Calculating Total Entropy Change for a Three-Step Process

[StonieJ]

Question:
Three moles of an ideal gas (CV,m = 7/2R) initially at 300K are taken through a series of three compression/expansion steps:

The gas is expanded isothermally and reversibly at 300K. This process involves 10.37 kJ of heat going into the system.
The gas is then expanded reversibly and adiabatically to a new volume and temperature. This process involves no heat.
The gas is then compressed in a process that is neither adiabatic nor isothermal until it is back to the original state where it started. This process involves an unknown amount of heat, but we do know that for this process ?Ssurroundings = 40 J/K.
What is dStotal for process 3?



I tried solving this by simply saying that the sum of dS for steps 1, 2, and 3 were zero, since the process is cyclic. Therefore:

dS1 + dS2 = -dS3

We are told the reversible heat for step 1, so we can find it by:

dS1 = qrev/T = 10.37 kJ / 300 K = 34.6 J/K

The second step is adiabatic, so q = 0, and therefore dS2 = 0. This results in:

dS3 = -dS1 = -34.6 J/K.

My biggest concern is that I'm not using enough information provided by the question.

 

[GCT]

you seem to be doing fine,

 

[Blueshift5]

I would say that your approach is correct in calculating the total entropy change for the three-step process. However, there may be some additional information that could provide a more accurate calculation. For example, the temperature and volume at the end of step 2 could provide more information about the gas and its properties, which could then be used to calculate the entropy change for step 3 more accurately. Additionally, it would be helpful to know the specific heat capacity at constant pressure (Cp) for the gas, as this would also affect the calculation of the entropy change. Without this information, the calculation may not be as precise. Overall, your approach is valid, but it may be beneficial to have more information to ensure a more accurate calculation.