cp_press.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Image, display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calcolo del calore specifico di una fase minerale in condizioni di alta pressione\n",
    "\n",
    "Come fatto presente nelle slide, non è difficile per via calorimetrica misurare il calore specifico di una sostanza a pressione ambiente. Molto più difficile e inaccurato è fare quelle misure in alta pressione. Per cui, la via che si segue nelle modellizzazioni termodinamiche, per cui occorre calcolare l'energia libera *G* in condizioni P/T generiche, è sfruttare il *Cp* per calcolare come varia *G* a *P* ambiente fino alla temperatura voluta *T* (cammino 2 nella figura sottostante), e poi calcolare il contributo barico a *G* sfruttando il termine *VdP* (cammino 3), il che implica usare l'equazione di stato alla temperatura *T*\n",
    "\n",
    "![](https://github.com/Mauro-Prencipe/geochimica/blob/master/G_P_T.png?raw=true)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una volta che si sia ottenuto il modo \\[per questa via (2+3)\\] di calcolare *G* ad ogni condizione P/T, possiamo però anche calcolarci il calore specifico e la sua dipendenza dalla temperatura in condizioni diverse da quelle della pressione ambiente.\n",
    "\n",
    "Per fare questo, sfruttiamo la definizione di entropia; a pressione costante:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$dS = \\frac{(\\delta Q)_P}{T} = \\frac{C_P(T)}{T}dT \\ \\rightarrow \\ C_P(T)=T\\left(\\frac{\\partial S}{\\partial T}\\right)_P$$\n",
    "\n",
    "Ma sappiamo anche che \n",
    "\n",
    "$$S =-\\left(\\frac{\\partial G}{\\partial T}\\right)_P \\ \\rightarrow \\ C_P(T)=-T\\left(\\frac{\\partial^2G}{\\partial T^2}\\right)_P$$\n",
    "\n",
    "In sostanza, calcoliamo il calore specifico a qualunque pressione e temperatura, dalla derivata seconda della $G(T,P)$ rispetto alla temperatura, a pressione costante.\n",
    "\n",
    "Ciò è proprio quello che faremo in questo notebook, per il piropo, sfruttando il programma *gibbs_tp* e il suo metodo *g_tp* della classe *mineral* per calcolare *G* a qualunque valore di *T* e *P* (a partire dal calore specifico a pressione ambiente e l'equazione di stato)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Come di consueto, carichiamo e lanciamo il programma gibb_tp.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%run gibbs_tp.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Controlliamo la presenza dei dati termodinamici su piropo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mineral: pyrope\n",
      "\n",
      "K0: 173.70 GPa, Kp: 4.00, dK0/dT: -0.0261 GPa/K, V0: 11.3180 J/bar\n",
      "G0: -5934105.00 J/mol, S0: 266.30 J/mol K\n",
      "\n",
      "Cp coefficients and powers:\n",
      "+6.3350e+02  +0.0\n",
      "-5.1961e+06  -2.0\n",
      "-4.3152e+03  -0.5\n",
      "\n",
      "Alpha coefficients and powers:\n",
      "+4.3600e-05  +0.0\n",
      "-4.3600e-04  -0.5\n"
     ]
    }
   ],
   "source": [
    "py.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A pressione ambiente, possiamo calcolare il calore specifico a qualunque temperatura sfruttando il metodo *cp_t*. Per esempio, a T=300 K, abbiamo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "326.627"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "py.cp_t(300).round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adesso scriviamo una funzione (*cp_p*) che ci consenta di calcolare il $C_P$ a partire dalla derivata seconda della $G$ rispetto a $T$ come descritto sopra. Il codice è riportato nella cella seguente.\n",
    "\n",
    "L'idea consiste in:\n",
    "\n",
    "- costruiamo una lista di 8 valori di temperatura centrata sul valore di $T$ per il quale vogliamo ottenere il $C_P$, a partire da $T_{min}=T-5$ fino a $T_{max}=T+5$\n",
    "- calcoliamoci i valori di $G$ per ogni temperatura nella lista e alla pressione $P$ voluta\n",
    "- facciamo un fit polinomiale del quarto ordine dei valori di $G(T)$\n",
    "- sulla polinomiale $G(T)$ ottenuta, facciamo la derivata seconda e, di questa derivata, calcoliamo il valore alla temperatura voluta\n",
    "- moltiplichiamo il valore della derivata ottenuta per $-T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cp_p(t,p):\n",
    "    dt=5.\n",
