How Do I Calculate Entropy of Surroundings in Adiabatic Expansion?

In summary: For processes that involve changes in temperature (ie, non-ideal gas), the relationships between work, entropy, and temperature may not hold. In summary, for an adiabatic process, q=0 so you can't use the aforementioned formulas to calculate entropy of the surroundings. However, you can still use them to calculate entropy of the system (either given or calculated).
  • #1
pilotpanda
3
0
How do I calculate the entropy of the surroundings for an adiabatic expansion? I know [tex]\Delta[/tex]Ssur = qrev/T for reversible process and qirrev/T for irreversible process. But q=0 for adiabatic process, so are there any other formulas that I could use to calculate [tex]\Delta[/tex]Ssurr (I know there is a [tex]\Delta[/tex]S = w/T formula but I'm not sure if it applies here)?

Thanks,

pilotpanda
 
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  • #2
Hi pilotpanda, welcome to PF!

A reversible adiabatic process is isentropic (total entropy change is zero), under the reasoning you describe. If you're analyzing an irreversible adiabatic process, try replacing the process with a combination of reversible processes that achieves the same end state (but these reversible processes will likely not be adiabatic). Does this answer your question?
 
  • #3
Hi Mapes

Thanks! I guess I'm just really confused about the adiabatic expansion. If the process is isothermal, I know how to approach the problem since qsys=qsur=-w, I can use [tex]\Delta[/tex]S = -w/T to calculate entropy of the surroundings and compare that with the system (either given or calculated) to determine whether I have a reversible or irreversible process. But for an adiabatic process, since q=0, I'm not sure if I can still use the abovementioned formulas to calculate [tex]\Delta[/tex]Ssurroundings (-w/T). I think there may be some concepts / formulas that I'm missing here so please help me on that.

pilotpanda
 
  • #4
Where does [itex]\Delta S=-w/T[/itex] come from? Reversible work doesn't carry entropy.

Also, isothermal only implies constant energy for an ideal gas. Definitely make sure you're familiar with the assumptions that go into these calculations.
 
  • #5
Well, for an isothermal process [tex]\Delta[/tex]S = nRln[tex]\frac{V2}{V1}[/tex] and since work for a reversible process is -nRTln[tex]\frac{V2}{V1}[/tex]...

After some struggle, I think I know the answer now. Thanks for your help!
 
  • #6
OK, cool, but note that those relationships only apply for an isothermal process on an ideal gas. They arise because as you increase or decrease volume, it's necessary to heat or cool the ideal gas to keep the temperature constant.
 

FAQ: How Do I Calculate Entropy of Surroundings in Adiabatic Expansion?

What is entropy and how does it relate to adiabatic expansion?

Entropy is a measure of the disorder or randomness within a system. In the context of thermodynamics, it is a measure of the number of possible microstates that a system can have. Adiabatic expansion refers to a process in which a gas expands without exchanging heat with its surroundings. The change in entropy during adiabatic expansion is related to the change in the number of possible microstates within the gas.

How does the entropy of a gas change during adiabatic expansion?

During adiabatic expansion, the volume of the gas increases while the temperature decreases. This results in a decrease in the number of possible microstates within the gas, leading to a decrease in entropy. This is because the gas molecules become more spread out and less chaotic as they expand, resulting in a decrease in disorder.

What is the formula for calculating the change in entropy during adiabatic expansion?

The change in entropy during adiabatic expansion can be calculated using the formula ΔS = nR ln(V2/V1), where n is the number of moles of gas, R is the gas constant, V2 is the final volume, and V1 is the initial volume.

How does adiabatic expansion affect the internal energy of a gas?

Since adiabatic expansion involves no exchange of heat, the internal energy of the gas remains constant. This means that the decrease in temperature during adiabatic expansion is offset by the increase in volume, resulting in no net change in internal energy.

Can the entropy of a gas ever increase during adiabatic expansion?

No, the entropy of a gas can only decrease during adiabatic expansion. This is because the process involves a decrease in disorder as the gas expands, and entropy is a measure of disorder. However, the change in entropy can be positive if the gas is compressed adiabatically, as this results in an increase in disorder and therefore an increase in entropy.

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