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The Ideal Gas Law
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})(window,document,'script','dataLayer','GTM-WH8MKZX');</script> <!-- End Google Tag Manager --> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3176996020956223" crossorigin="anonymous"></script> <script async src="https://fundingchoicesmessages.google.com/i/pub-3176996020956223?ers=1" nonce="kUwMyhBaatnOdZ-JwpEGCA"></script><script nonce="kUwMyhBaatnOdZ-JwpEGCA">(function() {function signalGooglefcPresent() {if (!window.frames['googlefcPresent']) {if (document.body) {const iframe = document.createElement('iframe'); iframe.style = 'width: 0; height: 0; border: none; z-index: -1000; left: -1000px; top: -1000px;'; iframe.style.display = 'none'; iframe.name = 'googlefcPresent'; document.body.appendChild(iframe);} else {setTimeout(signalGooglefcPresent, 0);}}}signalGooglefcPresent();})();</script> <script data-cfasync="false" type="text/javascript"> window.snigelPubConf = { "adengine": { "activeAdUnits": ["adhesive", "doc1", "doc2", "left1", "right", "top", "video", "incontent1", "incontent2"] } } </script> <script async data-cfasync="false" src="https://cdn.snigelweb.com/adengine/engineeringtoolbox.com/loader.js" type="text/javascript"></script> </head> <body> <div id="top"> <div id="logo"> <a href="https://www.engineeringtoolbox.com"> <img src="static/img/logo.jpg" width="350" height="60" alt="Engineering ToolBox" > </a> </div> <p id="intro" class="smallHide"> <a href="https://www.engineeringtoolbox.com"> Engineering ToolBox </a> - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!</p> <div id="adVideo" class="noPrint"> <div> <!-- adngin-video-0 --> <div id="adngin-video-0"></div> </div> </div> </div> <div id="center"> <div id="gooSearch"> <script async src="https://cse.google.com/cse.js?cx=6a091aba9f3e1fba3"></script> <div class="gcse-searchbox-only"></div> </div> <div id="content"> <div> <h1> <a href="ideal-gas-law-d_157.html"> The Ideal Gas Law </a> </h1> <h2> The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density. </h2> <div id="adSlotDoc1" class="noPrint"> <div> <!-- adngin-doc1-0 --> <div id="adngin-doc1-0"></div> </div> </div> <div> <p>In a perfect or ideal gas the correlations between pressure, volume, temperature and quantity of gas can be expressed by the <strong> Ideal Gas Law. </strong></p> <p>The <b> Universal Gas Constant, R<sub>u </sub> </b> is independent of the particular gas and is the same for all "perfect" gases, and is included in of The Ideal Gas Law:</p> <blockquote> <p style="text-align: center;">p V = n R<sub>u </sub> T (1)</p> </blockquote> <p>where</p> <blockquote> <p>p = absolute pressure [N/m<sup>2</sup>], [lb/ft<sup>2</sup>]</p> <p>V = volume [m<sup>3</sup> ], [ft<sup>3</sup> ]</p> <p>n = is the number of moles of the gas present</p> <p>R<sub>u </sub> = <a href="individual-universal-gas-constant-d_588.html" title="universal gas constant"> universal gas constant </a> [J/mol K], [lb<sub>f</sub> ft/(lb mol <sup> o </sup> R)]= 8.3145 [J/mol K]= 0.08206 [L atm/mol K] = 62.37 [L torr /mol K]</p> <p>T = absolute temperature [K], [ <sup> o </sup> R]</p> </blockquote> <p>For a given quantity of gas, both n and R<sub>u </sub> are constant, and Equation (1) can be modified to</p> <blockquote> <p style="text-align: center;">p<sub>1</sub> V<sub>1</sub> / T<sub>1</sub> = p<sub>2</sub>V<sub>2</sub>/ T<sub>2</sub>(2)</p> </blockquote> <p>expressing the relationship between different states for the given quantity of the gas.