    "    deg=4\n",
    "    tmin=t-dt\n",
    "    tmax=t+dt\n",
    "    t_list=np.linspace(tmin,tmax,8)\n",
    "    g_list=np.array([])\n",
    "    for it in t_list:\n",
    "        ig=py.g_tp(it,p)\n",
    "        g_list=np.append(g_list,ig)\n",
    "        \n",
    "    reg=np.polyfit(t_list,g_list,deg) # fit polinomiale\n",
    "    der2=np.polyder(reg,2)            # derivata seconda del fit\n",
    "    cpp=-1*t*np.polyval(der2,t)       # valore della derivata alla \n",
    "                                      # temperatura moltiplicata per -t\n",
    "    return cpp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proviamo la funzione a T=300 K e P ambiente (0 GPa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "326.628"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cp_p(300,0).round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Come si vede, il valore ottenuto è molto vicino a quello calcolato sopra, usando *cp_t*. \n",
    "\n",
    "Ma noi siamo *scettici*, e vogliamo controllare il risultato di *cp_p* su un intervallo più esteso di temperatura, a *P*=0, confrontandolo con i risultati di *cp_t* nello stesso intervallo di temperatura... Quindi scriviamo il codice che segue e lo eseguiamo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Errore medio sul Cp: 0.00011\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_list=np.linspace(300,1000,20)\n",
    "cp_new_list=np.array([])\n",
    "cp_old_list=np.array([])\n",
    "for it in t_list:\n",
    "    icpn=cp_p(it,0)\n",
    "    icpo=py.cp_t(it)\n",
    "    cp_new_list=np.append(cp_new_list,icpn)\n",
    "    cp_old_list=np.append(cp_old_list,icpo)\n",
    "    \n",
    "dcp=(cp_old_list-cp_new_list)**2\n",
    "error=np.sqrt(np.sum(dcp)/len(cp_new_list))\n",
    "print(\"\\nErrore medio sul Cp: %7.5f\" % error)    \n",
    "    \n",
    "plt.figure()\n",
    "plt.plot(t_list,cp_new_list,\"b-\", label=\"Cp from G\")\n",
    "plt.plot(t_list,cp_old_list,\"k*\", label=\"Cp from Cp(T)\")\n",
    "plt.xlabel(\"T (K)\")\n",
    "plt.ylabel(\"Cp (J/K mole)\")\n",
    "plt.legend(frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'errore medio sul $C_P$ (in J/K mole) è molto basso (una unità sulla 4^ decimale). La curva in blu mostra i dati calcolati con la nuova funzione *cp_p*; gli asterischi in nero mostrano il $C_P$ calcolato con la vecchia funzione *cp_t*: l'accordo tra i due metodi è eccellente: vuol dire che non abbiamo fatto errori sia \n",
    "\n",
    "- nella teoria, \n",
    "- nel modo con cui calcoliamo le derivate (8 punti in temperatura in un certo intervallo, interpolati con una polinomiale del quarto ordine... sono tutte scelte di *parametri numerici* fatte *a buon senso*, ma non è scontato che siano adeguate al caso, perciò è necessario fare i dovuti test e controlli incrociati), \n",
    "- nel codice python che è stato scritto. \n",
    "\n",
    "Adesso che ci *fidiamo* della nuova funzione, scriviamo il codice di un'altra funzione che la sfrutti per confrontare il $C_P$ in un certo intervallo di temperature, a pressioni crescenti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cp_p_serie(pmin,pmax,npp):\n",
    "    t_list=np.linspace(300,1000,20)\n",
    "    p_list=np.linspace(pmin,pmax,npp)\n",
    "    \n",
    "    plt.figure()\n",
    "    for ip in p_list:\n",
    "        cp_list=np.array([])\n",
    "        for it in t_list:\n",
    "            icpt=cp_p(it,ip)\n",
    "            cp_list=np.append(cp_list,icpt)\n",
    "            \n",
    "        lbl=\"P: \"+str(ip)+\" GPa\"    \n",
    "        plt.plot(t_list,cp_list,label=lbl)\n",
    "        \n",
    "    plt.xlabel(\"T (K)\")\n",
    "    plt.ylabel(\"Cp (J/K mole)\")\n",
    "    plt.legend(frameon=False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cacoliamo dunque, con questa funzione, l'andamento di $C_P(T)$ alle pressioni di 0, 15 e 30 GPa:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cp_p_serie(0,30,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Otteniamo curve quasi *parallele* che si spostano a valori via via più bassi al salire della pressione. Confrontare il risultato *numerico* ottenuto con le predizioni della *teoria* riportate a pagina 19 delle dispense (formula 1.49)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}