Question

Find the decrease in the volume of a sample of water from the following data. Initial volume $=1000c{m}^3,$ initial pressure $={10}^{5}N{m}^{-2}$ final pressure $={10}^{6}N{m}^{-2},$ compressibility of water $=50\times {10}^{-11}{m}^2{N}^{-1},$

• A. $0.35c{m}^3$
• B. $0.45c{m}^3$
• C. $0.55c{m}^3$
• D. $0.65c{m}^3$

Answer 1

The correct option is B $0.45c{m}^3$

The change in pressure
$=△P={10}^{6}N{m}^{-2}-{10}^{5}N{m}^{-2}$
$=9\times {10}^{5}N{m}^{-2}.$
Compressibility$=\frac{1}{Bulkmodulus}=\frac{△V/V}{△P}$
or, $50\times {10}^{-11}{m}^2{N}^{-1}=-\frac{△V}{\left({10}^{-3}{m}^3\right)\times (9\times {10}^{5}N{m}^{-2})}$
or, $△V=-50\times {10}^{-11}\times {10}^{-3}\times 9\times {10}^5{m}^3$
$=-4.5\times {10}^{-7}{m}^3=-0.45c{m}^3.$
Thus the decrease in volume is $0.45c{m}^3.$