# Cloud Micro Physics
#
# Assigment # 4
#
# Köhler Kurve

restart;
with(student);

# Konstante Variablen
v_w := 1000/18*1000; # mol/m^3
M_NaCl := 58.44/1000; # kg/mol
M_SiO2 := 60.1/1000; # kg/mol
M_w := 18/1000; # kg/mol
rho_NaCl := 2.165*1000; # kg/m^3
rho_SiO2 := 2.65*1000; # kg/m^3
rho_w := 1000; # kg/m^3
nu := 2; # NaCl => Na+ Cl- => 2 Ionen
sigma := 0.076; # N/m
R := 8.314472; # J/(mol K)
T := 273.15; # K

# Variablen mit verschiedenen Werten
m_NaCl := 10^(-16)/1000; # kg
# m_NaCl := 10^(-14)/1000; # kg
# m_NaCl := 10^(-12)/1000; # kg

#epsilon := 0.001;
# epsilon := 0.01;
 epsilon := 0.1;
# epsilon := 1;

# Gleichung
#koehler := S = ( 1 + (nu * m_NaCl/M_NaCl * v_w ) / (4/3 * Pi * a^3 - m_NaCl/rho_NaCl - m_NaCl/(epsilon * rho_SiO2) ) )^(-1) * exp( (2 * M_w * sigma)/(R * T * rho_w * a) );

S := ( 1 + (nu * m_NaCl/M_NaCl * v_w ) / (4/3 * Pi * a^3 - m_NaCl/rho_NaCl - m_NaCl/(epsilon * rho_SiO2) ) )^(-1) * exp( (2 * M_w * sigma)/(R * T * rho_w * a) );

plot(S, a=.0000000001..0.001);