466 lines
60 KiB
Text
466 lines
60 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "f225380f",
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"metadata": {},
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"source": [
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"# Homework: Calculate the heat capacity of ethane at different pressures\n",
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"\n",
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"The argument we made for using departure functions is that the heat capacity for a real substance depends on pressure (or molar volume). Here we will calculate the constant pressure heat capacity at different pressures for ethane.\n",
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"\n",
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"SIS is Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed.\n",
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"\n",
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"Eric Furst \n",
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"November 2025\n",
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"\n",
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"----"
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]
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},
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{
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"cell_type": "markdown",
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"id": "28594ad2",
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"metadata": {},
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"source": [
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"As ususal, we import the *numpy* and *matplotlib* libraries. We'll also use the *SciPy* constants library."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 61,
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"id": "8ba8e9f4",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy import constants\n",
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"import scipy.optimize as opt\n",
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"\n",
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"R = constants.R # Set the gas constant to R"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8672870c-eb49-47d7-b862-437a5b5515d6",
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"metadata": {},
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"source": [
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"## Problem statement\n",
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"\n",
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"Using a Jupyter Notebook, plot the constant pressure heat capacity of ethane between 30°C and 200°C for the pressures 0.1, 2, and 4 MPa. Compare these to the ideal gas values $ C_p (T) $ given by the correlation in Appendix A.II."
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]
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},
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{
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"cell_type": "markdown",
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"id": "d2e66192-d13c-4c0d-9677-6a0e88410ff3",
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"metadata": {},
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"source": [
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"To solve this problem, I will calculate the enthalpy of ethane as a function of temperature at constant pressure. From these values, I will take the numerical derivative to find\n",
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"\n",
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"$$ C_p(T) = \\left ( \\frac{\\partial \\underbar{H}}{\\partial T} \\right )_P \\approx \\left ( \\frac{\\Delta \\underbar{H}}{\\Delta T} \\right ) _P .$$\n",
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"\n",
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"The change in enthalpy will be calculated with departure functions\n",
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"$$ \\Delta \\underline{H} = \\Delta \\underline{H}^\\mathrm{IG} + \\Delta [ \\underline{H} - \\underline{H}^\\mathrm{IG}] $$\n",
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"\n",
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"\n",
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"or\n",
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"\n",
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"$$\\Delta \\underbar{H} = \\Delta \\underline{H}^\\mathrm{IG} + [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_2 - [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_1.$$\n",
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"\n",
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"The specific departure functions we will use are derived from the generalized Peng-Robinson equation of state. "
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]
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},
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{
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"cell_type": "markdown",
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"id": "9cacacf5",
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"metadata": {},
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"source": [
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"# Generalized Peng-Robinson Equation of State\n",
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"\n",
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"The Generalized Peng-Robinson equation of state is\n",
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"\n",
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"$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n",
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"\n",
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"with\n",
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"\n",
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"$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n",
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"$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n",
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"$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n",
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"$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n",
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"\n",
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"The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n",
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"\n",
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"Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n",
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"\n",
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"$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n",
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"\n",
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"where $Z$ is the compressibility factor\n",
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"\n",
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"$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n",
