Derive adiabatic equation of an ideal gas using 1st law of thermodynamic.
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Deriving the adiabatic relation for an ideal gas from a differential geometry point of view. Recall Q=dU+W (First Thermodynamic law, energy conservation). If Q=0 (for adiabatic process, either adiabatic expansion or contraction), and supposing W=pdV, then 0=dU+pdV.
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