{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "Ejercicios_T1.ipynb", "provenance": [], "collapsed_sections": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "source": [ "## Importamos librerías" ], "metadata": { "id": "ctgg3tv4d4a9" } }, { "cell_type": "code", "execution_count": 4, "metadata": { "id": "FNuY3zZTdbtN" }, "outputs": [], "source": [ "from sympy import * # Librería para trabajo simbólico\n", "import numpy as np # Librería para cálculo numérico\n", "import math # Librería para utilizar símbolos matemáticos como el número pi, que se escribe como math.pi\n", "import matplotlib.pyplot as plt # Librería para poder dibujar gráficas\n", "from scipy import integrate # Librería de integración" ] }, { "cell_type": "markdown", "source": [ "### Ejercicio \n", "\n", "Un gas con masa 1 kg y a una presión de $P_1=1$ bar se encuentra contenido en un dispositivo cilindro-pistón con un volumen inicial $V_1=1$ m$^3$. Considerando un proceso politrópico:\n", "\n", "$$PV^n=C$$\n", "\n", "a) Determinar $P_2$ si $n=1.1$ y $V_2=2$ m$^3$.\n", "\n", "b) Determinar $P_2$ si se considera un proceso isotermo y $V_2=2$ m$^3$.\n", "\n", "c) Determinar $P_2$ si se considera un proceso adiabatico y $V_2=2$ m$^3$.\n", "\n", "d) Determinar $P_2$ si se considera un proceso isóbaro y $V_2=2$ m$^3$." ], "metadata": { "id": "NwGQFoff3FOA" } }, { "cell_type": "code", "source": [ "P1=1.0 #bar\n", "V1= 1.0 #m3\n", "\n", "# a)\n", "n=1.1\n", "V2=2.0\n", "P2=(P1*V1**n)/(V2**n)\n", "print(\"a) La presión es es:\", P2, \"bar\")\n", "\n", "# b)\n", "n=1.0\n", "V2=2.0\n", "P2=(P1*V1**n)/(V2**n)\n", "print(\"b) La presión es es:\", P2, \"bar\")\n", "\n", "# c)\n", "n=1.4\n", "V2=2.0\n", "P2=(P1*V1**n)/(V2**n)\n", "print(\"c) La presión es es:\", P2, \"bar\")\n", "\n", "# d)\n", "n=0\n", "V2=2.0\n", "P2=(P1*V1**n)/(V2**n)\n", "print(\"d) La presión es es:\", P2, \"bar\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "QDKVuaWO6TUj", "outputId": "c3fefdfe-8035-4d86-d71a-fe2f8cfaa2dc" }, "execution_count": 5, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "a) La presión es es: 0.4665164957684037 bar\n", "b) La presión es es: 0.5 bar\n", "c) La presión es es: 0.37892914162759955 bar\n", "d) La presión es es: 1.0 bar\n" ] } ] }, { "cell_type": "markdown", "source": [ "### Problema 5\n", "\n", "Un gas en un dispositivo cilindro-pistón sufre un proceso de expansión para el que la relación entre la presión y el volumen viene dada por:\n", "\n", "$$PV^n=C$$\n", "\n", "Si $P_1=3$ bar, $V_1=0.1$ m$^3$ y $V_2=0.2$ m$^3$. Determínese el trabajo, en kJ, para el proceso, si:\n", "\n", "a) $n=1.5$\n", "\n", "b) $n=1.0$\n", "\n", "c) $n=0$" ], "metadata": { "id": "spnZkA_3zQMx" } }, { "cell_type": "markdown", "source": [ "### Resolución:\n", "\n", "Incluye definción de funciones, representación gráfica y calculo de la integral" ], "metadata": { "id": "FJBbg3y_e6Vs" } }, { "cell_type": "code", "source": [ "P1=3.0*100000 #Presion en Pa\n", "V1=0.1\n", "V2=0.2\n", "\n", "V=symbols('V')\n", "\n", "def Pa(V):\n", " n=1.5\n", " C=P1*V1**n\n", " return C/V**n\n", "\n", "def Pb(V):\n", " n=1.0\n", " C=P1*V1**n\n", " return C/V**n \n", "\n", "def Pc(V):\n", " n=0\n", " C=P1*V1**n\n", " return C/V**n \n", "\n", "npt=100\n", "V12 = np.linspace(V1, V2, npt) # la instrucción np.linspace(V1, V2, npt) genera un array de \"npt\" valores entre V1 y V2\n", "#print(\"Los valores de V entre V1 y V2 son\")\n", "#print(V12)\n", "\n", "P12a = Pa(V12) #Si evaluamos la función Pa pasándole el array entero V12, nos devuelve otro array P12a de presiones.