南京工業(yè)大學(xué)研究生工程應(yīng)用數(shù)學(xué)B下第二次作業(yè)

1、 .wd. .wd. .wd.工程應(yīng)用數(shù)學(xué)作業(yè)二專業(yè)：安全科學(xué)與工程 姓名：孫皓 學(xué)號(hào)：6520837000201、1將無(wú)限稀釋活度系數(shù)的估算過(guò)程用MATLAB實(shí)現(xiàn)，要求將ln1x22、-ln2x12和ln12與x1的關(guān)系圖畫出來(lái)。答：首先將列入表1-1，數(shù)據(jù)的第一行和最后一行包含需要求解的未知數(shù)，暫不考慮，將其它數(shù)據(jù)錄入為huoduxishu.m文件。表1-1X1Y1PmmHg1200178.0810.08190.1869202.741.4151.0080.21920.4065236.861.3431.0110.35840.5509266.041.251.0460.38310.5748270

2、.731.2421.0480.52560.6786293.361.1581.1160.84780.8741324.661.0231.5080.98720.9863327.3911.96811327.051huoduxishu.m文件內(nèi)容如下：X1=0.0819;0.2192;0.3584;0.3831;0.5256;0.8478;0.9872;X2=1-X1;Y1=0.1869;0.4065;0.5509;0.5748;0.6786;0.8741;0.9863;P=202.74;236.86;266.04;270.73;293.36;324.66;327.39;gama1=1.415;1.34

3、3;1.25;1.242;1.158;1.023;1;gama2=1.008;1.011;1.046;1.048;1.116;1.508;1.968;lng1g2=log(gama1./gama2);lng1x22=log(gama1)./(X2.2);lng2x12=(-1)*log(gama2)./(X1.2);在matlab命令窗中輸入如下：huoduxishuplot(X1,lng1g2,k*-);hold onplot(X1,lng2x12,b*-);hold onplot(X1,lng1x22,r*-);hold offlegend (lng1g2,lng1x12,lng1x22)

4、得到圖1-1，圖1-1ln1x22曲線和-ln2x12曲線分別與ln12曲線外推在x1=0和1處有交點(diǎn)。由圖可見(jiàn)，ln1x22曲線的后半段和-ln2x12曲線的前半段分別對(duì)其擬合計(jì)算可能有一定影響，考慮分別取前半段與后半段4或5個(gè)點(diǎn)進(jìn)展擬合計(jì)算。1編輯huoduxishux1.m文件內(nèi)容如下：X1=0.3831;0.5256;0.8478;0.9872;gama1=1.242;1.158;1.023;1;gama2=1.048;1.116;1.508;1.968;lng1g2=log(gama1./gama2);lng2x12=(-1)*log(gama2)./(X1.2);在matlab命令

5、窗中輸入如下：clear all huoduxishux1plot(X1,lng1g2,k*-);hold onplot(X1,lng2x12,b*-);hold offlegend (lng1g2,lng2x12)得到圖1-2，圖1-2運(yùn)行：P,S=polyfit(X1,lng2x12,1)得：P = -0.6032 -0.0820S = R: 2x2 double df: 2 normr: 0.0286由此得，-ln2x12 的擬合方程為Y= -0.6032X-0.0820。X1=1時(shí)，Y=-0.6852，輸入：Y=-0.6852;gama2wuqiongda=exp(-Y)，得到：gam

6、a2wuqiongda = 1.98422編輯huoduxishux2.m文件內(nèi)容如下：X1=0.0819;0.2192;0.3584;0.3831;X2=1-X1;gama1=1.415;1.343;1.25;1.242;gama2=1.008;1.011;1.046;1.048;lng1g2=log(gama1./gama2);lng1x22=log(gama1)./(X2.2);在matlab命令窗中輸入如下：clear all huoduxishux2plot(X1,lng1g2,k*-);hold onplot(X1,lng1x22,r*-);hold offlegend (lng1

7、g2,lng1x22)得到圖1-3，圖1-3運(yùn)行：P,S=polyfit(X1,lng1x22,1)得：P = 0.4991 0.3717S = R: 2x2 double df: 2 normr: 0.0111由此得，-ln1x22的擬合方程為Y= 0.4991X+0.3717。X1=0時(shí)，Y=0.3717，輸入：Y=0.3717;gama1wuqiongda=exp(Y)，得到：gama1wuqiongda = 1.4502。綜上，1=1.4502，2=1.9842。3編輯huoduxishuxhuatu.m文件內(nèi)容如下：X1=0;0.0819;0.2192;0.3584;0.3831;0

