We can express k 0 in terms of an effective temperature T e f f : k 0 2 = 4 π π e 2 n / k B T e f f , or k B T e f f = n ∂ ∂ μ μ / ∂ ∂ n . The general result for T e f f is T e f f T = 4 3 Γ Γ ( 1 / 2 ) ( E F / k B T ) 3 / 2 F − − 1 / 2 ( μ μ / k B T ) . In the classical limit k B T ≫ ≫ E F , we find T e f f = T , while in the degenerate limit k B T ≪ ≪ E F we find k B T e f f = ( 2 / 3 ) E F . A simple approximate form that recovers both limits correctly is k B T e f f = [ ( k B T ) p + ( 2 E F / 3 ) p ] 1 / p , for any power p . A value that gives decent agreement with the exact result for all k B T / E F is p = 1.8 , which has a maximum relative error of < 2.3%.