// Debye temperature (K)
dt = 343.5;
// Einstein temperature (K)
et = dt * (%pi / 6) ^ (1 / 3);
// gas constant (J/K/mol)
r = 8.314

// Temperature
T = [1:1:500];

// Einstein model
Ce = 3 * r * ((et ./ T) .^ 2) .* exp(et ./ T) ./ ((exp(et ./ T) - 1) .^ 2);
// Debye model
Cd = 9 * r * ((T ./ dt) .^ 3) .* integrate('(x .^ 4) .* exp(x) ./ ((exp(x) - 1) .^ 2)','x',0,dt ./ T);

plot(T,Ce,'--b');
plot(T,Cd,'-r');
legend(['Einstein model';'Debye model'],2);
xlabel("Temperature (K)");
ylabel("Specific heat (J/K/mol)");