When do formulas for adiabatic processes apply?

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The discussion centers on the application of formulas for adiabatic processes, specifically questioning the use of the PV^γ = constant equation. It is noted that equating pdV with the change in internal energy suggests an adiabatic process, but there is uncertainty about whether Q = 0 is a valid assumption. The participants clarify that the PV^γ formula cannot be applied to the entire system due to the presence of two initial pressures. Additionally, it is stated that applying the formula to one partition is incorrect because there is heat flow between the partitions. Understanding the conditions under which adiabatic equations are valid is crucial for accurate thermodynamic analysis.
phantomvommand
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Homework Statement
Please see the attached photo
Relevant Equations
Change in internal energy = nCvT
Screenshot 2021-03-14 at 4.29.36 PM.png


In this problem, the method used to solve the question is to equate pdV with change in internal energy. This implies an adiabatic process as Q = 0? (not sure about this claim) However, why is it not correct to simply apply the PV^ϒ = constant formula?

Thank you.
 
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phantomvommand said:
why is it not correct to simply apply the PV^ϒ = constant formula?
What would you apply that to? You cannot apply it to the system as a whole since there are two initial pressures. You cannot apply it to one partition since there is heat flow between them.
 
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