{"id":66971,"date":"2026-10-13T10:43:24","date_gmt":"2026-10-13T07:43:24","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66971"},"modified":"2026-10-13T10:43:24","modified_gmt":"2026-10-13T07:43:24","slug":"adiabatic-process-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/adiabatic-process-calculator\/","title":{"rendered":"Adiabatic Process Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Find the Final State of an Ideal Gas After Adiabatic Compression or Expansion<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66971\" data-favorite-title=\"Adiabatic Process\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/adiabatic-process-calculator\/\" data-favorite-excerpt=\"Calculate the final pressure, volume and temperature of an ideal gas after a reversible adiabatic (isentropic) compression or expansion. Enter the initial state, one final quantity and the heat-capacity ratio \u03b3.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-physic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/physics\/adiabatic-process-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66971\" data-post=\"66971\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">I know the final<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"i_know_the_final\"><option value=\"v2\" selected>Final volume (find final pressure)<\/option><option value=\"p2\">Final pressure (find final volume)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"is-single field\" id=\"input-2\"><span class=\"font-semibold\">Initial state<\/span><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Initial pressure (P\u2081)<\/label><div class=\"term\">P\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"initial_pressure_p\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 100\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"kpa\" selected>kPa<\/option><option value=\"bar\">bar<\/option><option value=\"atm\">atm<\/option><option value=\"psi\">psi<\/option><option value=\"mmhg\">mmHg<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Pressure at the start of the process. One atmosphere \u2248 101.3 kPa.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-5\">Initial volume (V\u2081)<\/label><div class=\"term\">V\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"initial_volume_v\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"m3\" selected>m\u00b3<\/option><option value=\"l\">L<\/option><option value=\"cm3\">cm\u00b3<\/option><option value=\"ft3\">ft\u00b3<\/option><option value=\"in3\">in\u00b3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Volume of the gas at the start of the process.<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-7\">Initial temperature (T\u2081)<\/label><div class=\"term\">T\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"initial_temperature_t\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 300\" min=\"0\" value=\"300\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"k\" selected>K<\/option><option value=\"c\">\u00b0C<\/option><option value=\"f\">\u00b0F<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Temperature at the start. Room temperature \u2248 293 K (20 \u00b0C).<\/small><\/div><div class=\"is-single field\" id=\"input-6\"><span class=\"font-semibold\">Final state<\/span><\/div><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-10\">Final volume (V\u2082)<\/label><div class=\"term\">V\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"final_volume_v\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.5\" min=\"0\" value=\"0.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"unit\" aria-label=\"Unit\"><option value=\"m3\" selected>m\u00b3<\/option><option value=\"l\">L<\/option><option value=\"cm3\">cm\u00b3<\/option><option value=\"ft3\">ft\u00b3<\/option><option value=\"in3\">in\u00b3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-10\">Volume at the end of the process. A value smaller than V\u2081 means compression; larger means expansion.<\/small><\/div><div class=\"field has-term\" id=\"input-8\" hidden><label for=\"field-12\">Final pressure (P\u2082)<\/label><div class=\"term\">P\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"final_pressure_p\" id=\"field-12\" aria-describedby=\"calc-info-12\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 200\" min=\"0\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-13\" name=\"unit\" aria-label=\"Unit\"><option value=\"kpa\" selected>kPa<\/option><option value=\"bar\">bar<\/option><option value=\"atm\">atm<\/option><option value=\"psi\">psi<\/option><option value=\"mmhg\">mmHg<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-12\">Pressure at the end of the process. A value larger than P\u2081 means compression; smaller means expansion.