Question

Find the decrease in the volume of a sample of water from the following data. Initial volume = 1000 cm³, initial pressure = 10⁵ N m^-2, final pressure = 10⁶ N m^-2, compressibility of water = 50 x 10^-11 m² N^-1.

• A. 0.90 c$m^4$
• B. 0.45 $c{m}^3$
• C. 0.25 $c{m}^3$
• D. 0.50 $c{m}^3$

Answer 1

The correct option is B

0.45 $c{m}^3$

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