Word Count : 430

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The adiabatic index (also called the heat capacity ratio) is denoted as \(\gamma\) and is defined as the ratio of the specific heat at constant pressure (\(C_P\)) to the specific heat at constant volume (\(C_V\)): \[ \gamma = \frac{C_P}{C_V} \] Now, let's use the first law of thermodynamics to derive the equation for an adiabatic expansion. ### First Law of Thermodynamics: The first law of thermodynamics states that: \[ dQ = dU + dW \] Where: - \(dQ\) is the heat added to the system, - \(dU\) is the change in internal energy, - \(dW\) is the work done by the system. For an adiabatic process, no _______ ________ ________ _________ __________ ________.
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