A gas is compressed from an initial volume of 5.55 L to a final volume of 1.22 L by an external pressure of 1.00 atm. During the compression the gas releases 124 J of heat. What is the change in internal energy of the gas?

Video transcript

All right. Hi, everyone. So this question says that a gas is compressed from an initial volume of 5.55 L to a final volume of 1.22 L by an external pressure of 1.00 atmospheres. During the compression, the gas releases 124 joules of heat. What is the change in internal energy of the gas? Option? A says 128 jewels. Option B says 563 jewels. Option C says negative 120 jewels and option D says 315 jewels. So let's go ahead and get started. Now, the change in internal energy or delta E can be represented by the following equation where delta E is equal to Q added to W. Now Q represent heat that's released or absorbed during the process and W equals the work. Now because we are given information about the volume and the pressure of the system, we can calculate the value of work because W or work is equal to negative P delta V. In other words, that would be negative one multiplied by the pressure multiplied by the change in volume throughout the process. So here we can also represent this equation as W equals negative P multiplied by the difference between the final and initial volumes. So using the information provided we can go ahead and solve for W so W is equal to the negative pressure thats 1.00 atmospheres multiplied by the difference in volume throughout the process. Now here because the gas has been compressed, right, the change in volume is going to be negative because the final volume is smaller than the initial. So V final is 1.22 L and this is subtracted by the initial volume which is 5.55 L move this off to the side slightly. So here, 1.22 L subtracted by 5.55 L means that delta V or the change in volume is equal to negative 4.33 L. And this will be multiplied by the negative volume. So negative one atmospheres multiplied by negative 4.33 L means that the work is equal to positive or 0.33 L atmospheres. But because our answer is expressed in units of jewels and so is the heat we're going to go ahead and convert the work into units of jewels. Now recall that 1, 101.325 or 101.325 joules is equal to 1 L atmospheres. So this is the conversion factor that were going to use to convert the work into units of jules. Now recall that when using a conversion factor, it's very important to make sure that your initial units are canceling out. So because of this, if I'm treating my conversion factor like a fraction, the portion of my conversion factor that contains units of leader atmospheres should be in the denominator, whereas jules should be in the numerator because this ensures that leader atmospheres cancel out. And so when I convert this quantity, I get that the work is equal to 438 0.73725 Jules. So I'm not going to round this number quite yet because I want my next calculation to be as accurate as possible. So now going back to the value of Q or the heat, right, in this case, heat has been released during the process being described. So this means that Q should be equal to negative 124 joules. He was negative because heat has been released. So now we can go ahead and plug in our respective values for Q and W into the expression for the change in internal energy. So delta E is equal to negative 124 Jews added to 438 0.73 725 Jules. And so this equals for Delta E that's 314 0.7 joules or approximately 315 joules or the change in internal energy. So this matches with option D in our multiple choice that's 315 jewels and there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.