C.E
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I got if from when you said "(v-Ax)^{\gamma}\approx v^\gamma-Ax\gamma" in post 8.
The discussion revolves around a thermodynamics problem involving a horizontal tube with a sliding piston, where the gas is thermally insulated. The problem requires analyzing the forces acting on the piston and the nature of its motion, particularly under adiabatic conditions.
Several participants have provided insights into the use of Taylor series for approximating expressions related to pressure and volume. There is ongoing exploration of how to relate the pressures on either side of the piston and how to derive the force acting on it. Some participants express confusion about the correct application of Taylor series and the implications of their results.
There is uncertainty regarding the ideal gas assumption and the specific equations that apply to the non-ideal gas scenario. Participants are also navigating the complexities of deriving expressions without complete information about temperature or the number of moles of gas.