Detailed Solution

Given B = 6×1011 Nm−2Mass = 210 gmVolume,V=massdensity=210×10-33500=0.06×10-3m3Bulk modulus , B=ΔP(−ΔVV)=(ΔP)V−ΔVΔV=(ΔP)VB=2×10100.06×10-36×1011=2×10-6m3=2cm3original volume=V+ΔV=60+2=62cm3

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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.