Question

Consider a closed system consisting of one mole of a monoatomic ideal gas X initially at 10.0 atm, a temperature of 487.5 K, and a volume of 4.00 L (state A). From state A, the system may expand isothermally and reversibly to state B, where the pressure is 2.50 atm. The system may also expand adiabatically and reversibly to state B, where the pressure is 2.50 atm. The system may also expand adiabatically and reversibly (through an intermediate state D) to a final state C (where P_D=P_B and V_C=V_B).  
a) Draw a PV diagram representing the pathways described above.  
b) Complete the following table for the properties of the system at each state:

State	Pressure (atm)	Volume (L)	Temperature(K)
A	10.0	4.0	487.5
B	2.5	16.0	487.5
C		16.0
D	2.5	16.0 (?)

c) Using the table from (b), label the diagram you drew in (a) with the appropriate values for P and V on the axes.
d) Complete the following table by providing values for the change in entropy of the system of each of the specific pathways:

	A→B	D→B	B→C	A→C	A→B→C→D→A	A→B→D→A
ΔSsys	.1138	0	0	.1138	0	0

e) Suppose that a temperature of 280.2 K and a pressure of 2.50 atm, substance X is on the gas-liquid coexistence curve, below which it is a liquid. For which pathway(s) above would the change(s) in entropy of the system be affected? What further information would be required to determine the correct change in entropy?

I understand the changes occurring as a result of the first isothermal process but am struggling with the adiabatic process and its intermediate, as well as part (e). My answers are italicized, but I have little faith when it comes to part (d). Any help would be appreciated.  

Answer 1

I just want to make one thing very clear that the state B is resulted from state A through a isothermal and reversible process. So this same state B can't be achieved from state A through any other different process. The question kind of confused by a statement which I have made very clear.

Joule's said that there is only one direct process between any two state on a thermodynamic space.

With this understanding, I have just 2 different paths as follows in the solution given by me below.