8、.5256;0.8478;0.9872;1;X2=1-X1;gama1=1.4502;1.415;1.343;1.25;1.242;1.158;1.023;1;1;gama2=1;1.008;1.011;1.046;1.048;1.116;1.508;1.968;1.9842;lng1g2=log(gama1./gama2)lng1x22=log(gama1)./(X2.2)lng2x12=(-1)*log(gama2)./(X1.2)在matlab命令窗中輸入如下：clear allhuoduxishuhuatu運(yùn)行得到：lng1g2 = 0.3717 0.3392 0.2840 0.178

9、2 0.1698 0.0369 -0.3880 -0.6770 -0.6852lng1x22 = 0.3717 0.4118 0.4837 0.5421 0.5695 0.6518 0.9816 0 NaNlng2x12 = NaN -1.1879 -0.2277 -0.3501 -0.3194 -0.3973 -0.5715 -0.6947 -0.6852再運(yùn)行：plot(X1,lng1g2,k*-);hold onplot(X1,lng2x12,b*-);hold onplot(X1,lng1x22,r*-);hold offlegend (lng1g2,lng1x12,lng1x22)得

10、到圖1-4，即ln1x22、-ln2x12和ln(12)與X1的關(guān)系圖。圖1-4ln1x22、-ln2x12和ln(12)與X1的關(guān)系根據(jù)以上結(jié)果完成表1-1并添加ln1x22、-ln2x12和ln(12)的數(shù)據(jù)得表1-2。表1-2X1Y1PmmHg12ln(12)ln1x22-ln2x1200178.081.450210.37170.37170.08190.1869202.741.4151.0080.33920.4118-1.18790.21920.4065236.861.3431.0110.28400.4837-0.22770.35840.5509266.041.251.0460.1782

11、0.5421-0.35010.38310.5748270.731.2421.0480.16980.5695-0.31940.52560.6786293.361.1581.1160.03690.6518-0.39730.84780.8741324.661.0231.508-0.38800.9816-0.57150.98720.9863327.3911.968-0.67700-0.694711327.0511.9842-0.6852-0.68522、分別采用梯形法求積分進(jìn)展熱力學(xué)一致性檢驗(yàn)，并將結(jié)果與辛普森積分法進(jìn)展比較。答：在matlab命令窗中輸入如下：clear allclcX1=0;0.0

12、819;0.2192;0.3584;0.3831;0.5256;0.8478;0.9872;1;gama1=1.4502;1.415;1.343;1.25;1.242;1.158;1.023;1;1;gama2=1;1.008;1.011;1.046;1.048;1.116;1.508;1.968;1.9842;lng1g2=(-1).*log(gama1./gama2)得：lng1g2 = -0.3717 -0.3392 -0.2840 -0.1782 -0.1698 -0.0369 0.3880 0.67700.6852繼續(xù)輸入：p = polyfit(X1,lng1g2, 2)得到：p

13、= 0.8868 0.1613 -0.3629即二次多項(xiàng)式擬合得到的方程為：Y=0.8868.*X1.2+0.1613.*X1-0.3629輸入：X = 0:.001:1;Y = 0.8868.*X.2+0.1613.*X-0.3629;T = trapz(X,Y)得到：T = 0.0134輸入：X = 0:.001:1;Y = 0.8868.*X.2+0.1613.*X-0.3629;Y=abs(Y);T2 = trapz(X,Y)得到：T2 = 0.2654一致性檢驗(yàn)：0.01340.2654=0.05048，合5.0%。其值比原方法大，但兩結(jié)果同樣是大于2%，誤差主要是由于采用多項(xiàng)式擬合

14、方程導(dǎo)致。3、在積分方法統(tǒng)一采用采用辛普森法下，采用線性插值描述ln(12)與的x1的關(guān)系，并將熱力學(xué)一致性檢驗(yàn)結(jié)果與樣條插值法進(jìn)展比較。答：編寫jianyan.m程序，內(nèi)容如下：clear allclcX=0;0.0819;Y=0.3717;0.3392;X1=0:.01: 0.0819;Y1=interp1(X,Y,X1, linear)X=0.0819;0.2192;Y=0.3392;0.2840;X2=0.0819:.01:0.2192;Y2=interp1(X,Y,X2, linear)X=0.2192;0.3584;Y=0.2840;0.1782;X3=0.2192:.01:0.3

15、584;Y3=interp1(X,Y,X3, linear)X=0.3584;0.3831;Y=0.1782;0.1698;X4=0.3584:.01:0.3831;Y4=interp1(X,Y,X4, linear)X=0.3831;0.5256;Y=0.1698;0.0369;X5=0.3831:.01:0.5256;Y5=interp1(X,Y,X5, linear)X=0.5256;0.8478;Y=0.0369;-0.3880;X6=0.5256:.01:0.8478;Y6=interp1(X,Y,X6, linear)X=0.8478;0.9872;Y=-0.3880;-0.677