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"\n",
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"For the Peng-Robinson EOS,\n",
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"\n",
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"$$ \\alpha = -1 + B $$\n",
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"$$ \\beta = A - 3B^2 -2B $$\n",
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"$$ \\gamma = -AB + B^2 + B^3 $$\n",
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"\n",
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"and \n",
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"\n",
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"$$ A = \\frac{aP}{(RT)^2} $$\n",
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"$$ B = \\frac{bP}{RT} $$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 62,
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"id": "f3d2f917",
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"metadata": {},
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"outputs": [],
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"source": [
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"\"\"\"\n",
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"Generalized Peng-Robinson EOS \n",
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"PR_pressure returns the pressure given V, T, Pc, Tc, omega\n",
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"PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n",
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"\"\"\"\n",
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"\n",
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"from scipy import constants\n",
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"from numpy.polynomial import Polynomial\n",
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"\n",
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"R = constants.R # Set the gas constant to R\n",
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"\n",
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"def calc_b(Pc,Tc):\n",
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" return 0.07780*R*Tc/Pc\n",
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"\n",
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"def calc_a(T,Pc,Tc,omega):\n",
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" kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n",
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" sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n",
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" return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n",
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"\n",
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"# Calculate the presure given V, T for PR EOS\n",
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"def PR_pressure(V,T,Pc,Tc,omega):\n",
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" a = calc_a(T,Pc,Tc,omega)\n",
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" b = calc_b(Pc,Tc)\n",
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"\n",
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" P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n",
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" return P\n",
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"\n",
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"# Solve for the compressibility factor given P, T for PR EOS in m^3/mol\n",
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"# Note that we can return multiple real roots (up to three)\n",
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"# The largest and smallest will be the vapor and liquid, respectively\n",
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"def PR_compressibility(P, T, Pc, Tc, omega):\n",
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" # Calculate a, b, A, and B\n",
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" a = calc_a(T, Pc, Tc, omega)\n",
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" b = calc_b(Pc, Tc)\n",
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" A = a*P/R**2/T**2\n",
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" B = b*P/R/T\n",
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"\n",
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" # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n",
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" alpha = -1 + B\n",
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" beta = A - 3*B**2 -2*B\n",
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" gamma = -A*B + B**2 + B**3\n",
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"\n",
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" # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n",
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" p = Polynomial([ gamma, beta, alpha, 1 ]) \n",
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"\n",
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" roots = p.roots() # returns all (possibly complex) roots of Z\n",
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" real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n",
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"\n",
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" return real_roots\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "74031b60-3999-49f8-91a2-eebfeeb09d83",
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"metadata": {},
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"source": [
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"## Data for ethane\n",
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"\n",
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"For ethane, we need the critical pressure and temperature and Pitzer's acentric factor:\n",
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"\n",
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"$P_c = 4.884$ MPa \n",
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"$T_c = 305.4$ K \n",
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"$\\underline{V}_c = 0.184\\,\\mathrm{m^3/kmol} = 9.9\\times10^{-5}\\,\\mathrm{m^3/mol}$ \n",
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"$\\omega = 0.098$ \n",
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"\n",
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"We also need heat capacity data in the ideal state. We use the empirical equation in SIS A.II:\n",
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"\n",
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"$$ C^*_p(T) = A + BT + CT^2 + DT^3 $$\n",
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"\n",
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"The code block below has values for several molecules, including ethane."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 63,
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"id": "7579e5f6",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Critical values for Ethane and the acentric factor\n",
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"# pressure in Pa, temperature in K\n",
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"Pc = 4.884e6\n",
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"Tc = 305.4\n",