</p> <p>Equation (1) can also be expressed as</p> <blockquote> <p style="text-align: center;">p V = N k T (3)</p> <p>N =number of molecules</p> <p>k = Boltzmann constant = 1.38066 10 <sup> -23 </sup> [J/K] = 8.617385 10 <sup> -5 </sup> [eV/K]</p> </blockquote> <ul> <li>One mole of an ideal gas at <a href="https://www.engineeringtoolbox.com/stp-standard-ntp-normal-air-d_772.html" title="standard temperature and pressure"> STP </a> occupies 22.4 liters.</li> </ul> <div id="adInContent1" class="noPrint"> <div> <!-- adngin-incontent1-0 --> <div id="adngin-incontent1-0"></div> </div> </div> <h4>The Ideal Gas Law and the Individual Gas Constant - <i> R </i></h4> <p>The <b> Ideal Gas Law </b> - or <strong> Perfect Gas Law </strong> - relates pressure, temperature, and volume of an <b> ideal or perfect gas </b> . The Ideal Gas Law can be expressed with the <b> Individual Gas Constant </b>.</p> <blockquote> <p style="text-align: center;">p V = m R T (4)</p> <p>where</p> <p>p = absolute pressure [N/m<sup>2</sup>], [lb/ft<sup>2</sup>]</p> <p>V = volume [m<sup>3</sup> ], [ft<sup>3</sup> ]</p> <p>m = mass [kg], [ <a href="mass-weight-d_589.html" title="slugs - mass and weight"> slugs </a> ]</p> <p>R = <a href="individual-universal-gas-constant-d_588.html" title="individual gas constant"> individual gas constant </a> [J/kg K], [ft lb/slugs <sup> o </sup> R]</p> <p>T = absolute temperature [K], [ <sup> o </sup> R]</p> </blockquote> <p>This equation (3) can be modified to:</p> <blockquote> <p style="text-align: center;">p = ρ R T (5)</p> <p>where the density</p> <p style="text-align: center;">ρ = m / V [kg/m<sup>3</sup> ], [slugs/ft<sup>3</sup> ] (6)</p> </blockquote> <p>The <a href="individual-universal-gas-constant-d_588.html" title="individual gas constant"> Individual Gas Constant </a> - <i> R </i> - depends on the particular gas and is related to the molecular weight of the gas. <br > See also <a href="non-ideal-gas-van-der-Waals-equation-constants-gas-law-d_1969.html"> Non-ideal gas - Van der Waal's equation and constants </a>, used to correct for non-ideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles and how to calculate <a href="partial-pressure-ideal-gas-law-total-mixture-blending-d_1968.html"> total pressure and partial pressures from Ideal gas law </a></p> <p><strong> Example: </strong> The Ideal Gas Law</p> <p>A tank with volume of <em> 1 ft<sup>3</sup> </em> is filled with air compressed to a gauge pressure of <em> 50 psi. </em> The temperature in tank is <em> 70 <sup>o</sup>F </em>.</p> <p>The air density can be calculated with a transformation of the ideal gas law (5) to:</p> <blockquote> <p style="text-align: center;">ρ = p / (R T) (7)</p> <p><span style="text-decoration: underline;"> ρ </span> = ((50 [lb/in<sup>2</sup>]+ 14.7 [lb/in<sup>2</sup>])*144 [in<sup>2</sup>/ft<sup>2</sup>]) / (1716 [ft.lb/slug. <sup> o </sup> R]* (70+ 460)[°R])</p> <p>= <span style="text-decoration: underline;"> 0.0102 [slugs/ft<sup>3</sup> ] </span></p> </blockquote> <p>The weight of the air is the product of <a href="density-specific-weight-gravity-d_290.html" title="specific weight"> specific weight </a> and the air volume. It can be calculated as:</p> <blockquote> <p style="text-align: center;">w = ρ g V (8)</p> <p><span style="text-decoration: underline;"> w </span> = 0.0102 [slugs/ft<sup>3</sup> ] * 32.2 [ft/s<sup>2</sup>]*1 [ft<sup>3</sup> ]</p> <p>= 0.32844 [slugs ft/s<sup>2</sup>]</p> <p>= <span style="text-decoration: underline;"> 0.32844 [lb] </span></p> </blockquote> <h3>Note!