FOUR PROCESS CYCLE:     

STEP	PROCESS	Q	W	U
1	IsovolumetricHeating	+	0	+
2	Isothermal Expansion	+	-	0
3	Isovolumetric Cooling	+	0	+
4	Isothermal Compression	-	+	0

For Step 1) The work done is negative due to the lack in change of volume, and because we are adding temperature, and temperature is directly proportional to the internal energy of a system, we must be adding heat to the system.

For Step 2) Because this is supposed to be an isothermal curve (and our temperature drop was exactly 2 degrees) we can say that the internal change in energy of the system is 0. Then, because the gas is doing work by expanding the piston, the sign is negative. This means heat must be added to the system to counter the work being done by the piston.

For Step 3) Like step 1, this is an isovolumetric process, meaning no work is done. Also, because the temperature is decreasing, (and therefore internal energy is decreasing) heat must be leaving the system.

For Step 4) Because this is an isothermal curve we can, like step 2, say that the internal change in energy of the system is 0. Thus, because the gas is doing work by expanding the piston, the sign on work negative meaning heat must increase to cancel out the work being done

2) The work under these curves is in fact equal to the amount of work done, and the sign is changing due to the direction of the volume change. An increasing volume (expansion) results in negative work, or work being done by the gas. A decreasing volume (compression) therefore means that work is being done on the gas.

3) During isothermal expansion and compression, the internal energy state of the system remains the same by adding heat and work such that they are in equal but opposite quantities such that they cancel out. Or in other words, ever unit of work gives rise to an equal unit of heat.

4)                                     

THREE PROCESS CYCLE:

Step	Process	Q	W
1	Isovolumetric Heating	-	0	+
2	Isothermal Expansion	+	-	0
3	Isobaric Compression	-	+	-

 Step 1) More pressure means an increase in temperature, which gives an increase in internal energy. This must be countered by heat leaving the system.

Step 2) Work is being done by the system (and therefore negative), so heat must be added to the system to maintain the internal energy change of 0

Step 3) Positive work is being done on the system, and the internal energy is going down because it is below the isothermal curve. This means that heat must not only come out of the system to counter the positive work, but also the negative internal energy.

2) To keep the pressure constant, one could cool the system as they compressed it. This cooling of the system would (should) counter the energy being added to the system by the compression