Hint 5.4

Always true:
   P V = n R T = N k T
   ΔE_int = Q + W
   dW = –p dV
   ΔE_int = n C_V ΔT
   C_P = C_V + R
   γ = C_P / C_V

Constant T:
   ΔE_int = 0
   W = n R T ln(V_f / V_i)

Constant V:
   W = 0
   Q = n C_V ΔT

Constant P:
   W = –P (V_f – V_i)
   Q = n C_P ΔT

Adiabatic
   Q = 0
   P V^γ = Constant

Degrees of freedom
   Translational: f = 3
   Diatomic, Rotational: f = 2
   Diatomic, Vibrational: f = 2
   Polyatomic, Rotational: f = 3
   Polyatomic, Vibrational: f varies
   C_V = fR/2, C_P = (f+2)R/2, γ = (f+2)/f

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