{"id":50202,"date":"2020-01-11T13:33:38","date_gmt":"2020-01-11T12:33:38","guid":{"rendered":"https:\/\/www.thermal-engineering.org\/que-es-el-proceso-isobarico-definicion\/"},"modified":"2020-01-11T13:39:40","modified_gmt":"2020-01-11T12:39:40","slug":"que-es-el-proceso-isobarico-definicion","status":"publish","type":"post","link":"https:\/\/www.thermal-engineering.org\/es\/que-es-el-proceso-isobarico-definicion\/","title":{"rendered":"\u00bfQu\u00e9 es el proceso isob\u00e1rico? Definici\u00f3n"},"content":{"rendered":"<div class=\"su-quote su-quote-style-default\">\n<div class=\"su-quote-inner su-clearfix\">Un proceso isob\u00e1rico o un proceso de presi\u00f3n constante es un proceso termodin\u00e1mico, en el que la presi\u00f3n del sistema permanece constante (p = const).\u00a0Ingenieria termal<\/div>\n<\/div>\n<div><\/div>\n<div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"lgc-column lgc-grid-parent lgc-grid-50 lgc-tablet-grid-50 lgc-mobile-grid-100 lgc-equal-heights  lgc-first\">\n<div class=\"inside-grid-column\">\n<h2><span>Proceso isob\u00e1rico<\/span><\/h2>\n<p><span>Un\u00a0<\/span><strong><span>proceso isob\u00e1rico<\/span><\/strong><span>\u00a0es un\u00a0<\/span><a title=\"Procesos termodin\u00e1micos.\" href=\"https:\/\/www.thermal-engineering.org\/es\/que-es-el-proceso-termodinamico-definicion\/\"><span>proceso termodin\u00e1mico<\/span><\/a><span>\u00a0, en el cual la\u00a0<\/span><a title=\"\u00bfQu\u00e9 es la presi\u00f3n? - F\u00edsica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\"><strong><span>presi\u00f3n<\/span><\/strong><\/a><span>\u00a0del sistema\u00a0<\/span><strong><span>permanece constante<\/span><\/strong><span>\u00a0(p = const).\u00a0La transferencia de calor dentro o fuera del sistema funciona, pero tambi\u00e9n cambia la energ\u00eda interna del sistema.<\/span><\/p>\n<p><span>Dado que hay cambios en\u00a0<\/span><a href=\"https:\/\/www.thermal-engineering.org\/es\/que-es-la-energia-interna-energia-termica-definicion\/\"><span>la energ\u00eda interna<\/span><\/a><span>\u00a0(dU) y cambios en el volumen del sistema (\u2206V), los ingenieros a menudo usan la\u00a0<\/span><a title=\"\u00bfQu\u00e9 es la entalp\u00eda?\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/\"><strong><span>entalp\u00eda<\/span><\/strong><\/a><span>\u00a0del sistema, que se define como:<\/span><\/p>\n<p><em><strong><span>H = U + pV<\/span><\/strong><\/em><\/p>\n<p><span>En muchos an\u00e1lisis termodin\u00e1micos es conveniente utilizar la\u00a0<\/span><strong><span>entalp\u00eda en<\/span><\/strong><span>\u00a0lugar de la energ\u00eda interna.\u00a0Especialmente en el caso de la\u00a0<\/span><a title=\"Primera ley en t\u00e9rminos de entalp\u00eda dH = dQ + Vdp\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/first-law-in-terms-of-enthalpy-dh-dq-vdp\/\"><strong><span>primera ley de la termodin\u00e1mica<\/span><\/strong><\/a><span>\u00a0.<\/span><\/p>\n<p><span>La entalp\u00eda es la expresi\u00f3n preferida de la energ\u00eda del sistema que cambia en muchas mediciones qu\u00edmicas, biol\u00f3gicas y f\u00edsicas\u00a0<\/span><strong><span>a presi\u00f3n constante<\/span><\/strong><span>\u00a0.\u00a0Es tan \u00fatil que est\u00e1 tabulado en las\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\"><strong><span>tablas de vapor<\/span><\/strong><\/a><span>\u00a0junto con\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-specific-volume\/\"><span>un volumen\u00a0<\/span><\/a><a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/specific-internal-energy\/\"><span>espec\u00edfico<\/span><\/a><span>\u00a0y\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/specific-internal-energy\/\">una energ\u00eda interna espec\u00edfica<\/a>\u00a0.\u00a0Es debido al hecho,\u00a0<\/span><strong><span>simplifica la descripci\u00f3n de la transferencia de energ\u00eda<\/span><\/strong><span>\u00a0.