<\/small><\/div><div class=\"field has-term\" id=\"input-9\"><label for=\"field-14\">Heat-capacity ratio (\u03b3)<\/label><div class=\"term\">\u03b3<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"heatcapacity_ratio_\" id=\"field-14\" aria-describedby=\"calc-info-14\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1.4\" min=\"1\" value=\"1.4\"\/><small id=\"calc-info-14\">\u03b3 = c\u1d58\/c\u1d5b. Monatomic gas \u2248 1.67, diatomic gas (air, N\u2082, O\u2082) \u2248 1.40, polyatomic (CO\u2082) \u2248 1.29.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66971\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Adiabatic Process Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Final pressure (P\u2082)<\/span><span class=\"result-term\">P\u2082<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Final volume (V\u2082)<\/span><span class=\"result-term\">V\u2082<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Final temperature (T\u2082)<\/span><span class=\"result-term\">T\u2082<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Work done and details<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66971\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center 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[]).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Adiabatic Process<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ P_1 V_1^{\\gamma} = P_2 V_2^{\\gamma} \\qquad T_1 V_1^{\\gamma-1} = T_2 V_2^{\\gamma-1} \\qquad W = \\frac{P_1 V_1 - P_2 V_2}{\\gamma - 1} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(P_1, V_1, T_1\\) \u2014 initial pressure, volume and absolute temperature of the gas<\/li>\n<li>\\(P_2, V_2, T_2\\) \u2014 final pressure, volume and absolute temperature<\/li>\n<li>\\(\\gamma = c_p \/ c_v\\) \u2014 heat-capacity ratio of the gas (1.67 for monatomic, 1.40 for diatomic gases such as air)<\/li>\n<li>\\(W\\) \u2014 work done <em>by<\/em> the gas during the process (J)<\/li>\n<\/ul>\n<p>These relations describe a reversible adiabatic (isentropic) process of an ideal gas: because no heat is exchanged with the surroundings, pressure, volume and temperature are linked by the constant \\(P V^{\\gamma}\\), and the work term follows from the first law of thermodynamics with \\(Q = 0\\), so \\(\\Delta U = -W\\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Adiabatic Process \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> 1 m\u00b3 of air at 100 kPa and 300 K is compressed adiabatically to half its original volume. For air, \u03b3 = 1.4.<\/p>\n<p>\\[ P_2 = P_1 \\left( \\frac{V_1}{V_2} \\right)^{\\gamma} = 100\\,\\text{kPa} \\times 2^{1.4} \\approx 263.9\\,\\text{kPa} \\]<\/p>\n<p>\\[ T_2 = T_1 \\left( \\frac{V_1}{V_2} \\right)^{\\gamma-1} = 300\\,\\text{K} \\times 2^{0.4} \\approx 395.85\\,\\text{K} \\; (\\approx 122.7\\,\\text{\u00b0C}) \\]<\/p>\n<p>\\[ W = \\frac{P_1 V_1 - P_2 V_2}{\\gamma - 1} = \\frac{100\\,000 \\times 1 - 263\\,902 \\times 0.5}{0.4} \\approx -79\\,877\\,\\text{J} \\]<\/p>\n<p><strong>Result:<\/strong> the final pressure is \u2248 263.9 kPa (\u2248 2.60 atm), the final temperature is \u2248 395.85 K (\u2248 122.7 \u00b0C), and about 79.9 kJ of work is done <em>on<\/em> the gas, which is why it warms up.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>In the <strong>\u201cI know the final\u201d<\/strong> dropdown, choose whether you are given the final volume (and want the final pressure) or the final pressure (and want the final volume).<\/li>\n<li>Enter the <strong>Initial pressure (P\u2081)<\/strong>, <strong>Initial volume (V\u2081)<\/strong> and <strong>Initial temperature (T\u2081)<\/strong>, selecting the unit for each field (kPa, bar, atm, psi, mmHg; m\u00b3, L, cm\u00b3, ft\u00b3, in\u00b3; K, \u00b0C, \u00b0F). All inputs are converted to SI units automatically.<\/li>\n<li>Enter the known final quantity: <strong>Final volume (V\u2082)<\/strong> or <strong>Final pressure (P\u2082)<\/strong>, depending on your choice in step 1.<\/li>\n<li>Enter the <strong>Heat-capacity ratio (\u03b3)<\/strong> of the gas \u2014 1.4 for air and other diatomic gases, 1.67 for monatomic gases such as helium or argon, about 1.29 for CO\u2082.