16、0;X7=0.8478:.01:0.9872;Y7=interp1(X,Y,X7, linear)X=0.9872;1;Y=-0.6770;-0.6852;X8=0.9872:.01:1;Y8=interp1(X,Y,X8, linear)運(yùn)行：jianyan得到：Y1 = 0.3717 0.3677 0.3638 0.3598 0.3558 0.3519 0.3479 0.3439 0.3400Y2 = 0.3392 0.3352 0.3312 0.3271 0.3231 0.3191 0.3151 0.3111 0.3070 0.3030 0.2990 0.2950 0.2910 0.28

17、69Y3 = 0.2840 0.2764 0.2688 0.2612 0.2536 0.2460 0.2384 0.2308 0.2232 0.2156 0.2080 0.2004 0.1928 0.1852Y4 = 0.1782 0.1748 0.1714Y5 = Columns 1 through 14 0.1698 0.1605 0.1511 0.1418 0.1325 0.1232 0.1138 0.1045 0.0952 0.0859 0.0765 0.0672 0.0579 0.0486 Column 15 0.0392Y6 = Columns 1 through 14 0.036

18、9 0.0237 0.0105 -0.0027 -0.0158 -0.0290 -0.0422 -0.0554 -0.0686 -0.0818 -0.0950 -0.1082 -0.1213 -0.1345Columns 15 through 28 -0.1477 -0.1609 -0.1741 -0.1873 -0.2005 -0.2137 -0.2268 -0.2400 -0.2532 -0.2664 -0.2796 -0.2928 -0.3060 -0.3192Columns 29 through 33 -0.3323 -0.3455 -0.3587 -0.3719 -0.3851Y7

19、= -0.3880 -0.4087 -0.4295 -0.4502 -0.4709 -0.4917 -0.5124 -0.5331 -0.5539 -0.5746 -0.5953 -0.6160 -0.6368 -0.6575Y8 = -0.6770 -0.6834輸入：X=0 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800;Y=0.3717 0.3677 0.3638 0.3598 0.3558 0.3519 0.3479 0.3439 0.3400;p1 = polyfit(X, Y, 1)X=0.0819 0.0919 0.

20、1019 0.1119 0.1219 0.1319 0.1419 0.1519 0.1619 0.1719 0.1819 0.1919 0.2019 0.2119;Y=0.3392 0.3352 0.3312 0.3271 0.3231 0.3191 0.3151 0.3111 0.3070 0.3030 0.2990 0.2950 0.2910 0.2869;p2 = polyfit(X, Y, 1)X=0.2192 0.2292 0.2392 0.2492 0.2592 0.2692 0.2792 0.2892 0.2992 0.3092 0.3192 0.3292 0.3392 0.34

21、92;Y=0.2840 0.2764 0.2688 0.2612 0.2536 0.2460 0.2384 0.2308 0.2232 0.2156 0.2080 0.2004 0.1928 0.1852;p3 = polyfit(X, Y, 1)X=0.36 0.37 0.38;Y=0.17820.17480.1714;p4 = polyfit(X, Y, 1)X=0.3831 0.3931 0.4031 0.4131 0.4231 0.4331 0.4431 0.4531 0.4631 0.4731 0.4831 0.4931 0.5031 0.5131 0.5231;Y=0.16980.

22、16050.15110.14180.13250.12320.11380.10450.09520.08590.07650.06720.05790.04860.0392;p5 = polyfit(X, Y, 1)X=0.5256 0.5356 0.5456 0.5556 0.5656 0.5756 0.5856 0.5956 0.6056 0.6156 0.6256 0.6356 0.6456 0.6556 0.6656 0.6756 0.6856 0.6956 0.7056 0.7156 0.7256 0.7356 0.7456 0.7556 0.7656 0.7756 0.7856 0.795

23、6 0.8056 0.8156 0.8256 0.8356 0.8456;Y=0.03690.02370.0105-0.0027-0.0158-0.0290-0.0422-0.0554-0.0686-0.0818-0.0950-0.1082-0.1213-0.1345-0.1477-0.1609-0.1741-0.1873-0.2005-0.2137-0.2268-0.2400-0.2532-0.2664-0.2796-0.2928-0.3060-0.3192-0.3323-0.3455-0.3587-0.3719-0.3851;p6 = polyfit(X, Y, 1)X=0.8478 0.

24、8578 0.8678 0.8778 0.8878 0.8978 0.9078 0.9178 0.9278 0.9378 0.9478 0.9578 0.9678 0.9778;Y=-0.3880-0.4087-0.4295-0.4502-0.4709-0.4917-0.5124-0.5331-0.5539-0.5746-0.5953-0.6160-0.6368-0.6575;p7 = polyfit(X, Y, 1)X=0.99 1;Y=-0.6770-0.6834;p8 = polyfit(X, Y, 1)得到p1 = -0.3965 0.3717p2 = -0.4021 0.3721p3