\u00a0A presi\u00f3n constante, el cambio de entalp\u00eda es igual a la energ\u00eda transferida desde el medio ambiente a trav\u00e9s del calentamiento\u00a0<\/span><strong><span>(Q = H\u00a0<\/span><\/strong><strong><sub><span>2<\/span><\/sub><\/strong><strong><span>\u00a0&#8211; H\u00a0<\/span><\/strong><strong><sub><span>1<\/span><\/sub><\/strong><strong><span>\u00a0)<\/span><\/strong><span>\u00a0u otro trabajo que no sea el trabajo de expansi\u00f3n.\u00a0Para un proceso de presi\u00f3n variable, la diferencia en entalp\u00eda no es tan obvia.<\/span><\/p>\n<p><span>Hay expresiones en t\u00e9rminos de variables m\u00e1s familiares como\u00a0<\/span><a href=\"https:\/\/www.thermal-engineering.org\/es\/que-es-la-temperatura-fisica-definicion\/\"><span>temperatura<\/span><\/a><span>\u00a0y\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\"><span>presi\u00f3n<\/span><\/a><span>\u00a0:<\/span><\/p>\n<p><strong><em><span>dH = C\u00a0<\/span><\/em><\/strong><strong><em><sub><span>p<\/span><\/sub><\/em><\/strong><strong><em><span>\u00a0dT + V (1-\u03b1T) dp<\/span><\/em><\/strong><\/p>\n<p><span>Donde\u00a0<\/span><strong><span>C\u00a0<\/span><\/strong><strong><sub><span>p<\/span><\/sub><\/strong><span>\u00a0es la\u00a0<\/span><strong><span>capacidad calor\u00edfica a presi\u00f3n constante<\/span><\/strong><span>\u00a0y\u00a0<\/span><strong><em><span>\u03b1<\/span><\/em><\/strong><span>\u00a0es el coeficiente de expansi\u00f3n t\u00e9rmica (c\u00fabica).\u00a0Para gas ideal \u03b1T = 1 y por lo tanto:<\/span><\/p>\n<p><strong><em><span>dH = C\u00a0<\/span><\/em><\/strong><strong><em><sub><span>p<\/span><\/sub><\/em><\/strong><strong><em><span>\u00a0dT<\/span><\/em><\/strong><\/p>\n<p><span>Para un proceso ideal de gas y politr\u00f3pico, el caso\u00a0<\/span><strong><em><span>n = 0<\/span><\/em><\/strong><span>\u00a0corresponde a un proceso isob\u00e1rico (presi\u00f3n constante).\u00a0A diferencia del proceso adiab\u00e1tico, en el que\u00a0<\/span><em><span>n =\u00a0<\/span><\/em><em><span>\u00a0y\u00a0<\/span><\/em><em><span>un sistema no intercambia calor con su entorno (Q = 0;\u00a0<\/span><\/em><em><span>\u2206T \u2260 0\u00a0<\/span><\/em><em><span>)\u00a0<\/span><\/em><em><span>, en un proceso isob\u00e1rico hay un cambio en la energ\u00eda interna (debido a \u2206T \u2260 0) y por lo tanto\u00a0<\/span><\/em><em><span>\u0394U\u00a0<\/span><\/em><em><span>\u2260\u00a0<\/span><\/em><em><span>0 (para gases ideales) y Q \u2260 0.<\/span><\/em><\/p>\n<p><span>En ingenier\u00eda, ambos ciclos termodin\u00e1micos muy importantes (ciclo de\u00a0<\/span><strong><span>Brayton y Rankine<\/span><\/strong><span>\u00a0) se basan en dos procesos isob\u00e1ricos, por lo tanto, el estudio de este proceso es crucial para las centrales el\u00e9ctricas.<\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-50 lgc-tablet-grid-50 lgc-mobile-grid-100 lgc-equal-heights  lgc-last\">\n<div class=\"inside-grid-column\">\n<figure id=\"attachment_17426\" class=\"wp-caption alignleft\" aria-describedby=\"caption-attachment-17426\"><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Isobaric-process-main-characteristics.png\"><img loading=\"lazy\" class=\"size-full wp-image-17426 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Isobaric-process-main-characteristics.png\" alt=\"Proceso isob\u00e1rico - caracter\u00edsticas principales\" width=\"381\" height=\"717\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Isobaric-process-main-characteristics.png\" \/><\/a><figcaption id=\"caption-attachment-17426\" class=\"wp-caption-text\"><span>Proceso isob\u00e1rico &#8211; caracter\u00edsticas principales<\/span><\/figcaption><\/figure>\n<figure id=\"attachment_17320\" class=\"wp-caption alignleft\" aria-describedby=\"caption-attachment-17320\"><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Charles-Law.gif\"><img loading=\"lazy\" class=\"size-full wp-image-17320 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Charles-Law.gif\" alt=\"La Ley de Charles es una de las leyes del gas.