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render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',{ref:\"intro\"},[_vm._v(\"\\n      Boyle's Law\\n    \")]),_vm._m(0),_c('h3',{ref:\"iso\"},[_vm._v(\"\\n      Isothermal Processes\\n    \")]),_vm._m(1),_c('h3',{ref:\"pg\"},[_vm._v(\"\\n      MagicGraph: Pressure & Volume in an Isothermal Process\\n    \")]),_c('p',[_vm._v(\"\\n      Through this visually interactive MagicGraph, students will learn how the volume of a gas contained in a closed vessel changes with its pressure during\\n      an isothermal process using Boyle's law.\\n    \")]),_c('h5',[_vm._v(\" To Get Started: \")]),_vm._m(2),_c('br'),_c('v-responsive',[_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}})]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('h5',[_vm._v(\" Liked this MagicGraph? Follow this link \"),_c('a',{staticClass:\"icn\",attrs:{\"href\":\"https://edliy.com/physics/concavemirrors#mgk\"}},[_c('i',{staticClass:\"fa fa-external-link-square\"})]),_vm._v(\" to explore more MagicGraphs.\")])])],1)],1)\n}\nvar staticRenderFns = [function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n      Boyle's law is an empirical law (i.e. a law derived based on experimental observations) that relates the volume of a gas to its pressure.\\n      Boyle's law states that the volume occupied by a fixed mass of gas changes inversely with the pressure exerted on it provided that the temperature of the gas is kept fixed.\\n      Mathematically, Boyle's law can be expressed as\\n      $$ V \\\\propto \\\\frac{1}{P}$$\\n      where \\\\(V\\\\) is the volume of a given mass of the gas and \\\\(P\\\\) is the pressure exerted on the gas.\"),_c('br'),_vm._v(\"\\n      By introducing a proportionality factor \\\\(\\\\kappa\\\\), Boyle's law can be expressed as\\n      $$ V = \\\\frac{\\\\kappa}{P}$$\\n      Note that the proportionality factor \\\\(\\\\kappa\\\\) remains constant as long as temperature is kept fixed. \\\\(\\\\kappa\\\\) will change if the temperature is changed.\\n      Thus, Boyle's law states that, at a fixed temperature, the product of the pressure and volume of gas is a constant.\\n      $$PV = \\\\kappa$$\\n    \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n      Boyle's law can be used to relate the volumes and pressures of a gas during an isothermal process.\\n      An isothermal process is defined as the process in which the temperature of the system remains constant. \"),_c('br'),_vm._v(\"\\n      Let's say a given mass of the gas occupies a volume \\\\(V_1\\\\) at pressure \\\\(P_1\\\\) at the beginning of the process.\\n      Let's say the same mass of gas occupies a volume \\\\(V_2\\\\) and is at pressure \\\\(P_2\\\\) at the end of the process.\\n      Then, Boyle's law can be used to relate pressures and volumes of the gas during the process as follows:\\n      $$P_1 V_1 = P_2 V_2$$\\n      \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n      You are given a cylindrical vessel containing a gas. The cross-section area of the vessel is 1 \\\\(m^2\\\\). The temperature of the\\n      gas in the cylinder is kept constant. The pressure of the gas can be increased (or decreased) by\\n      adding (or removing) weights.\\n      \"),_c('br'),_vm._v(\"\\n      Tap on the \"),_c('i',{staticClass:\"fa fa-plus-square\"}),_vm._v(\" button to add weights and \"),_c('i',{staticClass:\"fa fa-minus-square\"}),_vm._v(\" button to remove.\\n      As you add or remove weights, observe how the volume changes with pressure.