23.A volume of 5 litres of water is compressed by a pressure of 20 atmospheres. If the bulk
modulus of water is 20 x 108 N/m2, find the change produced in the volume of water. (1 atm =
1.013 x 105 N/m2)
Ans. 5.075 cc
Section - II: Bulk modulus
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Answer
Initial volume, V
1
=100.0l=100.0×10
−3
m
3
Final volume, V
2
=100.5l=100.5×10
−3
m
3
Increase in volume, V=V
2
−V
1
=0.5×10
−3
m
3
Increase in pressure, p=100.0atm=100×1.013×10
5
Pa
Bulk modulus = p/(ΔV/V
1
)=pV
1
/ΔV
= 100×1.013×10
5
×100×10
−3
/(0.5×10
−3
)
= 2.026×10
9
Pa
Bulk modulus of air = 1×10
5
Pa
Bulk modulus of water / Bulk modulus of air = 2.026×10
9
/(1×10
5
)=2.026×10
4
This ratio is very high because air is much more compressible than water.
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