Difference between revisions of "Thermodynamics"
Jump to navigation
Jump to search
slider.py example
(→Vapor-liquid equilibrium diagram ideal mixture) |
(→Vapor-liquid equilibrium diagram ideal mixture) |
||
| Line 16: | Line 16: | ||
| + | |||
| + | |||
<html lang="en"> | <html lang="en"> | ||
<head> | <head> | ||
| − | |||
<div align='center'> | <div align='center'> | ||
| Line 52: | Line 53: | ||
| − | <div class="bk-root" id=" | + | <div class="bk-root" id="8d6ef07f-ccfb-4c63-bdd3-f9c440aa36e2"></div> |
| Line 58: | Line 59: | ||
| − | <script type="application/json" id=" | + | <script type="application/json" id="1492"> |
| − | {" | + | {"0e6142b5-bab7-4c8f-971c-7b839d78c7f6":{"roots":{"references":[{"attributes":{"axis_label":"Mole fraction of A","formatter":{"id":"1423","type":"BasicTickFormatter"},"plot":{"id":"1371","subtype":"Figure","type":"Plot"},"ticker":{"id":"1381","type":"BasicTicker"}},"id":"1380","type":"LinearAxis"},{"attributes":{"callback":null},"id":"1372","type":"Range1d"},{"attributes":{"plot":null,"text":""},"id":"1421","type":"Title"},{"attributes":{"below":[{"id":"1380","type":"LinearAxis"}],"left":[{"id":"1385","type":"LinearAxis"}],"plot_height":400,"plot_width":400,"renderers":[{"id":"1380","type":"LinearAxis"},{"id":"1384","type":"Grid"},{"id":"1385","type":"LinearAxis"},{"id":"1389","type":"Grid"},{"id":"1398","type":"BoxAnnotation"},{"id":"1408","type":"GlyphRenderer"},{"id":"1413","type":"GlyphRenderer"}],"title":{"id":"1421","type":"Title"},"toolbar":{"id":"1396","type":"Toolbar"},"x_range":{"id":"1372","type":"Range1d"},"x_scale":{"id":"1376","type":"LinearScale"},"y_range":{"id":"1374","type":"Range1d"},"y_scale":{"id":"1378","type":"LinearScale"}},"id":"1371","subtype":"Figure","type":"Plot"},{"attributes":{},"id":"1423","type":"BasicTickFormatter"},{"attributes":{},"id":"1425","type":"BasicTickFormatter"},{"attributes":{},"id":"1427","type":"UnionRenderers"},{"attributes":{},"id":"1426","type":"Selection"},{"attributes":{"axis_label":"Vapor pressure (a.u.)","formatter":{"id":"1425","type":"BasicTickFormatter"},"plot":{"id":"1371","subtype":"Figure","type":"Plot"},"ticker":{"id":"1386","type":"BasicTicker"}},"id":"1385","type":"LinearAxis"},{"attributes":{"callback":null,"data":{"x":{"__ndarray__":"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","dtype":"float64","shape":[100]},"y0":{"__ndarray__":"AAAAAAAAFECBWr9SoNYTQAO1fqVArRNAhA8++OCDE0AFav1KgVoTQIbEvJ0hMRNACB988MEHE0CJeTtDYt4SQArU+pUCtRJAjC666KKLEkANiXk7Q2ISQI7jOI7jOBJAED744IMPEkCRmLczJOYRQBLzdobEvBFAk0022WSTEUAVqPUrBWoRQJYCtX6lQBFAF1100UUXEUCYtzMk5u0QQBoS83aGxBBAm2yyySabEEAcx3Ecx3EQQJ4hMW9nSBBAH3zwwQcfEEBArV8pUOsPQENi3s6QmA9ARhdddNFFD0BIzNsZEvMOQEuBWr9SoA5ATjbZZJNNDkBQ61cK1PoNQFKg1q8UqA1AVVVVVVVVDUBYCtT6lQINQFq/UqDWrwxAXXTRRRddDEBgKVDrVwoMQGLezpCYtwtAZJNNNtlkC0BnSMzbGRILQGr9SoFavwpAbLLJJptsCkBvZ0jM2xkKQHIcx3EcxwlAdNFFF110CUB2hsS8nSEJQHk7Q2LezghAfPDBBx98CEB+pUCtXykIQIFav1Kg1gdAgw8++OCDB0CGxLydITEHQIl5O0Ni3gZAiy666KKLBkCO4ziO4zgGQJCYtzMk5gVAk0022WSTBUCWArV+pUAFQJi3MyTm7QRAm2yyySabBECdITFvZ0gEQKDWrxSo