Determine the change in volume of 1.0 litre of kerosene upon being subjected to an additional pressure of 2.0 10^5 N m ⁻² , given the following data: density of kerosene = 800 kg m ⁻³ and speed of sound in kerosene = 1330 m s ⁻¹ .

Step-by-step solution

The speed of sound in a liquid is given by v = B , where B is the bulk modulus and is the density. Squaring both sides, the bulk modulus is B = v² . The bulk modulus is also defined as B = P V / V , where P is the change in pressure, V is the initial volume, and V is the change in volume. Equating the two expressions for B : P V V = v² Rearranging for V : V = P V v² Substituting the given values P = 2.0 10⁵ N m ⁻² , V = 1.0 litre = 10⁻³ m ³ , = 800 kg m ⁻³ , and v = 1330 m s ⁻¹ : V = 2.0 10⁵ 10⁻³ 800 (1330)² V = 20