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"omega = 0.098\n",
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"\n",
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"# Heat capacity data for N2, O2, CO2, CH4, C2H6\n",
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"params = np.array([\n",
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" [28.83, -0.157, 0.808, -2.871, 1800],\n",
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" [25.46, 1.519, -0.715, 1.311, 1800],\n",
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" [22.243, 5.977, -3.499, 7.464, 1800],\n",
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" [19.875, 5.021, 1.268, -11.004, 1500],\n",
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" [6.895, 17.255, -6.402, 7.280, 1500]\n",
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" ])\n",
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"\n",
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"i = params[4,:] # equation parameters for ethane"
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]
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},
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{
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"cell_type": "markdown",
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"id": "79739b7d",
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"metadata": {},
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"source": [
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"## Function to calculate the heat capacity $C_p^*(T)$\n",
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"\n",
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"Here, the ideal state constant pressure heat capacity $ C_p^*(T)$ is given by an empirical equation\n",
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"\n",
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"$$ C_p^*(T) = a + bT + cT^2 + dT^3 \\tag{Table A.II}$$\n",
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"\n",
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"where $T$ is in absolute temperature Kelvins and $C_p^*$ is in units J/(mol K)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 64,
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"id": "7f48f67a",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Calculate the heat capacity using SIS correlation in Appendix A.II\n",
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"\n",
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"def calc_Cp_IG(T, params):\n",
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" A, B, C, D = params[:]\n",
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" B *= 10**-2\n",
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" C *= 10**-5\n",
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" D *= 10**-9\n",
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" return A + B*T + C*T**2 + D*T**3"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9b0c2408-14d8-4e9b-b593-414804278b6d",
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"metadata": {},
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"source": [
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"## Function to calculate the enthalpy change in the ideal state\n",
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"$$\\Delta\\underline{H}^\\mathrm{IG} = \\int_{T_1}^{T_2}C_p^*(T)dT$$\n",
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"where we will use the ideal state heat capacities summarized in SIS Appendix A.II,\n",
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"$$C^*_p(T) = A + BT + CT^2 + DT^3$$\n",
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"resulting in\n",
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"$$\\Delta\\underline{H}^\\mathrm{IG} = A(T_2-T_1) + \\frac{1}{2}B(T_2^2 - T_1^2)+ \\frac{1}{3}C(T_2^3 - T_1^3) + \\frac{1}{4}D(T_2^4 - T_1^4)$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 65,
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"id": "b587ff94-888c-455a-b216-f68a3a7ff462",
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"def calc_deltaH_IG(T1,T2,params):\n",
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" A, B, C, D = params[:4]\n",
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" B *= 10**-2\n",
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" C *= 10**-5\n",
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" D *= 10**-9\n",
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" deltaHIG = A*(T2-T1) + B*(T2**2-T1**2)/2 + C*(T2**3-T1**3)/3 + D*(T2**4-T1**4)/4\n",
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" return deltaHIG"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4133d8cd",
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"metadata": {},
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"source": [
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"## Function for Generalized Peng-Robinson departure function \n",
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"The enthalpy departure function in $(P,T)$ control variables for the Peng-Robinson equuation of state is\n",
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"\n",
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"$$[\\underline{H} - \\underline{H}^\\mathrm{IG}] = RT(Z-1) + \\frac{T\\frac{da}{dT}-a}{2\\sqrt2 b}\\ln \\left [ \\frac{Z+(1+\\sqrt2)B}{Z+(1-\\sqrt2)B} \\right ] \\tag{Eq. 6.4-29}$$\n",
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"\n",
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"where we need to evaluate the compressibility factor,\n",
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"$$Z = \\frac{P\\underline{V}}{RT}$$\n",
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"the scaled value of $b$,\n",
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"$$B = \\frac{bP}{RT}$$\n",
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"and the deriviative of $a(T)$ with respect to temperature given in SIS (p. 264),\n",
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"$$\\frac{da}{dT} = - 0.45724 \\frac{R^2T_c^2}{P_c} \\kappa \\sqrt{\\frac{\\alpha}{T T_c}}$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 73,
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"id": "b9c7dd01-8aca-45eb-9d06-7eb0d1d1c084",
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"metadata": {},
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"outputs": [],
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"source": [
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"# With Z already calculated, we define a function to calculate the departure function\n",
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"\n",
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"\"\"\"\n",
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"Enthalpy departure function from the Peng-Robinson equation of state (eq. 6.4-29)\n",
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"For convenience, we recalculate b, kappa, sqrtalpha, and a(T) here, but we could\n",
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"use the earlier functions, too.\n",
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"\n",
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"Uses globals Tc, Pc, R\n",
