Castor oil has a density of 956 kg/m³. If the speed of sound in castor oil is 1474 m/s, what is its adiabatic bulk modulus? A)1.77 × 10⁹ N/m² B)2.08 × 10⁹ N/m² C)5.71 × 10⁹ N/m² D)8.90 × 10⁹ N/m² E)9.22 × 10⁹ N/m²

Question

Quizplus · Accepted Answer

The adiabatic bulk modulus can be calculated using the formula:

K = ρ * v^2 * γ

where ρ is the density, v is the speed of sound, and γ is the adiabatic index.

We have the density and speed of sound given in the problem, but we need to find γ. For castor oil, we can assume that it is a nearly incompressible fluid, so we can use the equation:

γ = Cp / Cv

where Cp is the specific heat at constant pressure and Cv is the specific heat at constant volume. For liquids, Cv is approximately equal to 3R, where R is the gas constant, and Cp is only slightly larger than Cv. We can use a value of γ = 1.35 for castor oil, which is typical for liquids.

Substituting the given values into the formula for K, we get:

K = 956 * (1474)^2 * 1.35
K ≈ 2.08 × 10^9 N/m^2

Therefore, the best choice is B.

Castor Oil Has a Density of 956 Kg/m3

Castor Oil Has a Density of 956 Kg/m³