\" width=\"533\" height=\"403\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Charles-Law.gif\" \/><\/a><figcaption id=\"caption-attachment-17320\" class=\"wp-caption-text\"><span>Para una masa fija de gas a presi\u00f3n constante, el volumen es directamente proporcional a la temperatura Kelvin.\u00a0Fuente: grc.nasa.gov La pol\u00edtica de derechos de autor de la NASA establece que &#8220;el material de la NASA no est\u00e1 protegido por derechos de autor a menos que se indique lo contrario&#8221;.<\/span><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<h2>Proceso isob\u00e1rico y la primera ley<\/h2>\n<p>La forma cl\u00e1sica de la\u00a0<a title=\"Primera ley de la termodin\u00e1mica\" href=\"https:\/\/www.thermal-engineering.org\/es\/que-es-la-primera-ley-de-la-termodinamica-definicion\/\">primera ley de la termodin\u00e1mica<\/a>\u00a0es la siguiente ecuaci\u00f3n:<\/p>\n<p><strong>dU = dQ &#8211; dW<\/strong><\/p>\n<p>En esta ecuaci\u00f3n, dW es igual a\u00a0<strong>dW = pdV<\/strong>\u00a0y se conoce como el\u00a0<a title=\"p\u0394V Work - Trabajo de l\u00edmite y V\u0394p Work\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/p%ce%b4v-work-boundary-work-and-v%ce%b4p-work\/\">trabajo l\u00edmite<\/a>\u00a0.<\/p>\n<p>En un proceso isob\u00e1rico y el gas ideal,\u00a0<strong>parte del calor agregado<\/strong>\u00a0al sistema se utilizar\u00e1 para\u00a0<strong>hacer el trabajo<\/strong>\u00a0y\u00a0<strong>parte del calor<\/strong>\u00a0agregado aumentar\u00e1 la\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/es\/que-es-la-energia-interna-energia-termica-definicion\/\"><strong>energ\u00eda interna<\/strong><\/a>\u00a0(aumentar\u00e1 la temperatura).\u00a0Por lo tanto, es conveniente utilizar la\u00a0<strong>entalp\u00eda en<\/strong>\u00a0lugar de la energ\u00eda interna. Dado que\u00a0<strong><em>H = U + pV<\/em><\/strong>\u00a0, entonces\u00a0<em><strong>dH = dU + pdV + Vdp<\/strong><\/em>\u00a0y sustituimos\u00a0<em><strong>dU = dH &#8211; pdV &#8211; Vdp<\/strong><\/em>\u00a0en la forma cl\u00e1sica de la ley:<\/p>\n<p><em><strong>dH &#8211; pdV &#8211; Vdp = dQ &#8211; pdV<\/strong><\/em><\/p>\n<p>Obtenemos la\u00a0<a title=\"Primera ley en t\u00e9rminos de entalp\u00eda dH = dQ + Vdp\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/first-law-in-terms-of-enthalpy-dh-dq-vdp\/\">ley en t\u00e9rminos de entalp\u00eda<\/a>\u00a0:<\/p>\n<p><strong><em>dH = dQ + Vdp<\/em><\/strong><\/p>\n<p>o<\/p>\n<p><strong><em>dH = TdS + Vdp<\/em><\/strong><\/p>\n<p>En esta ecuaci\u00f3n, el t\u00e9rmino\u00a0<em><strong>Vdp<\/strong><\/em>\u00a0es un\u00a0<strong>proceso de flujo de trabajo.\u00a0<\/strong>Este trabajo, \u00a0\u00a0<em><strong>Vdp<\/strong><\/em>\u00a0, se utiliza para\u00a0<strong>sistemas de flujo abierto<\/strong>\u00a0como una\u00a0<strong>turbina<\/strong>\u00a0o una\u00a0<strong>bomba<\/strong>\u00a0en la que hay un\u00a0<strong>&#8220;dp&#8221;<\/strong>\u00a0, es decir, un cambio de presi\u00f3n.\u00a0No hay cambios en el\u00a0<a title=\"Control Volume - Control Volume Analysis\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/fluid-dynamics\/control-volume-control-volume-analysis\/\">volumen de control<\/a>\u00a0.\u00a0Como puede verse, esta forma de ley\u00a0<strong>simplifica la descripci\u00f3n de la transferencia de energ\u00eda<\/strong>\u00a0.\u00a0<strong>A presi\u00f3n constante<\/strong>\u00a0, el\u00a0<strong>cambio de entalp\u00eda<\/strong>\u00a0es igual a la\u00a0<strong>energ\u00eda<\/strong>\u00a0transferida del ambiente a trav\u00e9s del calentamiento:<\/p>\n<p><strong>Proceso isob\u00e1rico (Vdp = 0):<\/strong><\/p>\n<p><strong>dH = dQ \u00a0 \u00a0\u00a0\u00a0\u2192\u00a0\u00a0 \u00a0 \u00a0Q = H\u00a0<\/strong><strong><sub>2<\/sub><\/strong><strong>\u00a0&#8211; H\u00a0<\/strong><strong><sub>1<\/sub><\/strong><\/p>\n<p><strong>En una entrop\u00eda constante<\/strong>\u00a0, es decir, en un proceso isentr\u00f3pico, el\u00a0<strong>cambio de entalp\u00eda<\/strong>\u00a0equivale al\u00a0<strong>trabajo del proceso de flujo<\/strong>\u00a0realizado en o por el sistema.