2006.sagews

2 system:sage

m=4.002602*1.66e-27

k=1.3806504e-23

T1=300

T2=1200

var('v T')

(v, T)

M1=4*pi*(m/(2*pi*k*T1))^(3/2)*v^2*exp(-m*v^2/(2*k*T1))

M2=4*pi*(m/(2*pi*k*T2))^(3/2)*v^2*exp(-m*v^2/(2*k*T2))

b1=plot(M1,0,6000,rgbcolor='red')

T1=text("300K",(4000,7e-4),rgbcolor='red')

T2=text("1200K",(4000,6e-4),rgbcolor='blue')

v(T)=(8*k*T/pi/m)^(1/2)

v(300)

1289.32263469406*sqrt(3)/sqrt(pi)

1289.32263469406*sqrt(3)/sqrt(pi)

1289.32263469406*sqrt(3)/sqrt(pi)

3^0.5

1.73205080756888

float(pi)

3.1415926535897931

float(v(300))

1259.932555929614

float(v(1200))

2519.8651118592279

plot(v,0,300)

b2=plot(M2,0,6000,rgbcolor='blue')

(b1+b2+T1+T2).show(axes_labels=['v[m/s]','Anteil Atome mit Geschw. v'])

T(v)=v^2*pi*m/8/k

plot(T(v),0,6000)