A specimen of oil having an initial volume of 600 cm3 is subjected to a pressure increase of 3.6×10^6 Pa, and the volume is found to decrease by 0.45 cm^3. What is the bulk modulus of the material and the compressibility?

Video transcript

welcome back everybody. When a car engine starts up, the oil inside starts to up and the change in pressure while it goes down by 10 to the seventh pascal's And we are also told that the initial volume of oil is 5000 cm cubed and we are told that the bulk module is is five times 10 to the ninth pascal's were tasked with finding two things. One what the change in volume is and to what the compressibility constant is. So let's go ahead and start out with the first part here. Well we know that the bulk module asse equal to the negative of the change in pressure divided by the change in volume divided by the initial volume, rearranging the equation around. We then get that uh change in volume are desired value is just negative. Change in pressure divided by our bulks module is divided by our initial volume. So let's go ahead and plug in those values that we know delta v is equal to negative negative 10 to the seventh. So the negatives are gonna cancel out, divided by five times 10 to the ninth, divided by 5000 giving us that. Our change in volume is 10 centimeters cute. Great. Now for part B we are trying to find the compressibility constant. Well the compressibility constant is just equal to one over the bulk modular. So one divided by five times 10 to the ninth gives us our compressibility constant of two times 10 to the negative 10th asking us to the negative one. We have now found our change in volume and our compressibility constant corresponding to answer choice. D thank you all so much for watching. Hope this video helped. We will see you all in the next one.