<\/p>\n<p><strong>Proceso isentr\u00f3pico (dQ = 0):<\/strong><\/p>\n<p><strong>dH = Vdp \u2192 W = H\u00a0<\/strong><strong><sub>2<\/sub><\/strong><strong>\u00a0&#8211; H\u00a0<\/strong><strong><sub>1<\/sub><\/strong><\/p>\n<p>Es obvio, ser\u00e1 muy \u00fatil en el an\u00e1lisis de los dos ciclos termodin\u00e1micos utilizados en la ingenier\u00eda de potencia, es decir, en el ciclo Brayton y el ciclo Rankine.<\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\"><\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<h2>Proceso isob\u00e1rico: ecuaci\u00f3n de gas ideal<\/h2>\n<p>Ver tambi\u00e9n:\u00a0<a title=\"\u00bfQu\u00e9 es el gas ideal?\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/what-is-ideal-gas\/\">\u00bfQu\u00e9 es un gas ideal?<\/a><\/p>\n<figure id=\"attachment_17427\" class=\"wp-caption alignright\" aria-describedby=\"caption-attachment-17427\"><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-work.png\"><img loading=\"lazy\" class=\"size-full wp-image-17427 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-work.png\" alt=\"proceso isob\u00e1rico - trabajo - diagrama pV\" width=\"296\" height=\"234\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-work.png\" \/><\/a><figcaption id=\"caption-attachment-17427\" class=\"wp-caption-text\">En un diagrama pV, el proceso ocurre a lo largo de una l\u00ednea horizontal (llamada isobar) que tiene la ecuaci\u00f3n p = constante.<\/figcaption><\/figure>\n<p>Supongamos una\u00a0<strong>adici\u00f3n de calor isob\u00e1rico<\/strong>\u00a0en un gas ideal.\u00a0En un\u00a0<a title=\"\u00bfQu\u00e9 es el gas ideal?\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/what-is-ideal-gas\/\">gas ideal<\/a>\u00a0, las mol\u00e9culas no tienen volumen y no interact\u00faan.\u00a0Seg\u00fan la\u00a0<a title=\"Ley del gas ideal\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/\">ley de los gases ideales<\/a>\u00a0, la\u00a0<a title=\"\u00bfQu\u00e9 es la presi\u00f3n? - F\u00edsica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\">presi\u00f3n<\/a>\u00a0var\u00eda linealmente con la\u00a0<a title=\"\u00bfQu\u00e9 es la temperatura? F\u00edsica\" href=\"https:\/\/www.thermal-engineering.org\/es\/que-es-la-temperatura-fisica-definicion\/\">temperatura<\/a>\u00a0y la cantidad, e inversamente con el\u00a0<a title=\"\u00bfQu\u00e9 es el volumen? - F\u00edsica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-volume-physics\/\">volumen<\/a>\u00a0.<\/p>\n<p><strong><em>pV = nRT<\/em><\/strong><\/p>\n<p>d\u00f3nde:<\/p>\n<ul>\n<li><em>p<\/em>\u00a0es la presi\u00f3n absoluta del gas<\/li>\n<li><em>n<\/em>\u00a0es la cantidad de sustancia<\/li>\n<li><em>T<\/em>\u00a0es la temperatura absoluta<\/li>\n<li><em>V<\/em>\u00a0es el volumen<\/li>\n<li><em>R<\/em>\u00a0\u00a0es la constante de gas ideal, o universal, igual al producto de la constante de Boltzmann y la constante de Avogadro,<\/li>\n<\/ul>\n<p>En esta ecuaci\u00f3n, el s\u00edmbolo R es una constante llamada constante de\u00a0<strong>gas universal<\/strong>\u00a0que tiene el mismo valor para todos los gases, es decir, R = 8.31 J \/ mol K.<\/p>\n<p>El proceso isob\u00e1rico se puede expresar con la ley de los gases ideales como:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-equation-2.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-17430 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-equation-2.png\" alt=\"proceso isob\u00e1rico - ecuaci\u00f3n - 2\" width=\"134\" height=\"63\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-equation-2.png\" \/><\/a><\/p>\n<p>o<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-equation-3.