\\n    \")])\n}]\n\nexport { render, staticRenderFns }","const Boxes = {\r\n  box1: function () {\r\n  JXG.Options.board.minimizeReflow = 'none';\r\n  var board1 = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-1, 13, 16, -4],\r\n  keepaspectratio: true, axis:true, grid:true, ticks:false, showCopyright:false, showNavigation:false,\r\n  pan:{enabled:false}, zoom:{enabled:false}});\r\n//Platform\r\nboard1.options.layer['image'] =15;\r\nboard1.options.layer['polygon'] =14;\r\nvar resize = function () {\r\n    board1.resizeContainer(board1.containerObj.clientWidth, board1.containerObj.clientHeight, true);\r\n    board1.fullUpdate();\r\n    };\r\nwindow.addEventListener(\"resize\", resize);\r\n//board1.offsetX = 2;\r\n//board1.moveOrigin(0,0, true);\r\nboard1.suspendUpdate();\r\n//Texts\r\nvar a=8; var b=3;\r\nboard1.create('text', [7.5, 12, '<b> Boyle\\'s Law ( V &propto; 1/P ) <b>'],{highlight:false, anchorX:'middle', anchorY:'bottom', fixed:true, CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(32*board1.canvasWidth/800)}});\r\nboard1.create('text', [7.5, 11, '(Change Pressure by Adding or Removing Weights)'],{highlight:false, anchorX:'middle', anchorY:'bottom', fixed:true, CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(22*board1.canvasWidth/800)}});\r\nvar platform=board1.create('polygon',[[-9+a,-10+b],[20+a,-10+b],[20+a,-3+b],[-9+a, -3.+b]], {fillColor:'grey', withLines:false, vertices:{visible:false}});\r\n//flask\r\nvar flask=board1.create('polygon',[[a+5,b-4.],[a+6,b-4.],[a+6,b+5],[a+5, b+5]], {fillColor:'black', fillOpacity:1, withLines:false, vertices:{visible:false}});\r\nboard1.create('polygon',[[a,b-4.],[a+1,b-4.],[a+1,b+5],[a, b+5]], {fillColor:'black', fillOpacity:1, withLines:false, vertices:{visible:false}});\r\nboard1.create('polygon',[[a,b-4.],[a+6,b-4.],[a+6,b-3],[a, b-3]], {fillColor:'black', fillOpacity:1, withLines:false, vertices:{visible:false}});\r\n\r\n//Interior\r\n//var interior=board1.create('polygon',[[a+1,b-3.],[a+5,b-3.],[a+5, b+5.01],[a+1, b+5.01]], {fillColor:'oldLace', withLines:false, fillOpacity:1, vertices:{visible:false}, borders:{visible:false}});\r\n//line\r\nvar line = board1.create('line', [[a+3,b], [a+3, b+10]], {visible: false, straightFirst: false, straightLast: false});\r\n//\r\nvar Q=0;\r\nvar i=1;\r\nvar m =5;\r\nvar g = 9.8;\r\nvar R = 8.315;\r\nvar Cv = function(){return (2+3)*R.valueOf()/2};\r\nvar To = 25;\r\nvar delt = function(){return Q.valueOf()/(Cv()+R);}\r\n//Pressure\r\nvar P = m*9.8/1.0;\r\n//height\r\nvar delh = function(){return R*delt/P};\r\n//Temp_inside\r\n//Temp_outside\r\nboard1.create('text', [3+a, b+7.0, 'T = Constant'], {highlight:false, anchorX:'middle',fixed:true, fontSize:function(){return 28*board1.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n//block\r\nvar up =board1.create('image', ['/assets/plus.svg', [a+2.5-0.75, b-5.75], [1.35,1.35]],{fixed:true});\r\nup.setLabel('Tap to add weight')\r\nup.label.setAttribute({visible:false, offset:[0, -25], CssStyle:'fontFamily:Oswald', fontSize:function(){return 20*board1.canvasHeight/800}});\r\nup.on('over', function () {this.label.setAttribute({visible:true});});\r\nup.on('out', function () {this.label.setAttribute({visible:false});});\r\nvar down =board1.create('image', ['/assets/minuss.svg', [a+2.5+0.75, b-5.75], [1.3,1.3]],{fixed:true});\r\ndown.setLabel('Tap to remove weight')\r\ndown.label.setAttribute({visible:false, offset:[0, -25], CssStyle:'fontFamily:Oswald', fontSize:function(){return 20*board1.canvasHeight/800}});\r\ndown.on('over', function () {this.label.setAttribute({visible:true});});\r\ndown.on('out', function () {this.label.setAttribute({visible:false});});\r\n//var pause = board1.create('image', ['pause.svg', [-2, -6], [1.5,1.5]]);\r\nvar mass = board1.create('point', [a+3, b+3], {name: '', size:0, face:'square', label:{offset:[-20, 0]}});\r\nboard1.create('segment', [[()=>(i+1).valueOf(), function(){return mass.Y();}],[()=>(i+1).valueOf(), 0.0]],{strokeWidth:1, dash:1, strokeColor:'black'});\r\nvar lin =board1.create('segment', [[a+1, function(){return mass.Y();}],[a-8,function(){return