第一定律(作业题解).ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,1 mol,水蒸气（,HO,，,g,）在,100,，,101.325 kPa,下全部凝结成液态水。求过程的功。假设：相对于水蒸气的体积，液态水的体积可以忽略不计。,2.2,H,2,O(l),100,101.325,kPa,H,2,O(g)100,101.325,kPa,W=,p,环,(,V,2,V,1,),=,p,(,V,1,),nRT,=1,8.314,373.15,3102.4J,4/8/2026,1,始态为,25,，,200,kPa,的,5,mol,理想气体,经,a,b,两不同途径到达相同的末态。途径,a,先经绝热膨胀到,28.57,，,100,kPa,，,步骤的功,W,a,=,5.57kJ,；,再恒容加热到压力,200,kPa,的末态,步骤的热,Q,a,=25.42kJ,。,途径,b,为恒压加热过程。求途径,b,的,W,b,及,Q,b,。,5,mol,Pg,p,1,=200kPa,T,1,25,5,mol,Pg,p,2,=100kPa,T,2,-28.57,5,mol,Pg,p,3,=200kPa,T,3,(,1),绝热,(,2),恒容,2.5,途径,b,恒压,4/8/2026,2,5,mol,Pg,p,1,=200kPa,T,1,25,5,mol,Pg,p,2,=100kPa,T,2,-28.57,5,mol,Pg,p,3,=200kPa,T,3,(,1),绝热,(,2),恒容,T,3,=2,T,2,2,（,273.15,28.57,）,489.16 K,U,Q,a,W,a,Q,b,W,b,W,b,=,p,环,(,V,3,V,1,),nR,T,=,5,8.314 191.01,7940.3J,Q,b,（,Q,a,W,a,）,W,b,=,(25.42,5.57)+7.94=27.79 kJ,途径,b,恒压,4/8/2026,3,某,理想气体,C,Vm,=,3/2,R,。,今有该,气体,5mol,在,恒容下温度升高,50,。求过程的,W,Q,U,及,H,.,W=,0,2.8,5mol,理想气体,T,1,V,1,5mol,理想气体,T,2,=,T,1,+50,V,2,=,V,1,恒,容,Q,=,U,=,nC,Vm,T,=5,3/2R 50=3.118,10,3,J,H,=,nC,pm,T,=5,5/2R 50=,5.196,10,3,J,4/8/2026,4,4mol,某,理想气体，C,p,m,=7/2R,。,由始态,100,kPa,100dm,3,先恒压加热使体积增大到,150,dm,3,，,再恒容加热使压力增大到,150,kPa,。,求过程的,W,Q,U,和,H.,U,n,C,V,m,(,T,3,T,1,),=,C,V,m,(,p,3,V,3,p,1,V,1,)/R=18750J,H,n C,p,m,(,T,3,T,1,),=C,p,m,(,p,3,V,3,p,1,V,1,)/R=31250J,W,=W,1,+,W,2,=W,1,=,p,2,(,V,2,V,1,),=,100,10,3,Pa,(150,100),10,3,m,3,=,5000J,Q=,U,W=,18750+5000=23750J,2.11,第四版,4,mol,Pg,p,1,=100kPa,V,1,=100dm,3,4 mol,Pg,p,2,=100kPa,V,2,=150dm,3,4 mol,Pg,p,3,=150kPa,V,2,=150dm,3,3,(,1),恒压,(,2),恒容,4/8/2026,5,解法,2,4/8/2026,6,4/8/2026,7,1mol,某,理想气体,于,27,，,101.325kPa,的始态下,先受某恒定外压恒温压缩至平衡态，再恒容升温至,97,，,250.00kPa,。,求过程的,W,Q,U,H,。已知气体的,C,V,m,=20.92,JmolK,-1,。,2.11,第五版,1mol,Pg,T,1,=300K,p,1,=,101.325kPa,1,mol,Pg,T,2,=,T,1,=300K,p,2,=,1,mol,Pg,T,3,=,370K,p,3,=,250.00kPa,(,1),恒温,(,2),恒容,4/8/2026,8,U,n,C,V,m,(,T,3,T,1,),=,20.92,(,370,300)=1464J,H,n,C,p,m,(,T,3,T,1,),=,（,20.92+8.314,）,(370,300)=2046J,p,2,=,p,3,T,2,/,T,3,=250 300/370=202.70kPa,W,=W,1,+,W,2,=W,1,=,p,2,(,V,2,V,1,),=,nRT,(1,p,2,/,p,1,),=,8.314,300,(1,202.70/101.325),=2496 J,Q=,U,W=,1464,2496,=,1032J,1mol,Pg,T,1,=300K,p,1,=,101.325kPa,1,mol,Pg,T,2,=,T,1,=300K,p,2,=,1,mol,Pg,T,3,=,370K,p,3,=,250.00kPa,(,1),恒温,(,2),恒容,4/8/2026,9,容积为,0.1,m,3,的恒容密闭容器中有一绝热隔板，其两侧分别为,0,，,4,mol,的,Ar,(g),及,150,，,2,mol,的,Cu(s),。