Adiabatic Expansion - proof of PV^(gamma) = constant

AI Thread Summary
The discussion centers on the derivation of the condition for adiabatic processes in ideal gases, specifically the equation PdV + VdP = nRdT. This equation arises from the application of the product rule in calculus, where the differential of the product PV is expressed as d(PV) = VdP + PdV. The user seeks clarification on the derivation and acknowledges the potential oversight of this fundamental calculus principle. Understanding this relationship is crucial for grasping the behavior of ideal gases during adiabatic changes. The conversation highlights the importance of foundational calculus in physics.
CAF123
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Hi,

I was looking at the proof for the derivation of the condition satisfied by adiabatic processes. (The proof can be found in many introductory physics textbooks, I am using Principles of Physics HRW 9th ed.) At some point , they say 'For an ideal gas PV=nRT and if P,V T are allowed to take on small variations we have that PdV + VdP = nRdT'. Where does the part in bold come from, specifically the PdV +VdP?

Sorry if I have overlooked something obvious.
 
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The derivative of product of variables. d(PV)=VdP +PdV
 
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