mass.Y();}]],{strokeWidth:1, dash:1, strokeColor:'black'});\r\n//tape\r\nvar wt=[];\r\nwt[0] =board1.create('image', ['/assets/weight.svg', [1.1+a, function(){return mass.Y();}], [0.75, 0.75]], {highlight:false, visible:function(){if(i>=1){return true}else{return false}}});\r\nwt[1] =board1.create('image', ['/assets/weight.svg', [1.85+a, function(){return mass.Y();}], [0.75, 0.75]],{highlight:false,visible:function(){if(i>=2){return true}else{return false}}});\r\nwt[2] =board1.create('image', ['/assets/weight.svg', [2.6+a, function(){return mass.Y();}], [0.75, 0.75]],{highlight:false,visible:function(){if(i>=3){return true}else{return false}}});\r\nwt[3] =board1.create('image', ['/assets/weight.svg', [3.35+a, function(){return mass.Y();}], [0.75, 0.75]],{highlight:false,visible:function(){if(i>=4){return true}else{return false}}});\r\nwt[4] =board1.create('image', ['/assets/weight.svg', [4.1+a, function(){return mass.Y();}], [0.75, 0.75]],{highlight:false,visible:function(){if(i>=5){return true}else{return false}}});\r\nup.on('down', function(){if(i<5){i+=1; mass.moveTo([3+a, 6/(1+Math.max(i,0))],1000)}else{return;}});\r\ndown.on('down', function(){if(i>0){i-=1;mass.moveTo([3+a, 6/(1+Math.max(i,0))],1000)}else{return;}});\r\n//\r\nboard1.create('text', [3+a, ()=>mass.Y()*0.5, ()=>'P = '+ (i+1).valueOf()+' kgf/m^2'], {anchorX:'middle',highlight:false,fontSize:function(){return 18*board1.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\nboard1.create('image', ['/assets/weight.svg', [2, -3], [0.75, 0.75]], {highlight:false, fixed:true});\r\nboard1.create('text', [3, -2.675, '= 1 kgf'], {highlight:false,fixed:true, fontSize:function(){return 28*board1.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\r\n//\r\nvar Pts=[];\r\nboard1.create('point', [1, 6/1], {name:'P_1, V_1', fixed:true, label:{anchorX:'middle', offset:[0, 20],cssStyle:'fontFamily:Oswald;'}, strokeColor:'black', visible:function(){if(i>=0){return true}else{return false}}})\r\nPts[0] =board1.create('point', [2, 6/2], {name:'P_2, V_2', fixed:true, label:{anchorX:'middle',offset:[0, 20],cssStyle:'fontFamily:Oswald;'}, strokeColor:'black', visible:function(){if(i>=1){return true}else{return false}}});\r\nPts[1] =board1.create('point', [3, 6/3], {name:'P_3, V_3', fixed:true, label:{anchorX:'middle',offset:[0, 20],cssStyle:'fontFamily:Oswald;'}, strokeColor:'black',visible:function(){if(i>=2){return true}else{return false}}});\r\nPts[2] =board1.create('point', [4, 6/4], {name:'P_4, V_4', fixed:true, label:{anchorX:'middle',offset:[0, 20],cssStyle:'fontFamily:Oswald;'},strokeColor:'black',visible:function(){if(i>=3){return true}else{return false}}});\r\nPts[3] =board1.create('point', [5, 6/5], {name:'P_5, V_5', fixed:true,label:{anchorX:'middle',offset:[0, 20],cssStyle:'fontFamily:Oswald;'},strokeColor:'black',visible:function(){if(i>=4){return true}else{return false}}});\r\nPts[4] =board1.create('point', [6, 6/6], {name:'P_6, V_6', fixed:true,label:{anchorX:'middle', offset:[0, 20],cssStyle:'fontFamily:Oswald;'}, strokeColor:'black',visible:function(){if(i>=5){return true}else{return false}}});\r\nvar v =0; var i=0; var j=0;\r\n//wt1.on('down', function(){if(i<=4 && j<1){wt1.moveTo([1+i, mass.Y()], 1000); v=+1; i+=1; j+=1;}});\r\n//wt2.on('down', function(){if(i<=4){wt2.moveTo([1+0.75*i,mass.Y()], 1000); v+=1; i+=1;}});\r\n//wt3.on('down', function(){if(i<=4){wt3.moveTo([1+0.75*i,mass.Y()], 1000); v+=1; i+=1;}});\r\n//wt4.on('down', function(){if(i<=4){wt4.moveTo([1+0.75*i,mass.Y()], 1000); v+=1; i+=1;}});\r\n//wt5.on('down', function(){if(i<=4){wt5.moveTo([1+0.75*i,mass.Y()], 1000);v+=1;  i+=1;}});\r\n//pause.on('down', function(){i=0; Q=0;});\r\nboard1.create('tapemeasure', [[6.5+a, -3+b], [6.5+a, function(){return mass.Y()}]], {name:'V(m^3)',\r\n withLabel: true, label:{fontSize:function(){return 