80 J of work are done on the gas in the process shown in FIGURE EX19.3. What is V₁ in cm^3?

Video transcript

Hi everyone in this practice problem, we will be asked to determine the value of V in leaders. We'll have a process showing in the diagram occurring on a guess during which the gas has 70 jules of work performed on it. The diagram is showing pressure in kilo pascals versus P volume where 0.1 is located at 0.5 volume or 0.5 P comma 50 kg pascals and 0.2 is at four P comma 150 kg pascals. The options given for the value of V in liters are a 0. liter, B, 0.2 liter C 0.3 liter and D 0.1 liter. The diagram showed that the gas is going to move from the properties of 0.2 to 0.1. So the work done on the gas or by the gas is going to be equal to the area under a beefy breath decreasing volume means that work is going to be done on the gas. So from 0.2 to 0.1 we know that it is going to be decreasing because it's going from 444 fee to 0.5 fee. So work is going to be done on the gas and increasing fee means work is done by the gas, the area under the curve off A PP graph. So area under the curve is going to be equal to the work done on the gas. So in this case, let's actually start with calculating the area under the curve. So I'm going to separate the area under the curve into two different areas. First is going to be the area of this rec uh triangle right here. And second is going to be the area of this rectangle underneath the triangle right here. So let's start with the area after the triangle. So area of triangle is going to be equal to half multiplied by base multiplied by height. So in this case, we know that the base is going to be going from 0. to four P. So I'm just going to put that in parentheses for V minus 0.5 P multiplied by the height which is going to be from 100 and 50 kg pascals to 50 kg pascals. And I'm going to represent that with 100 and 50 times 10 to the power of three pascals minus times 10 to the power of three pascals. So we want to convert that into si so calculating this, we will then get the area of triangle to then be equal to half multiplied by 3.5 P. Multiplied by 100 times 10 to the power of three pascals, which will then come up to a value of the area of the triangle to then be equal to 100 and 75 P multiplied by 10 to the power of three pascals. We're just going to keep it at that. And then moving on to calculating the area of the uh rectangle, the area of the rectangle is just going to be equal to the base multiplied by the height or the length multiplied by the width essentially. And similarly, the base is going to be four P minus 0.5 ft. So let's go uh put that here and the height is going to be going from 50 kg pascals to 0 kg pascals. So that'll be 50 times 10 to the power of three pascals minus zero pascals calculating this, the area of the rectangle would then come out to a value of 100 and 75 3 times 10 to the power of three pascals similar or the same as the area of the triangle. So the total work done or the total area will then come up to a value of 100 and 75 ft times to the power of three pascals which is going to come from the triangle just like. So plus 100 and 75 fe multiplied by 10 to the power of three pascals which is going to come from the rectangle and that will give us the total area of 350 ft times 10 to the power of three pascals. And this area under the curve will actually equal to the total work done, total work done, which is going to be 70 jus which is given by the problem statement. So in this case, let's equalize those two. So 70 jules will equal to 350 ft times to the power of three pascals. So the volume after rearrangement will then come out to a value of two times 10 to the power of negative 4 m cube. So now we need to find the volume or V in liters. So we wanna multiply this with 1000 liter for every 1 m cube which will then come out to a value of 0.2 liter. So the value of fee or the answer to this particular practice problem will be equal to 0.2 liter which will correspond to option B in our answer choices. So option B will be the answer to this particular practice problem and that will be it for this video. If you guys still have any sort of confusion, please feel free to check out our adolescent videos on similar topics available on our website. But other than that, that will be it for this video and thank you so much for watching. Bye bye.