Question

The volume of oil contained in a certain hydraulic press is $0.2m$${}^3$. The compressibility of oil is $20\times {10}^{-6}$ per atmosphere. The decrease in volume of the oil when subjected to $200$ atmospheres is (1 atmosphere $=1.02\times {10}^5$ N/m${}^2$)

• A. 4 x 10${}^{-4}{m}^3$
• B. 8 x 10${}^{-4}{m}^3$
• C. 16 x 10${}^{-4}{m}^3$
• D. 2 x 10${}^{-4}{m}^3$

Answer 1

The correct option is B 8 x 10${}^{-4}{m}^3$

Given:
Volume, $V=.2m^3$

Compressibility of oil, $K=20\times {10}^{-6}$ per atm

Pressure, $P=200$ Atm

$Compressibility=\frac{1}{\text{Bulk modulus}}=\frac{△v/v}{p}$

$△V=Compressibility\times P\times V$

$=20\times {10}^{-6}\times 200\times 0.2$

$=8\times {10}^{-4}{m}^3$