20*board1.canvasHeight/800},cssStyle:'fontFamily:Oswald;', highlight:false},\r\n fixed:true, point1:{size:3,face:'square',strokeColor:'red', fillColor:'red',fixed:true},\r\npoint2:{size:3,face:'square', color:'red', fixed:true}});\r\n//board1.create('tapemeasure', [[6.5+a, -3+b], [6.5+a, 3.0+b]], {name:'h_i', withLabel: true, ticks:false,label:{fontSize:16,cssStyle:'fontFamily:Oswald;'}, fixed:true, point1:{size:4,face:'<',color:'black'}, point2:{size:4,face:'<'}});\r\n//Piston\r\n//gas\r\nvar gas=board1.create('polygon',[[1+a,b-3.],[a+5,b-3.],[a+5,function(){return mass.Y();}],[1+a, function(){return mass.Y();}]], {fillColor:'lightblue', withLines:false, fillOpacity:1., vertices:{visible:false}});\r\n//\r\nvar piston = board1.create('polygon',[[1+a, function(){return mass.Y();}],[5+a,function(){return mass.Y();}],[5+a,function(){return mass.Y()-0.1;}],[1+a, function(){return mass.Y()-0.1;}]], {fillColor:'black', withLines:false, fillOpacity:1, vertices:{visible:false}});\r\n//\r\nboard1.create('text', [3+a, 9, ()=>'P_'+(i+1).valueOf()+'V_'+(i+1).valueOf() +' = '+((i+1).valueOf()).toFixed(1)+ ' x '+ (mass.Y()).toFixed(1) +' = 6'], {anchorX:'middle',highlight:false,fontSize:function(){return 24*board1.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n//\r\nboard1.create('functiongraph',[function(x){return 6/x}, 1, function(){return 1+i}],{strokeWidth:2, strokeColor:'black'});\r\n//\r\nboard1.create('text', [0.1, 12, 'V(m^3)'], {highlight:false, fontSize:function(){return 24*board1.canvasHeight/800}, cssStyle:'fontFamily:Oswald;',fixed:true});\r\nboard1.create('text', [4, -1., 'P(kgf/m^2)'], {highlight:false, fontSize:function(){return 24*board1.canvasHeight/800}, cssStyle:'fontFamily:Oswald;',fixed:true});\r\nboard1.unsuspendUpdate();},}\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3 ref=\"intro\">\n      Boyle's Law\n    </h3>\r\n    <p>\r\n      Boyle's law is an empirical law (i.e. a law derived based on experimental observations) that relates the volume of a gas to its pressure.\r\n      Boyle's law states that the volume occupied by a fixed mass of gas changes inversely with the pressure exerted on it provided that the temperature of the gas is kept fixed.\r\n      Mathematically, Boyle's law can be expressed as\r\n      $$ V \\propto \\frac{1}{P}$$\r\n      where \\(V\\) is the volume of a given mass of the gas and \\(P\\) is the pressure exerted on the gas.<br>\r\n      By introducing a proportionality factor \\(\\kappa\\), Boyle's law can be expressed as\r\n      $$ V = \\frac{\\kappa}{P}$$\r\n      Note that the proportionality factor \\(\\kappa\\) remains constant as long as temperature is kept fixed. \\(\\kappa\\) will change if the temperature is changed.\r\n      Thus, Boyle's law states that, at a fixed temperature, the product of the pressure and volume of gas is a constant.\r\n      $$PV = \\kappa$$\r\n    </p>\r\n    <h3 ref=\"iso\">\n      Isothermal Processes\n    </h3>\r\n    <p>\r\n      Boyle's law can be used to relate the volumes and pressures of a gas during an isothermal process.\r\n      An isothermal process is defined as the process in which the temperature of the system remains constant. <br>\r\n      Let's say a given mass of the gas occupies a volume \\(V_1\\) at pressure \\(P_1\\) at the beginning of the process.\r\n      Let's say the same mass of gas occupies a volume \\(V_2\\) and is at pressure \\(P_2\\) at the end of the process.\r\n      Then, Boyle's law can be used to relate pressures and volumes of the gas during the process as follows:\r\n      $$P_1 V_1 = P_2 V_2$$\r\n      <!--<div id=\"imgs\">\r\n<img src=\"/assets/picture.png\" width=300px>\r\n</div> -->\r\n    </p>\r\n    <h3 ref=\"pg\">\n      MagicGraph: Pressure & Volume in an Isothermal Process\n    </h3>\r\n    <p>\r\n      Through this visually interactive MagicGraph, students will learn how the volume of a gas contained in a closed vessel changes with its pressure during\r\n      an isothermal process using Boyle's law.