//Example 2-3 Variation of Density with Temperature and Pressure
T_i = 20 //initial temperature of water [degree C]
P_i = 1 //initial pressure of water [atm]
T_f = 50 //final temperature of water [degree C]
P_f = 100 //final pressure of water [atm]
alpha = 4.8 * 10**-5 //isothermal compressiblity of water [atm^-1]
rho = 998 //density of water at 20 degree celcius and 1 atm pressure [kg / m^3]
beta_ = 0.337 * 10**-3 //coefficient of colume expansion at average temperature 35 degree [1 / K]