Q & W for idealized processes undergone by an ideal gas

For an ideal gas, \( \Delta \)U = CV \( \Delta \)T      \( \Delta \)H = CP \( \Delta \)T     CP – CV = R

  • Constant Volume Process (const. V)

           W = 0, Q = CV \( \Delta \)T

  • Constant Pressure Process (const. P)
           W = -P \( \Delta \)V     Q = CP \( \Delta \)T

  •  Isothermal Process (const. T)
            \( \Delta \)U = 0, Q = -W,  W = RT ln(V1/V2) = RT ln(P2/P1)

  •  Reversible Adiabatic Process (Q = 0; PV\( \gamma \) = const., W = \( \Delta \)U)
             W = (P2V2-P1V1) / (\( \gamma \)-1) = R(T2-T1)/(\( \gamma \)-1)

  •    Polytropic Process (PVn = const.)
               W = (P2V2-P1V1) / (n-1) = R(T2-T1)/(n-1)
               Q = \( \Delta \)U - W