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

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To calculate state changes in a monatomic gas thermodynamic cycle, the initial conditions include five moles of gas at a volume of 0.1 m³ and a temperature of 280 K. The gas undergoes three processes: heating at constant volume to 600 K, isothermal expansion to its initial pressure, and isobaric compression back to the original volume. The pressure in state 3 can be determined using the ideal gas law, while the volume in state 3 can be found by applying the temperature and pressure calculated earlier. The work done during the transitions and the heat exchanged in each process can be calculated using thermodynamic equations. Understanding these calculations is essential for analyzing the complete cycle.
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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=NkBT
pVr=constant, r=Cp/Cv
dW=-PdV
W=nRT*ln(Vi/Vf)
Eint=3/2NkbT
Cv=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?
 
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You got it.
 
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