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Equation
       
    Name Adiabatic change
 
    Equation p ⁢ V γ = const .
 
    Definition of terms

p = pressure, V = volume, γ = Cp/Cv is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume.

 
    Comments   The equation above describes an ideal gas under adiabatic conditions, that is no heat is transferred to or from the gas. Since no heat is transferred dU = CvdT = −pdV.
From the ideal gas law d ⁢ T = p ⁢ d ⁢ V + V ⁢ d ⁢ p n ⁢ R .  Using the relation Cp − Cv = R, we obtain  C v C p - C v ( p ⁢ d ⁢ V + V ⁢ d ⁢ p ) = - p ⁢ d ⁢ V ,  which reduces to V ⁢ d ⁢ p + γ ⁢ p ⁢ d ⁢ V = d ( p ⁢ V γ ) = 0. ⁢  Hence ⁢   ⁢ p ⁢ V γ = const .
 
    References An Introduction to equilibrium thermodynamics , B Morrill, Pergamon Press, 1972
       


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