9QNAoosuuuiiA0ClQK1fKVADQKj1KwVq/QJAqqqqqqqqAkCtXylQ61cCQK8UqPUrBQJAsskmm2yyAUC0fqVArV8BQLczJObtDAFAuuiiiy66AEC8nSExb2cAQL9SoNavFABAgg8++OCD/z+IeTtDYt7+P47jOI7jOP4/kk022WST/T+YtzMk5u38P5whMW9nSPw/oosuuuii+z+m9SsFav36P6xfKVDrV/o/sskmm2yy+T+2MyTm7Qz5P7ydITFvZ/g/wAcffPDB9z/GcRzHcRz3P8rbGRLzdvY/0EUXXXTR9T/WrxSo9Sv1P9oZEvN2hvQ/4IMPPvjg8z/k7QyJeTvzP+pXCtT6lfI/8MEHH3zw8T/0KwVq/UrxP/qVArV+pfA/AAAAAAAA8D8=","dtype":"float64","shape":[100]},"y1":{"__ndarray__":"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","dtype":"float64","shape":[100]}},"selected":{"id":"1426","type":"Selection"},"selection_policy":{"id":"1427","type":"UnionRenderers"}},"id":"1370","type":"ColumnDataSource"},{"attributes":{"source":{"id":"1370","type":"ColumnDataSource"}},"id":"1409","type":"CDSView"},{"attributes":{"data_source":{"id":"1370","type":"ColumnDataSource"},"glyph":{"id":"1406","type":"Line"},"hover_glyph":null,"muted_glyph":null,"nonselection_glyph":{"id":"1407","type":"Line"},"selection_glyph":null,"view":{"id":"1409","type":"CDSView"}},"id":"1408","type":"GlyphRenderer"},{"attributes":{"callback":null,"end":5},"id":"1374","type":"Range1d"},{"attributes":{"bottom_units":"screen","fill_alpha":{"value":0.5},"fill_color":{"value":"lightgrey"},"left_units":"screen","level":"overlay","line_alpha":{"value":1.0},"line_color":{"value":"black"},"line_dash":[4,4],"line_width":{"value":2},"plot":null,"render_mode":"css","right_units":"screen","top_units":"screen"},"id":"1398","type":"BoxAnnotation"},{"attributes":{},"id":"1378","type":"LinearScale"},{"attributes":{},"id":"1395","type":"HelpTool"},{"attributes":{},"id":"1394","type":"ResetTool"},{"attributes":{"line_alpha":0.1,"line_color":"#1f77b4","line_width":3,"x":{"field":"x"},"y":{"field":"y0"}},"id":"1407","type":"Line"},{"attributes":{"overlay":{"id":"1398","type":"BoxAnnotation"}},"id":"1392","type":"BoxZoomTool"},{"attributes":{},"id":"1391","type":"WheelZoomTool"},{"attributes":{},"id":"1390","type":"PanTool"},{"attributes":{},"id":"1376","type":"LinearScale"},{"attributes":{},"id":"1381","type":"BasicTicker"},{"attributes":{"active_drag":"auto","active_inspect":"auto","active_multi":null,"active_scroll":"auto","active_tap":"auto","tools":[{"id":"1390","type":"PanTool"},{"id":"1391","type":"WheelZoomTool"},{"id":"1392","type":"BoxZoomTool"},{"id":"1393","type":"SaveTool"},{"id":"1394","type":"ResetTool"},{"id":"1395","type":"HelpTool"}]},"id":"1396","type":"Toolbar"},{"attributes":{},"id":"1386","type":"BasicTicker"},{"attributes":{},"id":"1393","type":"SaveTool"},{"attributes":{"line_alpha":0.6,"line_color":"red","line_width":3,"x":{"field":"x"},"y":{"field":"y0"}},"id":"1406","type":"Line"},{"attributes":{"children":[{"id":"1417","type":"WidgetBox"}]},"id":"1418","type":"Column"},{"attributes":{"children":[{"id":"1371","subtype":"Figure","type":"Plot"},{"id":"1418","type":"Column"}]},"id":"1419","type":"Row"},{"attributes":{"dimension":1,"plot":{"id":"1371","subtype":"Figure","type":"Plot"},"ticker":{"id":"1386","type":"BasicTicker"}},"id":"1389","type":"Grid"},{