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-17431 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-equation-3.png\" alt=\"proceso isob\u00e1rico - ecuaci\u00f3n - 3\" width=\"77\" height=\"67\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-equation-3.png\" \/><\/a><\/p>\n<p>En un\u00a0<strong>diagrama pV<\/strong>\u00a0, el proceso ocurre a lo largo de una l\u00ednea horizontal (llamada isobar) que tiene la ecuaci\u00f3n p = constante.<\/p>\n<p><strong>El trabajo de presi\u00f3n-volumen<\/strong>\u00a0del sistema cerrado se define como:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/pV-work-isobaric-process.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-17436 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/pV-work-isobaric-process.png\" alt=\"trabajo pV - proceso isob\u00e1rico\" width=\"157\" height=\"99\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/pV-work-isobaric-process.png\" \/><\/a><\/p>\n<p>Suponiendo que la cantidad de gas ideal permanece constante y aplicando la\u00a0<strong>ley del gas ideal<\/strong>\u00a0, esto se convierte en<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-work-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-17428 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-work-equation.png\" alt=\"proceso isob\u00e1rico - ecuaci\u00f3n de trabajo\" width=\"313\" height=\"45\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-work-equation.png\" \/><\/a><\/p>\n<p>Seg\u00fan el modelo de gas ideal, la\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/es\/que-es-la-energia-interna-energia-termica-definicion\/\">energ\u00eda interna<\/a>\u00a0se puede calcular mediante:<\/p>\n<p><strong><em>\u2206U = mc\u00a0<\/em><em><sub>v<\/sub><\/em><em>\u00a0\u2206T<\/em><\/strong><\/p>\n<p>donde la propiedad\u00a0<strong>c\u00a0<\/strong><strong><sub>v<\/sub><\/strong><strong>\u00a0(J \/ mol K)<\/strong>\u00a0se denomina\u00a0<a title=\"Capacidad de calor - Capacidad de calor espec\u00edfica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\"><strong>calor espec\u00edfico<\/strong><\/a>\u00a0(o\u00a0<strong>capacidad calor\u00edfica<\/strong>\u00a0) a un volumen constante porque, bajo ciertas condiciones especiales (volumen constante), relaciona el cambio de temperatura de un sistema con la cantidad de energ\u00eda agregada por transferencia de calor.<\/p>\n<p>Al sumar estas ecuaciones, obtenemos la ecuaci\u00f3n para el calor:<\/p>\n<p><strong>Q = \u00a0\u00a0<em>mc\u00a0<\/em><em><sub>v<\/sub><\/em><em>\u00a0\u2206T + m R\u00a0<\/em><em>\u2206T = m (c\u00a0<\/em><em><sub>v<\/sub><\/em><em>\u00a0+ R) \u2206T = m c\u00a0<\/em><em><sub>p<\/sub><\/em><em>\u00a0\u2206T<\/em><\/strong><\/p>\n<p>donde la propiedad\u00a0<strong>c\u00a0<\/strong><strong><sub>p<\/sub><\/strong><strong>\u00a0(J \/ mol K)<\/strong>\u00a0se denomina\u00a0<strong>calor espec\u00edfico<\/strong>\u00a0(o\u00a0<strong>capacidad calor\u00edfica<\/strong>\u00a0) a una presi\u00f3n constante.<\/p>\n<p>Ver tambi\u00e9n:\u00a0<a title=\"Calor espec\u00edfico a volumen constante y presi\u00f3n constante\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/specific-heat-constant-volume-pressure\/\">Calor espec\u00edfico a volumen constante y presi\u00f3n constante<\/a><\/p>\n<p>Ver tambi\u00e9n:\u00a0<a title=\"La relaci\u00f3n de Mayer: f\u00f3rmula de Mayer\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/mayers-relation-mayers-formula\/\">f\u00f3rmula de Mayer<\/a><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Ley de carlos<\/h2>\n<p><strong>La Ley de Charles<\/strong>\u00a0es una de las leyes del gas.\u00a0A finales del siglo XVIII, el inventor y cient\u00edfico franc\u00e9s\u00a0<strong>Jacques Alexandre C\u00e9sar Charles<\/strong>\u00a0estudi\u00f3 la relaci\u00f3n entre el\u00a0<strong>volumen<\/strong>\u00a0y la\u00a0<strong>temperatura<\/strong>\u00a0de un gas\u00a0<strong>a presi\u00f3n constante<\/strong>\u00a0.