</h3> <p>The Ideal Gas Law is accurate only at relatively low pressures and high temperatures. To account for deviation from the ideal situation an other factor is included. It is called the Gas Compressibility Factor, or Z-factor. This correction factor is dependent on pressure and temperature for each gas considered.</p> <p>The True Gas Law, or the Non-Ideal Gas Law, becomes:</p> <p style="padding-left: 30px;">P V = Z n R T (7)</p> <p style="padding-left: 30px;">where</p> <p style="padding-left: 30px;">Z = Gas Compressibility Factor</p> <p style="padding-left: 30px;">n = number of moles of gas present</p> <div id="adInContent2" class="noPrint"> <div> <!-- adngin-incontent2-0 --> <div id="adngin-incontent2-0"></div> </div> </div> <h3>Compressibility factor - Z - for Air</h3> <p id="fullTable">For full table - <strong> rotate the screen! </strong></p> <table class="large"><caption>Compressibility factor for Air <em> - Z - <br > </em></caption> <thead> <tr><th rowspan="2">Temperature <br > <i> [K] <br > <input class="addR" style="font-style: italic; color: blue; cursor: pointer;" type="button" value="[°R]" > </i></th><th class="bara" colspan="14">Pressure [ <em> bar absolute] <input class="addPsia" style="font-style: italic; color: blue; cursor: pointer;" type="button" value="[psia]" > </em></th></tr> <tr> <td><strong> 1 </strong></td> <td><strong> 5 </strong></td> <td><strong> 10 </strong></td> <td><strong> 20 </strong></td> <td><strong> 40 </strong></td> <td><strong> 60 </strong></td> <td class="smallHide"><strong> 80 </strong></td> <td class="smallHide"><strong> 100 </strong></td> <td class="smallHide"><strong> 150 </strong></td> <td class="smallHide"><strong> 200 </strong></td> <td class="smallHide"><strong> 250 </strong></td> <td class="smallHide"><strong> 300 </strong></td> <td class="smallHide"><strong> 400 </strong></td> <td class="smallHide"><strong> 500 </strong></td> </tr> </thead> <tbody> <tr> <td>75</td> <td>0.005</td> <td>0.026</td> <td>0.052</td> <td>0.104</td> <td>0.206</td> <td>0.308</td> <td class="smallHide">0.409</td> <td class="smallHide">0.510</td> <td class="smallHide">0.758</td> <td class="smallHide">1.013</td> <td class="smallHide"></td> <td class="smallHide"></td> <td class="smallHide"></td> <td class="smallHide"></td> </tr> <tr> <td class="kelvin">80</td> <td></td> <td>0.025</td> <td>0.050</td> <td>0.100</td> <td>0.198</td> <td>0.296</td> <td class="smallHide">0.393</td> <td class="smallHide">0.489</td> <td class="smallHide">0.726</td> <td class="smallHide">0.959</td> <td class="smallHide">1.193</td> <td class="smallHide">1.414</td> <td class="smallHide"></td> <td class="smallHide"></td> </tr> <tr> <td class="kelvin">90</td> <td>0.976</td> <td>0.024</td> <td>0.045</td> <td>0.094</td> <td>0.187</td> <td>0.278</td> <td class="smallHide">0.369</td> <td class="smallHide">0.468</td> <td class="smallHide">0.678</td> <td class="smallHide">0.893</td> <td class="smallHide">1.110</td> <td class="smallHide">1.311</td> <td class="smallHide">1.716</td> <td