"attributes":{"plot":{"id":"1371","subtype":"Figure","type":"Plot"},"ticker":{"id":"1381","type":"BasicTicker"}},"id":"1384","type":"Grid"},{"attributes":{"line_alpha":0.6,"line_width":3,"x":{"field":"x"},"y":{"field":"y1"}},"id":"1411","type":"Line"},{"attributes":{"line_alpha":0.1,"line_color":"#1f77b4","line_width":3,"x":{"field":"x"},"y":{"field":"y1"}},"id":"1412","type":"Line"},{"attributes":{"data_source":{"id":"1370","type":"ColumnDataSource"},"glyph":{"id":"1411","type":"Line"},"hover_glyph":null,"muted_glyph":null,"nonselection_glyph":{"id":"1412","type":"Line"},"selection_glyph":null,"view":{"id":"1414","type":"CDSView"}},"id":"1413","type":"GlyphRenderer"},{"attributes":{"source":{"id":"1370","type":"ColumnDataSource"}},"id":"1414","type":"CDSView"},{"attributes":{"args":{"freq":{"id":"1416","type":"Slider"},"source":{"id":"1370","type":"ColumnDataSource"}},"code":"\n var data = source.data;\n var k = freq.value;\n var x = data['x']\n var y0 = data['y0']\n var y1 = data['y1']\n for (var i = 0; i < x.length; i++) {\n y0[i] = k+(1-k)*x[i];\n y1[i] = k/(1-(1-k)*x[i]);\n }\n source.change.emit();\n"},"id":"1415","type":"CustomJS"},{"attributes":{"callback":{"id":"1415","type":"CustomJS"},"end":5,"start":0.1,"step":0.1,"title":"pB* (a.u.) =","value":5},"id":"1416","type":"Slider"},{"attributes":{"children":[{"id":"1416","type":"Slider"}]},"id":"1417","type":"WidgetBox"}],"root_ids":["1419"]},"title":"Bokeh Application","version":"1.0.2"}} |
</script> | </script> | ||
<script type="text/javascript"> | <script type="text/javascript"> | ||
| Line 68: | Line 69: | ||
function embed_document(root) { | function embed_document(root) { | ||
| − | var docs_json = document.getElementById(' | + | var docs_json = document.getElementById('1492').textContent; |
| − | var render_items = [{"docid":" | + | var render_items = [{"docid":"0e6142b5-bab7-4c8f-971c-7b839d78c7f6","roots":{"1419":"8d6ef07f-ccfb-4c63-bdd3-f9c440aa36e2"}}]; |
root.Bokeh.embed.embed_items(docs_json, render_items); | root.Bokeh.embed.embed_items(docs_json, render_items); | ||
| Line 96: | Line 97: | ||
})(); | })(); | ||
</script> | </script> | ||
| − | + | </div> | |
| − | |||
| − | |||
</body> | </body> | ||
</html> | </html> | ||
| − | |||
| − | |||
Revision as of 17:53, 21 April 2019
Vapor-liquid equilibrium diagram ideal mixture
The following plot shows the vapor-liquid phase diagram for a binary ideal mixture (components: A and B). The vapor pressures of the pure substances are [math]p_A^*[/math] and [math]p_B^*[/math], respectively.
The red curve shows the vapor pressure of the mixture [math]p[/math] as a function of the mole fraction of A in the liquid [math]x_A^l[/math]:
[math]p=p_B^*+(p_A^*-p_B^*)x_A^l[/math]
The black curve shows the vapor pressure of the mixture [math]p[/math] as a function of the mole fraction of A in the vapor [math]x_A^v[/math]:
[math]p=p_A^*p_B^*/(p_A^*-(p_A^*-p_B^*)x_A^v)[/math]
In the example below [math]p_A^*=1[/math] (a.u.) and the value of [math]p_B^*[/math] can be changed moving the slider below.