\u00a0Los resultados de ciertos experimentos con gases a una presi\u00f3n relativamente baja llevaron a Jacques Alexandre C\u00e9sar Charles a formular una ley bien conocida.\u00a0Se afirma que:<\/p>\n<p><em>Para una masa fija de gas a presi\u00f3n constante, el volumen es directamente proporcional a la temperatura Kelvin.<\/em><\/p>\n<p>Eso significa que, por ejemplo, si duplica la temperatura, duplicar\u00e1 el volumen.\u00a0Si reduce a la mitad la temperatura, reducir\u00e1 a la mitad el volumen.<\/p>\n<p>Puede expresar esto matem\u00e1ticamente como:<\/p>\n<p><strong><em>V = constante.\u00a0T<\/em><\/strong><\/p>\n<p>S\u00ed, parece ser id\u00e9ntico al\u00a0<strong>proceso isob\u00e1rico<\/strong>\u00a0del gas ideal.\u00a0Estos resultados son totalmente consistentes con\u00a0<strong>la ley del gas ideal<\/strong>\u00a0, que determina que la constante es igual a\u00a0<strong>nR \/ p<\/strong>\u00a0.\u00a0Si reorganiza la ecuaci\u00f3n pV = nRT dividiendo ambos lados por p, obtendr\u00e1:<\/p>\n<p><strong><em>V = nR \/ p.\u00a0T<\/em><\/strong><\/p>\n<p>donde nR \/ p es constante y:<\/p>\n<ul>\n<li><em>p<\/em>\u00a0es la presi\u00f3n absoluta del gas<\/li>\n<li><em>n<\/em>\u00a0es la cantidad de sustancia<\/li>\n<li><em>T<\/em>\u00a0es la temperatura absoluta<\/li>\n<li><em>V<\/em>\u00a0es el volumen<\/li>\n<li><em>R<\/em>\u00a0\u00a0es la constante de gas ideal, o universal, igual al producto de la constante de Boltzmann y la constante de Avogadro,<\/li>\n<\/ul>\n<p>En esta ecuaci\u00f3n, el s\u00edmbolo R es una constante llamada constante de gas universal que tiene el mismo valor para todos los gases, es decir, R = 8.31 J \/ mol K.<\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Ejemplo de proceso isob\u00e1rico: adici\u00f3n de calor isob\u00e1rico<\/h2>\n<figure id=\"attachment_16843\" class=\"wp-caption alignright\" aria-describedby=\"caption-attachment-16843\"><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/first-law-example-brayton-cycle.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16843 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/first-law-example-brayton-cycle-300x244.png\" alt=\"primera ley - ejemplo - ciclo de brayton\" width=\"300\" height=\"244\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/first-law-example-brayton-cycle-300x244.png\" \/><\/a><figcaption id=\"caption-attachment-16843\" class=\"wp-caption-text\">El ciclo ideal de Brayton consiste en cuatro procesos termodin\u00e1micos.\u00a0Dos procesos isentr\u00f3picos y dos procesos isob\u00e1ricos.<\/figcaption><\/figure>\n<p>Supongamos el\u00a0\u00a0<strong>ciclo Brayton ideal<\/strong>\u00a0\u00a0que describe el funcionamiento de un\u00a0\u00a0<strong>motor de calor a\u00a0<\/strong><strong>presi\u00f3n constante<\/strong>\u00a0\u00a0.\u00a0<strong>Los modernos<\/strong>\u00a0\u00a0motores de\u00a0<strong>turbina de gas<\/strong>\u00a0y los motores de\u00a0\u00a0<strong>inyecci\u00f3n de aire<\/strong>\u00a0\u00a0tambi\u00e9n siguen el ciclo Brayton.<\/p>\n<p>El ciclo ideal de Brayton consiste en cuatro procesos termodin\u00e1micos.\u00a0Dos procesos isentr\u00f3picos y dos procesos isob\u00e1ricos.<\/p>\n<ol>\n<li><strong>Compresi\u00f3n isentr\u00f3pica<\/strong>\u00a0\u00a0: el aire ambiente ingresa al compresor, donde se presuriza (1 \u2192 2).\u00a0El trabajo requerido para el compresor viene dado por\u00a0\u00a0<strong>W\u00a0<sub>C<\/sub>\u00a0\u00a0= H\u00a0<sub>2<\/sub>\u00a0\u00a0&#8211; H\u00a0<sub>1<\/sub>\u00a0.<\/strong><\/li>\n<li><strong>adici\u00f3n de calor isob\u00e1rico<\/strong>\u00a0\u00a0: el aire comprimido pasa a trav\u00e9s de una c\u00e1mara de combusti\u00f3n, donde se quema el combustible y se calienta el aire u otro medio (2 \u2192 3).\u00a0Es un proceso de presi\u00f3n constante, ya que la c\u00e1mara est\u00e1 abierta para fluir hacia adentro y hacia afuera.