,现将隔板撤掉，整个系统达到热平衡，求末态温度及过程的,H.,已知：,Ar,(g),和,Cu(s),的,摩尔定压热容,C,p,m,分别为,20.786,JmolK,1,及,24.435,JmolK,1,，,且假设均不随温度而变。,Q=,0,，,W,=0,，,U,0,U,U,Ar,(g)+,U,Cu(s),=0,U,n C,V,m,Ar,(g)(,T,T,1,)+,n C,p,m,Cu(s),(,T,T,2,),=0,T=347.38 K,H,=n C,p,m,Ar,(g)(,T,T,1,)+,n C,p,m,Cu(s),(,T,T,2,),=2469J,2.15,4/8/2026,10,已知水在,100,，,101.325 kPa,下的摩尔蒸发焓,vap,H,m,=,40.668 kJmol,-1,，试分别计算下列过程的,Q,W,U,及,H,。,（,1,）在,100,，,101.325 kPa,下，,1kg,水蒸发为水蒸汽；,（,2,）在恒定,100,的真空容器中，,1kg,水全部蒸发为水蒸汽，并且水蒸汽压力恰好为,101.325 kPa,。,2.21,n mol H,2,O(l,),100,101.325,kPa,n mol H,2,O,(g)100,101.325,kPa,（,1,）,T p,（,2,）向真空蒸发,n=,1000/18=55.56 mol,4/8/2026,11,恒压、,W,=0,的过程，,Q,p,=,H,n,vap,H,m,=55.56mol,40.668 kJmol,-1,=2259kJ,W,=,p(V,g,V,l,)=,pV,g,=,nRT,=,55.56,8.314 373.15=,172.3,10,3,J=,172.3 kJ,U,Q+,W,=,2259,172=2087 kJ,n mol,H,2,O(l,),100,101.325,kPa,n mol,H,2,O,(g),100,101.325,kPa,（,1,）,T p,4/8/2026,12,向真空蒸发，,p,环,=0,，,W,=0,，,Q=,U,过程（,2,）与过程（,1,）始终态相同，所以两过程,U,及,H,相同。,Q=,U,=2087 kJ,，,H,2259kJ,n mol H,2,O(l,),100,101.325,kPa,n mol H,2,O,(g),100,101.325,kPa,（,2,）向真空蒸发,p,amb,=0,4/8/2026,13,已知水,(H,2,O,l),在,100,的摩尔蒸发焓,vap,H,m,=,40.668 kJmol,-1,，水和水蒸汽在,25,100,间的平均摩尔定压热容分别为,C,p,m,(,H,2,O,l,)=75.75,Jmol,-1,K,-1,和,C,p,m,(,H,2,O,g,)=33.76,Jmol,-1,K,-1,。求在,25,时水的摩尔蒸发焓,。,2.26,4/8/2026,14,某,双,原子,理想气体,1mol,从始态,350K,，,200kPa,经过如下四个不同过程达到各自的平衡态，求各过程的功,W,。,（,1,）,恒温可逆膨胀到,50kPa,；,（,2,）,恒温反抗,50kPa,恒外压不可逆膨胀；,（,3,）恒温向真空膨胀到,50kPa,；,（,4,）绝热可逆膨胀到,50kPa,；,（,5,）绝热反抗,50kPa,恒外压不可逆膨胀。,2.38,4/8/2026,15,4/8/2026,16,4/8/2026,17,4/8/2026,18,4/8/2026,19,25,下，密闭恒容的容器中有,10g,固体萘,C,10,H,8,(s),在过量的,O,2,(g),中完全燃烧成,C,O,2,(g),和,H,2,O(l),。过程放热,401.727 kJ,。求：,（,1,）,C,10,H,8,(s)+12O,2,(g)=10,C,O,2,(g)+4H,2,O(l),的反应进度；,（,2,）,C,10,H,8,(s),的,（,3,）,C,10,H,8,(s),的,2.27,4/8/2026,20,25,下，密闭恒容的容器中有,10g,固体萘,C,10,H,8,(s),在过量的,O,2,(g),中完全燃烧成,C,O,2,(g),和,H,2,O(l),。过程放热,401.727 kJ,。求：,（,1,）,C,10,H,8,(s)+12O,2,(g)=10,C,O,2,(g)+4H,2,O(l),的反应进度；,（,2,）,C,10,H,8,(s),的,（,3,）,C,10,H,8,(s),的,4/8/2026,21,已知,25,甲酸甲酯的标准摩尔燃烧焓 为,-979.5kJmol,-1,甲酸（,HCOOH,l,）、甲醇（,CH,3,OH,l,）、水（,H,2,O,l,）及二氧化碳（,C,O,2,g,）的标准摩尔生成焓分别为,-424.72kJmol,-1,，,-238.66kJmol,-1,-285.83kJmol,-1,及,-393.509 kJmol,-1,。应用这些数据求,25,时下列反应的标准摩尔反应焓。,HCOOH(l)+CH,3,OH(l)=H,C,OOCH,3,(l)+H,2,O(l),2.31,4/8/2026,22,4/8/2026,23,4/8/2026,24,+2O,2,+2O,2,4/8/2026,25,思考题,2.,一气体从某一状态出发，经绝热可逆压缩或经恒温可逆压缩到一固定的体积，哪种压缩过程所需的功大，为什么？如果是膨胀，情况又将如何？,4/8/2026,26,绝热过程,Q=0 U=w,4/8/2026,27,