# Boltzmann distribution for x-velocity
#
# first, define variables:

# mass of CO2: 44 Da; 44 g/mol or .044 kg/mol
m  = 44.0/1000

# Boltzman const in J/K [ J = kg m^2 s^-2 ]
k = 1.38e-23

# Avogadro's no.; molecules/mol
N = 6.023e+23

# now, define the function:
# we'll use a(x) for T=77 K (boiling T of liquid N2)
a(x) = ((m/(2*pi*77*k*N))**0.5)*exp((-m*x**2)/(2*77*k*N))
# we'll use b(x) for T=273 K (freezing point of water)
b(x) = ((m/(2*pi*273*k*N))**0.5)*exp((-m*x**2)/(2*273*k*N))
# we'll use c(x) for T=373 K (boiling point of water)
c(x) = ((m/(2*pi*373*k*N))**0.5)*exp((-m*x**2)/(2*373*k*N))

# now plot them:
set samples 1000
set title "Boltzmann probability distribution for x-velocities of CO2 molecules"
set ylabel "Probability (s/m)"
set xlabel "x-velocity (m/s)"
plot [-1000:1000] a(x), b(x), c(x)

#set term post lw 2 "Courier" 18; set output "file.ps"
#plot [-1000:1000] a(x), b(x), c(x)