\u00a0El calor neto agregado viene dado por\u00a0\u00a0<strong>Q\u00a0<sub>add<\/sub>\u00a0\u00a0= H\u00a0<sub>3\u00a0<\/sub>\u00a0&#8211; H\u00a0<sub>2<\/sub><\/strong><\/li>\n<li><strong>Expansi\u00f3n isentr\u00f3pica<\/strong>\u00a0\u00a0: el aire calentado y presurizado se expande en la turbina y abandona su energ\u00eda.\u00a0El trabajo realizado por la turbina viene dado por\u00a0\u00a0<strong>W\u00a0<sub>T<\/sub>\u00a0\u00a0= H\u00a0<sub>4<\/sub>\u00a0\u00a0&#8211; H\u00a0<sub>3<\/sub><\/strong><\/li>\n<li><strong>rechazo de calor isob\u00e1rico<\/strong>\u00a0\u00a0: el calor residual debe rechazarse para cerrar el ciclo.\u00a0El calor neto rechazado viene dado por\u00a0\u00a0<strong>Q\u00a0<sub>re<\/sub>\u00a0\u00a0= H\u00a0<sub>4\u00a0<\/sub>\u00a0&#8211; H\u00a0<sub>1<\/sub><\/strong><\/li>\n<\/ol>\n<p>Suponga una\u00a0<strong>adici\u00f3n de calor isob\u00e1rico<\/strong>\u00a0(2 \u2192 3) en un intercambiador de calor.\u00a0En las turbinas de gas t\u00edpicas, la etapa de alta presi\u00f3n recibe gas (punto 3 en la figura; p\u00a0<sub>3<\/sub>\u00a0=\u00a0<strong>6,7 MPa<\/strong>\u00a0; T\u00a0<sub>3<\/sub>\u00a0= 1190 K (917 \u00b0 C)) de un intercambiador de calor.\u00a0Adem\u00e1s, sabemos que el compresor recibe gas (punto 1 en la figura; p\u00a0<sub>1<\/sub>\u00a0=\u00a0<strong>2.78 MPa<\/strong>\u00a0; T\u00a0<sub>1<\/sub>\u00a0= 299 K (26 \u00b0 C)) y sabemos que la eficiencia isentr\u00f3pica del compresor es\u00a0<strong>\u03b7\u00a0<\/strong><strong><sub>K<\/sub><\/strong><strong>\u00a0= 0.87 (87 %)<\/strong>\u00a0.<\/p>\n<p><strong>Calcule el calor agregado por el intercambiador de calor (entre 2 \u2192 3).<\/strong><\/p>\n<p><strong>Soluci\u00f3n:<\/strong><\/p>\n<p>A partir de la\u00a0<strong>primera ley de la termodin\u00e1mica<\/strong>\u00a0, el calor neto agregado viene dado por\u00a0<strong>Q\u00a0<\/strong><strong><sub>add<\/sub><\/strong><strong>\u00a0= H\u00a0<\/strong><strong><sub>3<\/sub><\/strong><strong>\u00a0&#8211; H\u00a0<\/strong><strong><sub>2<\/sub><\/strong>\u00a0o\u00a0<strong>Q\u00a0<sub>add<\/sub>\u00a0= C\u00a0<sub>p<\/sub>\u00a0. (T\u00a0<sub>3<\/sub>\u00a0-T\u00a0<sub>2s<\/sub>\u00a0),<\/strong>\u00a0pero en este caso no sabemos la temperatura (T\u00a0<sub>2s<\/sub>\u00a0) a la salida del compresor.\u00a0Resolveremos este problema en variables intensivas.\u00a0Tenemos que reescribir la ecuaci\u00f3n anterior (para incluir\u00a0<strong>\u03b7\u00a0<\/strong><strong><sub>K<\/sub><\/strong>\u00a0) usando el t\u00e9rmino (+\u00a0<strong>h\u00a0<\/strong><strong><sub>1<\/sub><\/strong><strong>\u00a0&#8211; h\u00a0<\/strong><strong><sub>1<\/sub><\/strong>\u00a0) para:<\/p>\n<p>Q\u00a0<sub>add<\/sub>\u00a0=\u00a0<strong>h\u00a0<\/strong><strong><sub>3<\/sub><\/strong><strong>\u00a0&#8211; h\u00a0<\/strong><strong><sub>2<\/sub><\/strong><strong>\u00a0= h\u00a0<\/strong><strong><sub>3<\/sub><\/strong><strong>\u00a0&#8211; h\u00a0<\/strong><strong><sub>1<\/sub><\/strong><strong>\u00a0&#8211; (h\u00a0<\/strong><strong><sub>2s<\/sub><\/strong><strong>\u00a0&#8211; h\u00a0<\/strong><strong><sub>1<\/sub><\/strong><strong>\u00a0) \/\u00a0<\/strong><strong>\u03b7\u00a0<\/strong><strong><sub>K<\/sub><\/strong>\u00a0<strong>\u00a0<\/strong><\/p>\n<p>Q\u00a0<sub>add\u00a0<\/sub><strong>=<\/strong>\u00a0c\u00a0<sub>p<\/sub>\u00a0(T\u00a0<sub>3<\/sub>\u00a0-T\u00a0<sub>1<\/sub>\u00a0) &#8211; (c\u00a0<sub>p<\/sub>\u00a0(T\u00a0<sub>2s<\/sub>\u00a0-T\u00a0<sub>1<\/sub>\u00a0)\u00a0<strong>\/\u00a0<\/strong><strong>\u03b7\u00a0<\/strong><strong><sub>K<\/sub><\/strong>\u00a0)<\/p>\n<p>Luego calcularemos la temperatura, T\u00a0<sub>2s<\/sub>\u00a0, usando\u00a0<strong>p, V, T Relaci\u00f3n<\/strong>\u00a0para el proceso adiab\u00e1tico entre (1 \u2192 2).<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/pVT-relation-isentropic-process.