class="smallHide">2.111</td> </tr> <tr> <td class="kelvin">100</td> <td>0.980</td> <td>0.887</td> <td>0.045</td> <td>0.090</td> <td>0.178</td> <td>0.264</td> <td class="smallHide">0.350</td> <td class="smallHide">0.434</td> <td class="smallHide">0.639</td> <td class="smallHide">0.838</td> <td class="smallHide">1.040</td> <td class="smallHide">1.223</td> <td class="smallHide">1.594</td> <td class="smallHide">1.954</td> </tr> <tr> <td class="kelvin">120</td> <td>0.988</td> <td>0.937</td> <td>0.886</td> <td>0.673</td> <td>0.178</td> <td>0.256</td> <td class="smallHide">0.337</td> <td class="smallHide">0.413</td> <td class="smallHide">0.596</td> <td class="smallHide">0.772</td> <td class="smallHide">0.953</td> <td class="smallHide">1.108</td> <td class="smallHide">1.509</td> <td class="smallHide">1.737</td> </tr> <tr> <td class="kelvin">140</td> <td>0.993</td> <td>0.961</td> <td>0.921</td> <td>0.830</td> <td>0.586</td> <td>0.331</td> <td class="smallHide">0.374</td> <td class="smallHide">0.434</td> <td class="smallHide">0.591</td> <td class="smallHide">0.770</td> <td class="smallHide">0.911</td> <td class="smallHide">1.039</td> <td class="smallHide">1.320</td> <td class="smallHide">1.590</td> </tr> <tr> <td class="kelvin">160</td> <td>0.995</td> <td>0.975</td> <td>0.949</td> <td>0.895</td> <td>0.780</td> <td>0.660</td> <td class="smallHide">0.570</td> <td class="smallHide">0.549</td> <td class="smallHide">0.634</td> <td class="smallHide">0.756</td> <td class="smallHide">0.884</td> <td class="smallHide">1.011</td> <td class="smallHide">1.259</td> <td class="smallHide">1.497</td> </tr> <tr> <td class="kelvin">180</td> <td>0.997</td> <td>0.983</td> <td>0.966</td> <td>0.931</td> <td>0.863</td> <td>0.798</td> <td class="smallHide">0.743</td> <td class="smallHide">0.708</td> <td class="smallHide">0.718</td> <td class="smallHide">0.799</td> <td class="smallHide">0.900</td> <td class="smallHide">1.007</td> <td class="smallHide">1.223</td> <td class="smallHide">1.436</td> </tr> <tr> <td class="kelvin">200</td> <td>0.998</td> <td>0.989</td> <td>0.977</td> <td>0.954</td> <td>0.910</td> <td>0.870</td> <td class="smallHide">0.837</td> <td class="smallHide">0.814</td> <td class="smallHide">0.806</td> <td class="smallHide">0.855</td> <td class="smallHide">0.931</td> <td class="smallHide">1.019</td> <td class="smallHide">1.205</td> <td class="smallHide">1.394</td> </tr> <tr> <td class="kelvin">250</td> <td>0.999</td> <td>0.996</td> <td>0.991</td> <td>0.982</td> <td>0.967</td> <td>0.955</td> <td class="smallHide">0.946</td> <td class="smallHide">0.941</td> <td class="smallHide">0.945</td> <td class="smallHide">0.971</td> <td class="smallHide">1.015</td> <td class="smallHide">1.070</td> <td class="smallHide">1.199</td> <td class="smallHide">1.339</td> </tr> <tr> <td class="kelvin">300</td> <td>1.000</td> <td>0.999</td> <td>0.997</td> <td>0.995</td> <td>0.992</td> <td>0.990</td> <td class="smallHide">0.990</td> <td class="smallHide">0.993</td> <td class="smallHide">1.007</td> <td class="smallHide">1.033</td> <td class="smallHide">1.067</td> <td class="smallHide">1.109</td> <td class="smallHide">1.207</td> <td class="smallHide">1.316</td> </tr> <tr> <td class="kelvin">350</td> <td>1.000</td> <td>1.000</td> <td>1.000</td> <td>1.001</td> <td>1.004</td> <td>1.008</td> <td class="smallHide">1.012</td> <td class="smallHide">1.018</td> <td