1、一元线性拟合
求HNO 3的正常沸点温度T b 及摩尔汽化热。 程序如下:
>> t=[0 20 40 50 70 80 90 100]; >> t=t+273.15;
>> p=[1919.52 6385.07 17728.9 27726.4 62251.1 89311 124902.1 170890.6] p =
1.0e+005 *
0.0192 0.0639 0.1773 0.2773 0.6225 0.8931 1.2490 >> subplot 121 >> plot(t,p,'o',t,p) >> t1=1./t;p2=log(p); >> pp=polyfit(t1,p2,1) pp =
1.0e+003 *
-4.5691 0.0243 >> subplot 122
>> plot(t1,p2,'o',t1,p2)
>> gtext('p/pa'),gtext('T/K'),GTEXT('lnP/Pa'),gtext('T^-^1/K')
~
由克拉贝龙-克劳修斯方程式,ln P =-∆H v
RT
+C 作ln P ~T
-1
得一直线:ln P =-4.569⨯103
T -1
+24.30
~
斜率为:-4.569⨯103
=-
∆H v
R
1.7089
所以摩尔汽化热为:∆H v =4.569⨯103⨯8.314=37.99(kJ ⋅mol -1) 并根据拟合方程,求得一大气压时 T
-1
~
=2.80⨯10-3
则正常沸点为:T b =357K
2、多元线性拟合:
某气体混合物由四种气体组成,在常压或低压下其粘度η与各组分摩尔分数x 1,x 2,x 3,x 4之间有如下线性关系:η=b 0+b 1x 1+b 2x 2+b 3x 3+b 4x 4
试根据下表所列实验数据用最小二乘法确定上式中的各个系数,并计算其复相关系数。
Matlab 程序如下:
>> a=[1.0 0.402 0.153 0.058 0.387;1.0 0.503 0.301 0.183 0.013; 1.0 0.306 0.109 0.224 0.361; 1.0 0.296 0.365 0.009 0.330; 1.0 0.309 0.405 0.109 0.177; 1.0 0.055 0.153 0.506 0.289] a =
1.0000 0.4020 0.1530 0.0580 0.3870 1.0000 0.5030 0.3010 0.1830 0.0130 1.0000 0.3060 0.1090 0.2240 0.3610 1.0000 0.2960 0.3650 0.0090 0.3300 1.0000 0.3090 0.4050 0.1090 0.1770 1.0000 0.0550 0.1530 0.5060 0.2890
>> y=[0.00625 0.00826 0.01182 0.01944 0.02372 0.03243]' y =
0.0063 0.0083 0.0118 0.0194 0.0237 0.0324
>> b=a.'*a
b =
6.0000 1.8710 1.4860 1.0890 1.5570 1.8710 0.6944 0.4879 0.2481 0.4408 1.4860 0.4879 0.4466 0.2132 0.3388 1.0890 0.2481 0.2132 0.3550 0.2742 1.5570 0.4408 0.3388 0.2742 0.5040
>> c=a.'*y c =
0.1019 0.0252 0.0264 0.0237 0.0268
>> coeff=b\c
coeff = 0.2267 -0.2627 -0.1620 -0.1889 -0.2058
>> regress(c,b,0.05) ans =
0.2267 -0.2627 -0.1620 -0.1889 -0.2058
1、一元线性拟合
求HNO 3的正常沸点温度T b 及摩尔汽化热。 程序如下:
>> t=[0 20 40 50 70 80 90 100]; >> t=t+273.15;
>> p=[1919.52 6385.07 17728.9 27726.4 62251.1 89311 124902.1 170890.6] p =
1.0e+005 *
0.0192 0.0639 0.1773 0.2773 0.6225 0.8931 1.2490 >> subplot 121 >> plot(t,p,'o',t,p) >> t1=1./t;p2=log(p); >> pp=polyfit(t1,p2,1) pp =
1.0e+003 *
-4.5691 0.0243 >> subplot 122
>> plot(t1,p2,'o',t1,p2)
>> gtext('p/pa'),gtext('T/K'),GTEXT('lnP/Pa'),gtext('T^-^1/K')
~
由克拉贝龙-克劳修斯方程式,ln P =-∆H v
RT
+C 作ln P ~T
-1
得一直线:ln P =-4.569⨯103
T -1
+24.30
~
斜率为:-4.569⨯103
=-
∆H v
R
1.7089
所以摩尔汽化热为:∆H v =4.569⨯103⨯8.314=37.99(kJ ⋅mol -1) 并根据拟合方程,求得一大气压时 T
-1
~
=2.80⨯10-3
则正常沸点为:T b =357K
2、多元线性拟合:
某气体混合物由四种气体组成,在常压或低压下其粘度η与各组分摩尔分数x 1,x 2,x 3,x 4之间有如下线性关系:η=b 0+b 1x 1+b 2x 2+b 3x 3+b 4x 4
试根据下表所列实验数据用最小二乘法确定上式中的各个系数,并计算其复相关系数。
Matlab 程序如下:
>> a=[1.0 0.402 0.153 0.058 0.387;1.0 0.503 0.301 0.183 0.013; 1.0 0.306 0.109 0.224 0.361; 1.0 0.296 0.365 0.009 0.330; 1.0 0.309 0.405 0.109 0.177; 1.0 0.055 0.153 0.506 0.289] a =
1.0000 0.4020 0.1530 0.0580 0.3870 1.0000 0.5030 0.3010 0.1830 0.0130 1.0000 0.3060 0.1090 0.2240 0.3610 1.0000 0.2960 0.3650 0.0090 0.3300 1.0000 0.3090 0.4050 0.1090 0.1770 1.0000 0.0550 0.1530 0.5060 0.2890
>> y=[0.00625 0.00826 0.01182 0.01944 0.02372 0.03243]' y =
0.0063 0.0083 0.0118 0.0194 0.0237 0.0324
>> b=a.'*a
b =
6.0000 1.8710 1.4860 1.0890 1.5570 1.8710 0.6944 0.4879 0.2481 0.4408 1.4860 0.4879 0.4466 0.2132 0.3388 1.0890 0.2481 0.2132 0.3550 0.2742 1.5570 0.4408 0.3388 0.2742 0.5040
>> c=a.'*y c =
0.1019 0.0252 0.0264 0.0237 0.0268
>> coeff=b\c
coeff = 0.2267 -0.2627 -0.1620 -0.1889 -0.2058
>> regress(c,b,0.05) ans =
0.2267 -0.2627 -0.1620 -0.1889 -0.2058