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-17281 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/pVT-relation-isentropic-process.png\" alt=\"Relaci\u00f3n p, V, T - proceso isentr\u00f3pico\" width=\"209\" height=\"72\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/pVT-relation-isentropic-process.png\" \/><\/a><\/p>\n<p>En esta ecuaci\u00f3n, el factor para helio es igual a\u00a0<strong>= c\u00a0<sub>p<\/sub>\u00a0\/ c\u00a0<sub>v<\/sub>\u00a0= 1.66<\/strong>\u00a0.\u00a0De la ecuaci\u00f3n anterior se deduce que la temperatura de salida del compresor, T\u00a0<sub>2s<\/sub>\u00a0, es:<\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-17429 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-example.png\" alt=\"proceso isob\u00e1rico - ejemplo\" width=\"492\" height=\"84\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/isobaric-process-example.png\" \/><\/a><\/p>\n<p>Seg\u00fan la\u00a0<a title=\"Ley del gas ideal\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/\">Ley del Gas Ideal<\/a>\u00a0, sabemos que el calor espec\u00edfico molar de un\u00a0<a title=\"Energ\u00eda interna del gas ideal: gas monoat\u00f3mico, mol\u00e9cula diat\u00f3mica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/internal-energy-ideal-gas-monatomic-gas-diatomic-molecule\/\">gas ideal monoat\u00f3mico<\/a>\u00a0es:<\/p>\n<p><strong><em>C\u00a0<\/em><\/strong><strong><em><sub>v<\/sub><\/em><\/strong><strong><em>\u00a0= 3 \/ 2R = 12.5 J \/ mol K<\/em><\/strong>\u00a0y<strong><em>\u00a0C\u00a0<\/em><\/strong><strong><em><sub>p<\/sub><\/em><\/strong><strong><em>\u00a0= C\u00a0<\/em><\/strong><strong><em><sub>v<\/sub><\/em><\/strong><strong><em>\u00a0+ R = 5 \/ 2R = 20.8 J \/ mol K<\/em><\/strong><\/p>\n<p>Transferimos las capacidades de calor espec\u00edficas en unidades de\u00a0<strong>J \/ kg K a trav\u00e9s de:<\/strong><\/p>\n<p><strong><em>c\u00a0<\/em><\/strong><strong><em><sub>p<\/sub><\/em><\/strong><strong><em>\u00a0= C\u00a0<\/em><\/strong><strong><em><sub>p<\/sub><\/em><\/strong><strong><em>\u00a0.\u00a01 \/ M (peso molar de helio) = 20.8 x 4.10\u00a0<\/em><\/strong><strong><em><sup>-3<\/sup><\/em><\/strong><strong><em>\u00a0= 5200 J \/ kg K<\/em><\/strong><\/p>\n<p>Usando esta temperatura y la\u00a0<a title=\"Eficiencia isentr\u00f3pica - Turbina \/ Compresor \/ Boquilla\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-processes\/isentropic-process\/isentropic-efficiency-turbinecompressornozzle\/\">eficiencia del compresor isentr\u00f3pico<\/a>\u00a0, podemos calcular el calor agregado por el intercambiador de calor:<\/p>\n<p><strong>Q\u00a0<sub>add<\/sub>\u00a0=<\/strong>\u00a0c\u00a0<sub>p<\/sub>\u00a0(T\u00a0<sub>3<\/sub>\u00a0-T\u00a0<sub>1<\/sub>\u00a0) &#8211; (c\u00a0<sub>p<\/sub>\u00a0(T\u00a0<sub>2s<\/sub>\u00a0-T\u00a0<sub>1<\/sub>\u00a0)\u00a0<strong>\/\u00a0<\/strong><strong>\u03b7\u00a0<\/strong><strong><sub>K<\/sub><\/strong>\u00a0) = 5200. (1190 &#8211; 299) &#8211; 5200. (424-299) \/0.87 = 4.633 MJ \/ kg &#8211; 0.747 MJ \/ kg =\u00a0<strong>3.886 MJ \/ kg<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"su-divider su-divider-style-dotted\"><\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-50 lgc-tablet-grid-50 lgc-mobile-grid-100 lgc-equal-heights lgc-last\">\n<div class=\"inside-grid-column\"><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Un proceso isob\u00e1rico o un proceso de presi\u00f3n constante es un proceso termodin\u00e1mico, en el que la presi\u00f3n del sistema permanece constante (p = const).\u00a0Ingenieria termal Proceso isob\u00e1rico Un\u00a0proceso isob\u00e1rico\u00a0es un\u00a0proceso termodin\u00e1mico\u00a0, en el cual la\u00a0presi\u00f3n\u00a0del sistema\u00a0permanece constante\u00a0(p = const).\u00a0La transferencia de calor dentro o fuera del sistema funciona, pero tambi\u00e9n cambia la energ\u00eda interna &#8230; <a title=\"\u00bfQu\u00e9 es el proceso isob\u00e1rico? 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