\n", "P12b = Pb(V12)\n", "P12c = Pc(V12)\n", "\n", "fig, ax1 = plt.subplots(figsize=(12, 5)) #con esta intrucción creamos una figura \"fig\", con ejes llamados \"ax1\", de tamaño 12x5\n", "ax1.plot(V12,P12a) #dibuja la función P12a \n", "ax1.plot(V12,P12b)\n", "ax1.plot(V12,P12c)\n", "ax1.set_xlabel(\"V (m^3)\") #etiqueta del eje x\n", "ax1.set_ylabel(\"P (Pa)\") #etiqueta del eje y\n", "\n", "\n", "print(\"La función P(V) del apartado a) es:\", Pa(V), \"y el trabajo en J es:\")\n", "print(integrate.quad(Pa, V1, V2)) #integral definida de Pa·dV entre V1 y V2\n", "print(\"La función P(V) del apartado b) es:\", Pb(V), \"y el trabajo en J es:\")\n", "print(integrate.quad(Pb, V1, V2))\n", "print(\"La función P(V) del apartado c) es:\", Pc(V), \"y el trabajo en J es:\")\n", "print(integrate.quad(Pc, V1, V2))\n", "\n", "print(\"El trabajo en J es:\", (Pa(V2)*V2-P1*V1)/(1-1.5))\n", "\n", "\n", "Vaux=V12\n", "Paux=P12a\n", "Wexact=integrate.quad(Pa, V1, V2)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 458 }, "id": "IFtZBEaEb-Hg", "outputId": "568788d3-ce05-4827-ca65-f181d7360dcf" }, "execution_count": 6, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "La función P(V) del apartado a) es: 9486.83298050514*V**(-1.5) y el trabajo en J es:\n", "(17573.593128807148, 1.951060771699614e-10)\n", "La función P(V) del apartado b) es: 30000.0*V**(-1.0) y el trabajo en J es:\n", "(20794.415416798358, 2.308643877934986e-10)\n", "La función P(V) del apartado c) es: 300000.000000000 y el trabajo en J es:\n", "(30000.0, 3.3306690738754696e-10)\n", "El trabajo en J es: 17573.593128807144\n" ] }, { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "source": [ "### Resolución numérica (Opcional)\n", "\n", "Aqui vamos a resolver el apartado a) \"sin hacer integrales\". Para ello se utilizará lo que se denomina \"integración numérica\", que se basa en trocear el area bajo la curva utilizando trapecios y sumar el area de cada uno de esos trozos." ], "metadata": { "id": "dmrasiEafbsq" } }, { "cell_type": "code", "source": [ "npt=4 #numero de puntos escogidos. Modificar para ver lo que ocurre...\n", "V12 = np.linspace(V1, V2, npt)\n", "\n", "P12a = Pa(V12)\n", "\n", "fig, ax1 = plt.subplots(figsize=(12, 5))\n", "ax1.plot(V12,P12a,'-ok')\n", "ax1.fill_between(V12,np.zeros(npt),P12a)\n", "\n", "sum=0.0\n", "for ii in range(len(V12)): #bucle entre 0 y len(V12)-1, donde len(V12) es la longitud del array V12 (es decir, npt)\n", " ax1.plot([V12[ii],V12[ii]],[0,P12a[ii]],'-k')\n", " if ii<(len(V12)-1):\n", " sum+=0.5*(P12a[ii]+P12a[ii+1])*(V12[ii+1]-V12[ii]) #Regla del trapecio de integración numérica: se suman las areas de los trapecios\n", "\n", "ax1.plot(Vaux,Paux,'--r') #esta es la curva exacta\n", "ax1.set_xlabel(\"V (m^3)\") \n", "ax1.set_ylabel(\"P (Pa)\") \n", "\n", "\n", "print(\"La integral aproximada es:\")\n", "print(sum, \" J\\n\")\n", "print(\"Se han usado\", npt-1, \"trapecios y el error es:\")\n", "print(sum-Wexact[0], \" J\\n\")\n", "\n" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 440 }, "id": "vlwnpUfhev50", "outputId": "59c42461-2797-4ae0-96bc-f632d74b57a0" }, "execution_count": 7, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "La integral aproximada es:\n", "17910.537496798563 J\n", "\n", "Se han usado 3 trapecios y el error es:\n", "336.94436799141477 J\n", "\n" ] }, { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "code", "source": [ "V1= 0.09 #m3\n", "V2= 0.03 #m3\n", "\n", "def Pres(V):\n", " return (-14*V+2.44)*1.e5\n", "\n", "P1=Pres(V1)\n", "P2=Pres(V2)\n", "\n", "print(P1,P2)\n", "\n", "print(integrate.quad(Pres, V1, V2))\n", "\n", "print(1.18*(0.09-0.03)+(2.02-1.18)*0.5*(0.09-0.03))" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "wJqZUjNciVOS", "outputId": "7d22a2ba-cb02-4df6-fbca-a393a176509a" }, "execution_count": 8, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "118000.0 202000.0\n", "(-9600.0, 1.0658141036401503e-10)\n", "0.09599999999999999\n" ] } ] } ] }