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"\"\"\"\n",
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"def calc_depH(T,P,Z):\n",
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" b = 0.07780*R*Tc/Pc\n",
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" B = b*P/R/T\n",
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" kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n",
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" sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n",
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" a = 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n",
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" dadT = -0.45724*R*R*Tc*Tc/Pc*kappa*sqrtalpha/(T*Tc)**0.5\n",
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"\n",
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" depH = R*T*(Z-1)+(T*dadT-a)/(2*np.sqrt(2)*b) \\\n",
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" *np.log((Z+(1+np.sqrt(2))*B)/(Z+(1-np.sqrt(2))*B))\n",
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" return depH"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ad238854-9629-4ce9-9f2a-0c92edcecc92",
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"metadata": {},
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"source": [
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"# Enthalpy calculation function\n",
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"\n",
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"We will define a function to calculate the enthalpy."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 74,
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"id": "327f42c7",
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"metadata": {},
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"outputs": [],
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"source": [
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"def del_H(T1, T2, P1, P2, params):\n",
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" '''\n",
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" params should include: A, B, C, D for Cp correlation '''\n",
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"\n",
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" # Calculate the compressibility factor\n",
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" # Use the maximum value in case there are multiple roots\n",
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" Z1 = np.max(PR_compressibility(P1,T1,Pc,Tc,omega))\n",
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"\n",
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" # Calculate the first departure function\n",
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" depH1 = calc_depH(T1,P1,Z1)\n",
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"\n",
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" # Calculate the compressibility factor\n",
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" # Use the maximum value in case there are multiple roots\n",
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" Z2 = np.max(PR_compressibility(P2,T2,Pc,Tc,omega))\n",
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"\n",
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" # Calculate the second departure function\n",
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" depH2 = calc_depH(T2,P2,Z2)\n",
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"\n",
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" # Calculate the ideal gas contribution\n",
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" deltaH_IG = calc_deltaH_IG(T1,T2,params)\n",
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"\n",
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" # Add for the total change in enthalpy\n",
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" return deltaH_IG + (depH2 - depH1)\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2dd02464",
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"metadata": {},
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"source": [
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"# Routine to calculate heat capacity"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 82,
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"id": "bb8d3194-40ce-463c-9914-5eed37d4f7de",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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||
"Text(0.5, 1.0, 'Heat capacity for ethane at different pressures')"
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||
]
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||
},
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||
"execution_count": 82,
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"metadata": {},
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||
"output_type": "execute_result"
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},
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{
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"data": {
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||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Known values in problem\n",
|
||
"# The initial and final temperatures are\n",
|
||
"Ti = 30 + 273.15 # Beginning temperature in K\n",
|
||
"Tf = 200 + 273.15 # final temperature in K\n",
|
||
"delta_T = 1 # use increments to calculate numerical derivative\n",
|
||
"\n",
|
||
"fig, ax = plt.subplots()\n",
|
||
"\n",
|
||
"for P in [0.1e6, 2e6, 4e6]:\n",
|
||
"\n",
|
||
" T = np.arange(Ti, Tf + 1, delta_T)\n",
|
||
"\n",
|
||
" cp_values = np.zeros_like(T, dtype=float)\n",
|
||
"\n",
|
||
" for idx, T0 in enumerate(T):\n",
|
||
" # Compute ΔH over 1 K interval for each temperature\n",
|
||
" dH = del_H(T0, T0 + delta_T, P, P, i[:4])\n",
|
||
" cp_values[idx] = dH / delta_T\n",
|
||
"\n",
|
||
" ax.plot(T, cp_values, label=f'P = {P/1e6:.1f} MPa')\n",
|
||
"\n",
|
||
"cp_ideal = calc_Cp_IG(T, i[:4])\n",
|
||
"ax.plot(T, cp_ideal, '--', label='Ideal Gas')\n",
|
||
"\n",
|
||
"ax.legend()\n",
|
||
"plt.xlabel('T (K)')\n",
|
||
"plt.ylabel(\"$C_p$ (J/molK)\")\n",
|
||
"plt.title('Heat capacity for ethane at different pressures')"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5e87754",
|
||
"metadata": {},
|
||
"source": [
|
||
"This makes sense. The isotherms on the pressure-enthalpy plot tend to bend toward lower values of enthalpy with higher pressures. That is, $(\\partial P/\\partial \\underbar{H})_T$ has a lower and negative slope on the plot. Thus, at $P = 4$ MPa, for each 10 degree difference in temperature, there is nearly double the amount of enthalpy change. Pretty interesting!\n",
|
||
"\n",
|
||
"Second, the non-lienar behavior also makes sense. This isobar eventually intersects the VLE curve (it’s below the critical pressure) and so you expect the heat capacity to diverge! Why? Think of the intersecting isotherm and what the slope represented by looks like in the VLE region. Then, as you go to higher temperatures along the isobar away from the VLE curve, you begin to recover more ideal-like behavior (and its temperature dependence)."
|
||
]
|
||
}
|
||
],
|
||
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|
||
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|
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