\n    </p>\r\n    <h5> To Get Started: </h5>\r\n    <p>\r\n      You are given a cylindrical vessel containing a gas. The cross-section area of the vessel is 1 \\(m^2\\). The temperature of the\r\n      gas in the cylinder is kept constant. The pressure of the gas can be increased (or decreased) by\r\n      adding (or removing) weights.\r\n      <br>\r\n      Tap on the <i class=\"fa fa-plus-square\" /> button to add weights and <i class=\"fa fa-minus-square\" /> button to remove.\r\n      As you add or remove weights, observe how the volume changes with pressure.\r\n    </p>\r\n    <br>\r\n    <v-responsive>\r\n      <v-layout justify-center>\r\n        <div id=\"jxgbox1\" class=\"edliy-box-about\" />\r\n      </v-layout>\r\n      <v-layout justify-center>\r\n        <h5> Liked this MagicGraph? Follow this link <a class=\"icn\" href=\"https://edliy.com/physics/concavemirrors#mgk\"> <i class=\"fa fa-external-link-square\" /></a> to explore more MagicGraphs.</h5>\r\n      </v-layout>\r\n    </v-responsive>\r\n  </div>\r\n</template>\r\n<script>\r\nimport Boxes from './Boxes.js'\r\nexport default {\r\n  name: 'BoylesLaw',\r\n  components: {\r\n  },\r\n  data () {\r\n    return {\r\n      style: {layout: \"margin: 10px\"},\r\n    }\r\n  },\r\n  created: function () {\r\n    this.$store.commit('navigation/resetState');\r\n    let title = 'Boyle\\'s Law';\r\n    this.$store.commit('navigation/changeTitle', title);\r\n    this.$store.commit('navigation/changeMenu', title);\r\n    let newTopics = [\r\n      {title: 'Boyle\\'s Law',img:'/assets/number-1.svg', action: () => this.goto('intro')},\r\n      {title: 'Isothermal Processes', img:'/assets/number-2.svg', action: () => this.goto('iso')},\r\n      {title: 'MagicGraph', img:'/assets/touch.svg', action: () => this.goto('pg')},\r\n    ];\r\n    this.$store.commit('navigation/replaceTopics', newTopics);\r\n    let newshowhome = false;\r\n    this.$store.commit('navigation/toggleshowhome', newshowhome);\r\n    let newChem =true;\r\n    this.$store.commit('navigation/replaceChem', newChem);\r\n    let newLeftArrow =true;\r\n    this.$store.commit('navigation/replaceLeftArrow', newLeftArrow);\r\n    let newModule=true;\r\n    this.$store.commit('navigation/replaceModule', newModule);\r\n  },\r\n  mounted () {\r\n    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\r\n    Boxes.box1();\r\n  },\r\n  metaInfo() {\r\n  return{ title: 'Boyle\\'s Law',\r\n          titleTemplate: '%s - Learn interactively',\r\n          meta: [ {name: 'viewport', content: 'width=device-width, initial-scale=1'},\r\n                  {name: 'description', content: 'Learn interactively about Boyle\\'s law'}\r\n                ]\r\n        }\r\n   },\r\n}\r\n</script>\r\n<style lang=\"scss\">\r\n@import 'src/styles/edliy-box.scss';\r\n@import 'src/styles/subtopic-menu.scss';\r\n@import 'src/styles/edliy-box-about.scss';\r\n@import 'src/styles/screen-sizes.scss';\r\n.icn{\r\ncolor: var(--v-red-base);;\r\n}\r\n</style>\r\n","import mod from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Lesson.vue?vue&type=template&id=37d9039e&\"\nimport script from \"./Lesson.vue?vue&type=script&lang=js&\"\nexport * from \"./Lesson.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Lesson.vue?vue&type=style&index=0&id=37d9039e&prod&lang=scss&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  null,\n  null\n  \n)\n\nexport default component.exports","export * from \"-!../../../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../../../node_modules/sass-loader/dist/cjs.js??ref--8-oneOf-1-3!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=style&index=0&id=37d9039e&prod&lang=scss&\""],"sourceRoot":""}