The air within a piston equipped with a cylinder absorbs 565 J of heat and expands from an initial volume of 0.10 L to a final volume of 0.85 L against an external pressure of 1.0 atm. What is the change in internal energy of the air within the piston?

Video transcript

Hey everyone. And welcome back to another video. The air within a piston equipped with a cylinder absorbs 712 toes of heat and expands from an initial volume of 0.25 L to a final volume of 1.30 L against an external pressure of 1.2 atmospheres. What is the change in internal energy of the air within the piston? Therefore, answer choices. A 584 B 711 C 234 and D 441 all given in jules. So let's solve this problem. And let's recall that the change in internal energy delta U is equal to Q plus W which essentially corresponds to heat and work respectively. First of all, we know that the heat absorbed this 712 joules. So that's our key. We can say that it's positive because the system absorbs heat. If the system releases heat it's negative, but in this case, it absorbs heat. So we can say that it's positive. Now, what about the work done? Well, essentially, we have to recall that the amount of work done is equal to negative pressure multiplied by the change in volume. So we can say negative P multiplied by V final minus V initial. Let's recall that we need to use the SI units for this formula. Our pressure is 1.2 atmospheres. We want to convert that into pascals. We simply want to recall that one atmosphere is 101325 pascals. So this is how we get our pressure. We then calculate the change in volume. So we are multiplying by our final volume is 1.30 L. Our initial volume is 0.25 L. So we subtract them. And of course, we want to add our conversion factor such that we get meters cube instead of liters, we know that 1 m cubed is 1000 L. So that's our conversion factor. And of course, from here, we get our work. So now for work, we end up with a negative of 128 joules. And from here, of course, we can now calculate the change in internal energy. We take our heat 712 tools and we add the amount of work done. So that's negative 128 tools. If we calculate the result, we get 584 Jews, which essentially corresponds to the answer to a thank you for watching.