It's been a little while since I did thermodynamics, but I stared at it for a while and it looks to me like you do not actually need to know any of the volumes. Let me see if I can get you started. The second step in the Carnot cycle is an isentropic expansion, which means P2 * V2^k = P3 * V3^k. You can do some rearranging with that and the ideal gas law to get the volume ratio V3/V2 to drop out and leave you with the pressure ratio P3/P2 in terms of the temperature ratio T3/T2. Since you know P3, T2, and T3, you can easily solve for P2. The same trick will work for the isentropic compression. For work: on the isothermal steps, you can once again use the ideal gas law to convert integral(P dV) into an integral involving pressure only, since temperature will be known and constant. On the isentropic steps, when you go to convert integral(P dV) into an integral over temperature, you'll find that a lot of things drop out and the work takes a particularly simple form... Let me know if you have more specific questions! (I'm assuming, btw, that what your professor calls "k" is the adiabatic index (which is about 1.4 for air). That threw me for a loop - I'm used to seeing the Greek letter gamma for the adiabatic index.)

(And I'm used to seeing k for Boltsmann's constant when I'm doing thermo, so blithely giving it a convenient number threw me for a loop as well.)

yeah, it is the adiabatic index. honestly i have no idea why he refers to it as k, i learned it as gamma too. our prof is confusing that makes a ton of sense! i didn't realize the side processes were isentropic, i thought they were just adiabatic, but actually looking at the definition now... i feel really silly. whoop whoop it works, thank you so much

What's the point of Poisson brackets? Additional q: why is my dynamics lecturer so bad at explaining thing and why is his voice so indistinct

Because I think at some point, every faculty member has to do some lecturing, no matter how terrible they are at it. Also, with regards to this thread and Maths In General, I suppose I can be a little helpful, although I specialise in very applied maths to physics.

Apparently he worked at CERN for a bit, so like, kudos I guess, but everything he says is very hard to understand in every way. Snitch what is the point of Poisson brackets. And is it, like my friend suggested, a type of inner product?

One more q: I'm going to be doing a lot of dynamics revision over the Xmas holidays, would people prefer if I made a separate thread for my questions? Because I basically have to cover an entire course of material that I haven't understood.

I think dynamics will fit here pretty well, since most of it really comes down to coming up with a system of vectors and playing games with them. But if you start a new thread, go ahead and tag me so I don't miss it! It's been a long time, but I was really good at dynamics, back in the day.

Is there any conceivable way to get the radius of a quarter circle with only the perimeter of the quatercircle? And pi? Ixl is dumb sometimes. Either that or I'm dumb.

okay, so I'm really sleepy and out of it and a sanity check is not happening on my end, but I think it's doable? Sorry for my poor choices in variable letters, I wrote what they mean at the bottom

Shiiiit Whenever something is directly next to another thing, it means it's a multiplication, right? (Baby Imo has not gotten to formulas without multiplication symbols yet)

@spockandawe I think you dropped a 2 in your last step on the right? I get: p = 2×r + a Circumference = 2×π×r a = circumference/4 = π×r/2 p = (2+π/2)×r (Edited to add multiplication symbols)

Okay, I am also super tired, and out of it. Are any of these doable with just Pi and the perimeter of the quarter circle? (That was the point, so I assume so, I am just at a very dead state of mind rn) Edit: wait, these are steps? Maybe? I am so confused. I should go to bed

Ah, yes, that is a simpler way to do it :P I am missing something in mine, because my numbers don't quite work out, but even when I wrote it out again different, my brain is glazing over on where I went wrong. Probably I shouldn't try to try to help when I'm this tired, sorry.

Okay my brother just made an educated guess, and it ended being right. So uh.... Yeah. He like, guessed a number that could plausibly be the radius, then we subtracted it from the perimeter we had in the question, Which gave us a plausible curve length. We then took the plausible diameter, and did the stuff for circumference, then divided it by four, and it gave the same number. So it is right. Holy shit bro.

For the curious folk: Perimeter of the quarter circle: 10.71 Bro's estimated radius: 3 10.71 - 3 - 3 = 4.71 The curve = 4.71 3 + 3 = 6 Diameter = 6 3.14 x 6 = 18.84 Circumference = 18.84 18.84 / 4 = 4.71 4.71 checks out both ways as the curve measurement, using 3 as the radius. Fucks sake math

OK, here's your quarter circle. It has 2 straight sides and 1 curved side. The sum of the lengths of all 3 sides is the perimeter, right? So if you can express all 3 sides in terms of the radius, you can figure out what the relationship between the radius and the perimeter is. The two straight sides are easy. Because they go from the center of the circle to the edge of the circle, they are...the radius! (Which I've labeled "r" on the diagram.) spockandawe and I have called the length of the curved side "a". Four of those curved sides would make a full circle, so "a" has to be 1/4 of the circumference of the circle. Since the circumference of a circle is 2πr, a is 1/4 of that, or a=πr/2. Now you have all 3 sides expressed in terms of r: perimeter = r + r + a = 2r + πr/2 All I did in my last step was factor out the r that's in both terms: perimeter = (2+π/2)r

But I never had r......? The only number I had starting out was the sum of all three sides. The perimeter. That was the only number. I needed to find r. I had the perimeter. I was confused because I assumed I needed a calculation, but I just needed to make some educated guesses, and then test them to see if they worked.