A hydraulic press contains 0.25 m 3(250 L ) of oil. Find the decrease in volume of the oil (in %) when it is subjected to a pressure increase Δ p=1.6 × 107 Pa. The bulk modulus of the oil is B=5.0 × 109 Pa.

Question

A hydraulic press contains 0.25 m 3(250 L ) of oil. Find the decrease in volume of the oil (in %) when it is subjected to a pressure increase Δ p=1.6 × 107 Pa. The bulk modulus of the oil is B=5.0 × 109 Pa. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

B =-(Δ p/Δ V / V0)=-((0.25 m 3)(1.6 × 107 Pa )/5.0 × 109 Pa ) =-8.0 × 10-4 m 3=-0.80 L Even through the pressure increase is very large, the fractional change in volume is very small. ∴ Δ V / V0=(-8.0 × 10-4 m 3) /(0.25 m 3)=-0.0032 or = -0.32 %

Q. A hydraulic press contains 0.25m3(250L) of oil. Find the decrease in volume of the oil (in %) when it is subjected to a pressure increase Δp=1.6×107Pa. The bulk modulus of the oil is B=5.0×109Pa.

B=−ΔV/V0​Δp​=−5.0×109Pa(0.25m3)(1.6×107Pa)​ =−8.0×10−4m3=−0.80L Even through the pressure increase is very large, the fractional change in volume is very small. ∴ΔV/V0​=(−8.0×10−4m3)/(0.25m3)=−0.0032 or =−0.32%

Q. A hydraulic press contains $0.25 m^{3} (250 L)$ of oil. Find the decrease in volume of the oil (in %) when it is subjected to a pressure increase $Δ p = 1.6 \times 1 0^{7} P a$ . The bulk modulus of the oil is $B = 5.0 \times 1 0^{9} P a$ .