Theoretical Physics VI-Thermodynamics Sheet 12

Problem 12.2

omega1 = 250; omega2 = 670; omega3 = 7; h = 6.626 10^(-34); 
    kb = 1.381 10^(-23); N1 = 10^7;

h (omega1 omega2 omega3)^(1/3)/
        kb (N1/Zeta[3])^(1/3)

Problem 12.3

Solve[c T^(3/2) - b T^(1/2) - a == 0, T]

a = n/ω (h/Sqrt[2 π m kb ])^3; 
    b = 4/3 (π/kb m g L)^(1/2); c = Zeta[3/2, 1]; 
    g = 9.81;

(((((((h^3) (Sqrt[kb m]) n)/((kb^2) (m^2) ω Zeta[(3/2)]))))^(2/3))/(2 π)) - 
      (1/18) (((16 (Sqrt[((g L m)/kb)]) (Sqrt[π]))/Zeta)[(3/2)] - (64 (2^(1/3)) g (kb^2) L (m^4) (π^4) (ω^2))/(((1024 g (kb^8) L (m^10) (Sqrt[((g L m)/kb)]) (π^(21/2)) (ω^6) Zeta[(3/2)]^3 - 729 (h^6) (kb^6) (m^6) (n^2) (π^6) (ω^4) Zeta[(3/2)]^4 + 27 √(-2048 g (h^6) (kb^14) L (m^16) (Sqrt[((g L m)/kb)]) (n^2) (π^(33/2)) (ω^10) Zeta[(3/2)]^7 + 729 (h^12) (kb^12) (m^12) (n^4) (π^12) (ω^8) Zeta[(3/2)]^8)))^(1/3)) - (((1024 g (kb^8) L (m^10) (Sqrt[((g L m)/kb)]) (π^(21/2)) (ω^6) Zeta[(3/2)]^3 - 729 (h^6) (kb^6) (m^6) (n^2) (π^6) (ω^4) Zeta[(3/2)]^4 + 27 √(-2048 g (h^6) (kb^14) L (m^16) (Sqrt[((g L m)/kb)]) (n^2) (π^(33/2)) (ω^10) Zeta[(3/2)]^7 + 729 (h^12) (kb^12) (m^12) (n^4) (π^12) (ω^8) Zeta[(3/2)]^8)))^(1/3))/((2^(1/3)) (kb^3) (m^3) (π^3) (ω^2) Zeta[(3/2)]^2))