How Do You Calculate State Changes in a Monatomic Gas Thermodynamic Cycle?

[rchenkl]

Homework Statement

Five moles of an ideal monotomic gas initially occupies a volume of 100 x 10^-3m³ at a temperature of 280 K. (state 1)
The gas is then subject to the following processes in sequence:
* heated at constant volume to a temperature of 600K (state 2)
* allowed to expand isothermally to its initial pressure (state 3)
* compressed isobarically to its original volume (state 1)

(a) Find the pressure and volume of the gas in state 3
(b) Calculate the work done on the gas in going from state2 to state 3.
(c) Calculate the heat exchanged between the gas and its environment during each of the 3 processes of the cycle 1->2, 2->3, 3->1.
In each case, indicate whether the heat enters or leaves the gas.
(d) Calculate the net work done on the gas in one cycle

Homework Equations

PV=nRT=Nk_BT
pV^r=constant, r=C_p/C_v
dW=-PdV
W=nRT*ln(V_i/V_f)
E_int=3/2Nk_bT
C_v=5/2R

The Attempt at a Solution

I'm stuck on question (a).
I calculated the pressure using PV=nRT where the initial volume, temperature and number of moles of gas is provided. P=(5*8.314*280)/(100x10^-3)
Now, I don't know how to calculate the volume in state 3. Do I use T=600K and P=the above I calculated, to obtain the volume?

 

[Mapes]

You got it.