What is the change in the volume of 1.0 L kerosene, when it is subjected to an extra pressure of 2.0 ×100000 N/m^2 if the density of the kerosene =800kg m^-3 and speed of sound in kerosene is 1300ms^-1
To calculate the change in volume of the kerosene, we can use the bulk modulus formula:
Change in Volume = -(Pressure / Bulk modulus) * Original Volume
The bulk modulus (K) is a measure of the resistance of a substance to compressibility. In this case, we can assume that kerosene is an incompressible fluid, so it has a very high bulk modulus value.
Therefore, we can use the formula:
Change in Volume = -(Pressure / Bulk modulus) * Original Volume
First, let's calculate the bulk modulus (K):
Bulk modulus (K) = Density * (Speed of sound)^2
Given that the density of kerosene (ρ) is 800 kg/m³ and the speed of sound in kerosene (v) is 1300 m/s, we can substitute these values into the formula to find the bulk modulus:
Bulk modulus (K) = 800 kg/m³ * (1300 m/s)^2
Now we can calculate the change in volume:
Change in Volume = -(Pressure / Bulk modulus) * Original Volume
Given that the extra pressure (P) is 2.0 × 100000 N/m² and the original volume (V) is 1.0 L (which can be converted to cubic meters by dividing by 1000), we can substitute these values into the formula to find the change in volume:
Change in Volume = -((2.0 × 100000 N/m²) / Bulk modulus) * (1.0 L / 1000 m³)
Now you can plug in the calculated value for the bulk modulus and evaluate the expression to find the change in volume.