<\/li>\n<li>Read the results: the final pressure in several units, the final volume in several units, the final temperature in K, \u00b0C and \u00b0F, and the energy balance (work done, change in internal energy, and the constant \\(P V^{\\gamma}\\) in both states).<\/li>\n<\/ol>\n<h2>What is an adiabatic process?<\/h2>\n<p>An adiabatic process is a thermodynamic process in which a gas exchanges no heat with its surroundings (\\(Q = 0\\)). Energy can still enter or leave the gas \u2014 but only in the form of mechanical work. When the gas is compressed, the work done on it increases its internal energy and the temperature rises; when it expands, the gas spends its own internal energy on pushing the surroundings away and cools down. This is why a bicycle pump gets warm when you pump quickly, and why compressed air from an aerosol can feels cold as it expands.<\/p>\n<p>This calculator models the <em>reversible<\/em> (quasi-static, isentropic) adiabatic process of an <em>ideal<\/em> gas. In that case the state variables obey \\(P V^{\\gamma} = \\text{constant}\\) and \\(T V^{\\gamma-1} = \\text{constant}\\). Compared with an isothermal process, the pressure changes more steeply with volume, because temperature changes at the same time: doubling the density of air (\\(\\gamma = 1.4\\)) raises the pressure by a factor \\(2^{1.4} \\approx 2.64\\), not by a factor of 2.<\/p>\n<p>The sign of the work tells you the direction of the process: a negative \\(W\\) means work was done <em>on<\/em> the gas (compression, heating), a positive \\(W\\) means the gas did work <em>on<\/em> its surroundings (expansion, cooling). Because \\(Q = 0\\), the first law of thermodynamics reduces to \\(\\Delta U = -W\\): the temperature change you see in the results is a direct consequence of the work exchanged.<\/p>\n<h2>Assumptions, limitations and practical tips<\/h2>\n<ul>\n<li><strong>Ideal gas:<\/strong> the relations hold for pressures where the ideal-gas approximation is valid. At very high pressures or near condensation, real-gas effects become important and the results deviate.<\/li>\n<li><strong>Reversible and truly adiabatic:<\/strong> the calculation assumes the process is slow enough to be quasi-static and fast enough (or well enough insulated) that no heat leaks in or out. Rapid, turbulent compression or expansion generates irreversibilities and gives different final temperatures.<\/li>\n<li><strong>Constant \u03b3:<\/strong> the heat-capacity ratio is treated as independent of temperature. Over ranges of a few hundred kelvin this is a good approximation for air; for very large temperature swings, tabulated \\(\\gamma(T)\\) values should be used.<\/li>\n<li><strong>Choose \u03b3 carefully:<\/strong> using 1.4 for a monatomic gas (or vice versa) can shift the final temperature by tens of kelvin. Check the gas you are modelling before trusting the result.<\/li>\n<li><strong>Mass conservation:<\/strong> the calculator assumes a fixed amount of gas. Use the <a href=\"https:\/\/wpcalc.com\/en\/physics\/density-calculator\/\">Density calculator<\/a> if you need to convert between the mass and the amount of gas, and the <a href=\"https:\/\/wpcalc.com\/en\/physics\/pressure-calculator\/\">Pressure calculator<\/a> for unit checks on the pressures.<\/li>\n<\/ul>\n<p>Adiabatic compression and expansion are central to engines, compressors, turbines and atmospheric physics \u2014 for example, the cooling of rising air parcels is approximated as adiabatic. To place these processes in the wider context of heat engines and their efficiency limits, see the <a href=\"https:\/\/wpcalc.com\/en\/physics\/carnot-efficiency-calculator\/\">Carnot Efficiency calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the final pressure, volume and temperature of an ideal gas after a reversible adiabatic (isentropic) compression or expansion. Enter the initial state, one final quantity and the heat-capacity ratio \u03b3.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[62],"tags":[91],"class_list":["post-66971","post","type-post","status-publish","format-standard","hentry","category-physics","tag-energy-work"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66971","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66971"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66971\/revisions"}],"predecessor-version":[{"id":66972,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66971\/revisions\/66972"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}