<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:8px"><div id="yiv1009176525"><div><div style="color: rgb(0, 0, 0); font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 8px; background-color: rgb(255, 255, 255);"><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7523" style=""><span class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7522" style="">Caros colegas, uso alguns modelos de isotermas de adsorção, para o modelo de Langmuir existem algumas linearizações, como faço para avaliar no R se o modelo não linear é melhor que o modelo linearizado?</span></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7521" style="background-color:transparent;"><span class="yiv1009176525" style=""><br class="yiv1009176525"
style=""></span></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7519" style="background-color:transparent;"><span class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7520" style="">Att,</span></div><div class="yiv1009176525" style=""></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7518" style=""> </div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7452" style=""><span class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7517" style="font-weight:bold;font-style:italic;">Ari Clecius Alves de Lima</span><br class="yiv1009176525" style="font-weight:bold;font-style:italic;"><span class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7516" style="font-weight:bold;font-style:italic;">Engenheiro Químico</span><br class="yiv1009176525" style="font-weight:bold;font-style:italic;"><span class="yiv1009176525"
id="yiv1009176525yui_3_16_0_1_1414144791333_7515" style="font-weight:bold;font-style:italic;">Me. Engenharia Civil</span><br class="yiv1009176525" style="font-weight:bold;font-style:italic;"><span class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7527" style="font-weight:bold;font-style:italic;">(085)88412345</span><br class="yiv1009176525" style="font-weight:bold;font-style:italic;"><span class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7528" style="font-weight:bold;font-style:italic;">(085)33669042</span></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7529" style="font-style:italic;background-color:transparent;"><span class="yiv1009176525" style="font-weight:bold;"><br class="yiv1009176525" style=""></span></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7531" style="font-style:italic;background-color:transparent;"><span class="yiv1009176525"
id="yiv1009176525yui_3_16_0_1_1414144791333_7530" style="font-weight:bold;">#CRM</span></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7534" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7533" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7532" style="">ce=c(0.66450,0.92395,1.22510,1.53040,12.89600,32.44400,70.93000,135.54800)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7537" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7536" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7535" style="">qe=c(0.65864,0.83815,1.09135,1.42049,11.57060,15.42198,16.41500,20.42020)</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525"
style="">#########Modelo linear####################</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7540" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7539" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7538" style="">ce_inv=1/ce</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">qe_inv=1/qe</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">Langmuir_Linear=lm(qe_inv~ce_inv)</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">summary(Langmuir_Linear)</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b
class="yiv1009176525" style=""><i class="yiv1009176525" style="">names(Langmuir_Linear)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7597" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">Langmuir_Linear$coefficients</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">Langmuir_Linear$coefficients[1]</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">qmax_L=1/Langmuir_Linear$coefficients[1]</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">qmax_L</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7543" style="background-color:transparent;"><b
class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7542" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7541" style="">kl_L=1/qmax*Langmuir_Linear$coefficients[2]</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7546" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7545" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7544" style="">kl_L</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7549" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7548" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7547" style="">qe_est_L=qmax_L* kl_L*ce/(1+ kl_L *ce)</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i
class="yiv1009176525" style="">plot(ce,qe)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7552" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7551" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7550" style="">lines(ce,qe_est_L,col="blue")</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">##########################################</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7553" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style=""><br class="yiv1009176525" style=""></i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7556" style="background-color:transparent;"><b class="yiv1009176525"
id="yiv1009176525yui_3_16_0_1_1414144791333_7555" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7554" style="">library(nlstools)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7559" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7558" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7557" style="">adsorption=list(ce,qe)</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">langmuir<-nls(qe~qmax*kl*ce/(1+kl*ce),adsorption,start=list(qmax=30,kl=0.02))</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7562" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7561" style=""><i class="yiv1009176525"
id="yiv1009176525yui_3_16_0_1_1414144791333_7560" style="">summary(langmuir)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7563" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style=""><br class="yiv1009176525" style=""></i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7566" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7565" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7564" style="">qe_Est_NL=21.40602* 0.07498 *ce/(1+ 0.07498 *ce)</i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">qe_Est_NL</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7596" style="background-color:transparent;"><b
class="yiv1009176525" style=""><i class="yiv1009176525" style="">plot(ce,qe)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7586" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">lines(ce,qe_Est_NL,col="red")</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7583" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">legend("top",legend=c("LangmuirExp","Langmuir_Est_NL"), lty=c(NA,1), col=c("black","red"),pch=c(3,NA),cex=0.6)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7587" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">########################################</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7595"
style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style="">#############################################</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7578" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7577" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7576" style="">plot(ce,qe)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7575" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7574" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7573" style="">lines(ce,qe_est_L,col="blue")</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7572" style="background-color:transparent;"><b class="yiv1009176525"
id="yiv1009176525yui_3_16_0_1_1414144791333_7571" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7570" style="">lines(ce,qe_Est_NL,col="red")</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7569" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7568" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7567" style="">legend("topleft",legend=c("LangmuirExp","Langmuir_Est_L","Langmuir_Est_NL"), lty=c(NA,1,1), col=c("black","blue","red"),pch=c(3,NA,NA),cex=0.6)</i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7588" style="background-color:transparent;"><b class="yiv1009176525" style=""><i class="yiv1009176525" style=""><br class="yiv1009176525" style=""></i></b></div><div class="yiv1009176525" style="background-color:transparent;"><b class="yiv1009176525" style=""><i
class="yiv1009176525" style=""><span class="yiv1009176525" style=""></span></i></b></div><div class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7591" style="background-color:transparent;"><b class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7590" style=""><i class="yiv1009176525" id="yiv1009176525yui_3_16_0_1_1414144791333_7589" style="">#####################################################</i></b></div></div></div></div></div></body></html>