class="smallHide">1.038</td> <td class="smallHide">1.064</td> <td class="smallHide">1.095</td> <td class="smallHide">1.130</td> <td class="smallHide">1.212</td> <td class="smallHide">1.302</td> </tr> <tr> <td class="kelvin">400</td> <td>1.000</td> <td>1.001</td> <td>1.003</td> <td>1.005</td> <td>1.010</td> <td>1.016</td> <td class="smallHide">1.023</td> <td class="smallHide">1.031</td> <td class="smallHide">1.053</td> <td class="smallHide">1.080</td> <td class="smallHide">1.109</td> <td class="smallHide">1.141</td> <td class="smallHide">1.212</td> <td class="smallHide">1.289</td> </tr> <tr> <td class="kelvin">450</td> <td>1.000</td> <td>1.002</td> <td>1.003</td> <td>1.006</td> <td>1.013</td> <td>1.021</td> <td class="smallHide">1.029</td> <td class="smallHide">1.037</td> <td class="smallHide">1.061</td> <td class="smallHide">1.091</td> <td class="smallHide">1.118</td> <td class="smallHide">1.146</td> <td class="smallHide">1.209</td> <td class="smallHide">1.278</td> </tr> <tr> <td class="kelvin">500</td> <td>1.000</td> <td>1.002</td> <td>1.003</td> <td>1.007</td> <td>1.015</td> <td>1.023</td> <td class="smallHide">1.032</td> <td class="smallHide">1.041</td> <td class="smallHide">1.065</td> <td class="smallHide">1.091</td> <td class="smallHide">1.118</td> <td class="smallHide">1.146</td> <td class="smallHide">1.205</td> <td class="smallHide">1.267</td> </tr> <tr> <td class="kelvin">600</td> <td>1.000</td> <td>1.002</td> <td>1.004</td> <td>1.008</td> <td>1.016</td> <td>1.025</td> <td class="smallHide">1.034</td> <td class="smallHide">1.043</td> <td class="smallHide">1.068</td> <td class="smallHide">1.092</td> <td class="smallHide">1.117</td> <td class="smallHide">1.143</td> <td class="smallHide">1.195</td> <td class="smallHide">1.248</td> </tr> <tr> <td class="kelvin">800</td> <td>1.000</td> <td>1.002</td> <td>1.004</td> <td>1.008</td> <td>1.016</td> <td>1.024</td> <td class="smallHide">1.032</td> <td class="smallHide">1.041</td> <td class="smallHide">1.062</td> <td class="smallHide">1.084</td> <td class="smallHide">1.106</td> <td class="smallHide">1.128</td> <td class="smallHide">1.172</td> <td class="smallHide">1.215</td> </tr> <tr> <td class="kelvin">1000</td> <td>1.000</td> <td>1.002</td> <td>1.004</td> <td>1.007</td> <td>1.014</td> <td>1.022</td> <td class="smallHide">1.029</td> <td class="smallHide">1.037</td> <td class="smallHide">1.056</td> <td class="smallHide">1.074</td> <td class="smallHide">1.095</td> <td class="smallHide">1.113</td> <td class="smallHide">1.152</td> <td class="smallHide">1.189</td> </tr> </tbody> </table> <style><!-- @media all and (max-width: 560px){ #fullTable {display: inline;} .smallHide {display:none;} } @media all and 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<i>lbf</i> </label> <br > <input type="button" id="weight_calculate2" value="Convert!" > <div id="resultMenuWeight"> </div> </blockquote> <br > <blockquote> <label for="velocity_value2"> <a href="velocity-units-converter-d_1035.html"> Velocity </a> </label> <input type="number" id="velocity_value2" value="1.0" > <input type="radio" name="velocity_unit2" id="velocity_unit2_m_per_s" value="m_per_s" checked="checked" > <label for="velocity_unit2_m_per_s"> <i>m/s</i> </label> <br > <input type="radio" name="velocity_unit2" id="velocity_unit2_km_per_h" value="km_per_h" > <label for="velocity_unit2_km_per_h"> <i>km/h</i> </label> <br > <input type="radio" name="velocity_unit2" id="velocity_unit2_ft_per_min" value="ft_per_min" > <label for="velocity_unit2_ft_per_min"> <i>ft/min</i> </label> <br > <input type="radio" name="velocity_unit2" id="velocity_unit2_ft_per_s" value="ft_per_s" > <label for="velocity_unit2_ft_per_s"> <i>ft/s</i> </label> <br > <input type="radio" name="velocity_unit2" id="velocity_unit2_mph" value="mph" > <label for="velocity_unit2_mph"> <i>mph</i> </label> <br > <input type="radio" name="velocity_unit2" id="velocity_unit2_knots" value="knots" > <label for="velocity_unit2_knots"> <i>knots</i> </label> <br > <input type="button" id="velocity_calculate2" value="Convert!" > <div id="resultMenuVelocity"> </div> </blockquote> <br > <blockquote> <label for="pressure_value2"> <a href="pressure-units-converter-d_569.html"> Pressure </a> </label> <input type="number" id="pressure_value2" value="1.0" > <input type="radio" name="pressure_unit2" id="pressure_unit2_Pa" value="Pa" checked="checked" > <label for="pressure_unit2_Pa"> <i>Pa</i> </label> <br > <input type="radio" name="pressure_unit2" id="pressure_unit2_bar" value="bar" > <label for="pressure_unit2_bar"> <i>bar</i> </label> <br > <input type="radio" name="pressure_unit2" id="pressure_unit2_atmosphere" value="atmosphere" > <label for="pressure_unit2_atmosphere"> <i>atmosphere</i> </label> <br > <input type="radio" name="pressure_unit2" id="pressure_unit2_mmH2O" value="mmH2O" > <label for="pressure_unit2_mmH2O"> <i>mm H<sub>2</sub>O</i> </label> <br > <input type="radio" name="pressure_unit2" id="pressure_unit2_kg_per_cm2" value="kg_per_cm2" > <label for="pressure_unit2_kg_per_cm2"> <i>kg/cm<sup>2</sup></i> </label> <br > <input type="radio" name="pressure_unit2" id="pressure_unit2_psi" value="psi" > <label for="pressure_unit2_psi"> <i>psi</i> </label> <br > <input type="radio" name="pressure_unit2" id="pressure_unit2_inH2O" value="inH2O" > <label for="pressure_unit2_inH2O"> <i>inches H<sub>2</sub>O</i> </label> <br > <input type="button" id="pressure_calculate2" value="Convert!" > <div id="resultMenuPressure"> </div> </blockquote> <br > <blockquote> <label for="flow_value2"> <a href="flow-units-converter-d_405.html"> Flow </a> </label> <input type="number" id="flow_value2" value="1.0" > <input type="radio" name="flow_unit2" id="flow_unit2_cubic_meters_per_second" value="cubic_meters_per_second" checked="checked" > <label for="flow_unit2_cubic_meters_per_second"> <i>m<sup>3</sup>/s</i> </label> <br > <input type="radio" name="flow_unit2" id="flow_unit2_cubic_meters_per_hour" value="cubic_meters_per_hour" > <label for="flow_unit2_cubic_meters_per_hour"> <i>m<sup>3</sup>/h</i> </label> <br > <input type="radio" name="flow_unit2" id="flow_unit2_us_gallons_per_minute" value="us_gallons_per_minute" > <label for="flow_unit2_us_gallons_per_minute"> <i>US gpm</i> </label> <br > <input type="radio" name="flow_unit2" id="flow_unit2_cubic_feet_per_minute" value="cubic_feet_per_minute" > <label for="flow_unit2_cubic_feet_per_minute"> <i>cfm</i> </label> <br > <input type="button" id="flow_calculate2" value="Convert!" > <div id="resultMenuFlow"> </div> </blockquote> </div> <p id="tstamp"> 11.25.10 </p> <div id="adSlotStickyLeft" class="noPrint"> <div> <!-- adngin-left1-0 --> <div id="adngin-left1-0"></div> </div> </div> <a 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