PV diagram full circle cycle help

[blackdog666]

Homework Statement

I'm given a PV diagram, it goes from A, B, C, D, in a full circle, counter-clock wise. A is at the top, and is at 30 Pa and 25 m^3 for volume. B is at 20 Pa and 15 m^3. C is at 10 Pa and 25 m^3, and D is at 20 Pa and 35 m^3 (It goes in a full circle with A and C having the same volume, and B and D having the same pressure) Sorry I can't post a real picture of it. The question now asks:

Calculate:

A) The total internal energy in a full cycle from A-->B-->C-->D-->A

B) The total work done on or by the system in a full cycle from A-->B-->C-->D-->A.

C) The total heat flow in a full cycle from A-->B-->C-->D-->A

D) The work done on or by the system from A-->B-->C

Homework Equations

PV=nRT
(delta)U = Q - W

The Attempt at a Solution

I've thought about A, and see that in a full cycle the total change in internal energy would be 0, however I don't think that it's asking for the total change, just the total. Also for B, C, and D I'm having trouble trying to find the right equation, as I can't determine if this cycle would be isobaric, isochoric, isothermal, or adiabatic. Please help.

 

[anathema]

Thank you for sharing your PV diagram and questions with us. From your diagram, it appears that the system goes through a full cycle of four states - A, B, C, and D - with each state having different pressure and volume values.

To answer your first question, you are correct in thinking that the total change in internal energy over a full cycle is 0. This is because the internal energy of the system at state A is the same as at state C, and the internal energy at state B is the same as at state D. Therefore, the total internal energy in a full cycle is equal to the internal energy at any one state, which in this case is state A. So, the total internal energy in a full cycle from A-->B-->C-->D-->A is simply the internal energy at state A, which can be calculated using the ideal gas law, PV = nRT.

For the second question, the total work done on or by the system in a full cycle can be calculated by adding up the work done in each individual step of the cycle. From your diagram, it seems that the system undergoes a clockwise cycle, which means that the work done in the first half of the cycle (A-->B-->C) is negative, and the work done in the second half (C-->D-->A) is positive. You can use the equation W = -PΔV to calculate the work done in each step, where P is the pressure and ΔV is the change in volume. Add up the work done in each step to find the total work done on or by the system in a full cycle.

For the third question, the total heat flow in a full cycle can be calculated using the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat flow (Q) into the system minus the work (W) done by the system. Since the total change in internal energy over a full cycle is 0, as we discussed in the first question, the total heat flow must also be 0.

Finally, for the fourth question, the work done on or by the system from A-->B-->C can be calculated using the same equation as in the second question, W = -PΔV. In this case, you will only need to consider the work done in the first half of the cycle, as the system