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????????-????????????? ??????? ? ???????? ??????:
"?????? ?????????? ?????????? ???????? ?????? ? ?????? ????????? ?????????"
?? ?????????? "???????? ????????? ? ?????"
??????? ?1
????????: ??????? ??. 2301
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?.?.?. ??????? ?. ?.
??????, 2010?.
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????????????? ???????: 50 ???., 5 ???., 4 ??????, 3 ??????????, 3 ?????????.
??????????? ????????????: 1 ???? ??????? A3.
????? ??????????? ???????, ??????? ?????????????? ?????, ??????????? ???????, ????? ??????, ????????, ???????????, ????????, ??????, ?????? ?????? ??????????, ????? ????, ?????? ??????? ?????, ??????? ?????, ?????????? ??????? ????, ????????? ???.
? ?????? ???????? ?????? ????????? ??????? ?????????????? ?????????? ?????? ????????? ?????????, ?????????? ?????????? ???????? ?????? ? ?????? ????????? ?????????, ????? ???????? ???????????? ? ??????????, ????????? ??????? ????????? ???????? ???????.
??????? ????? ????????? ? ????????????? ????? ? ????????? ???????? 0, ????? ???????? ?, ???????? ???????? a, ??????? ??????? ????? ?????????????? S0, S?, Sa. ?? ????? ??? ???????? ?? ??????? ?????, ???????? ? ??????? ????? (???????? ?????????? ??????) ? ?? (?????? ??????? ????????).
???????
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??? ?????????, ????????. ??????? ???? ? ????? ????????, ????????????, ???????????????????. ?????? ? ?????? ??????? ??????????. ? ??????? 0 - ?????????? ??????? ?????. ?????? ?????????? ? ??????? ?????? ?????? ? ???????????????????. ?? ?????? ??????? ????? ???????? ? ?????????? ????? ? ????????? ?????? ???????? ????????? (pa=p?). ????? ??????? ??????? ???????? ?????????, ??????????? ??? ?????? (??? ?????).
?????????????? ?????? ???????? ??????
? ???????? ?????? ?????????????? ????????? ?????? ?????????? ?????? ? ????????????? ?????:
1) ????????? ????? ??????? ????, ??????????????? ?????????????? ????? (????? ??????).
2) ??????????? ????? ??????? ????, ??????????????? ?????????????? ????? ?? ??????? ?????????? ? ???????? ??????? a.
3) ??????????? ????? ??????? ????, ??????????????? ?????????????? ????? ?? ??????? ?????????? ? ??????? 5.
4) ??????????? ????? ??????? ????, ??????????????? ?????????????? ????? ?? ??????? ?????????? ? ??????? 4.
5) ?????????? ??????? ???? ?? ????? ??????, ?? ??? ??????????? ????????? ???????? ?????? ? ????? ??????? (??= 1).
?????? ???????? ? ???? ???????????:
1) ????????: ???????? ?? ??????? ????? ????? ???????? ? ???????? ??????? ????? ().
2) ?????? ??????? ???????: ???????? ?? ??????? ????? ????? ?? ().
???????? ??????:
? = 1,33 ry = 61
R = 288 ??/??? rk = 1,7
?0 = 5 ??? ra = 1,71
?0* = 293 ? xa = 3,93 ??* = 2800 ? �a = 3 ?
S0 = 0,3 �y = 17 ?
??????????
???????2
???????3
?????????????? ???????3
1. ?????????? ??????? ?????? ????????? ?????????.7
2. ?????? ??????? ???????? ???????? ??????.8
3. ?????? ??????? ???????? ???????? ??????.23
4. ?????? ???????? ???????? ???????? ??????.25
5. ?????? ?????????? ???????? ???????? ??????.28
6. ?????? ?????? ???????? ???????? ??????.33
7. ?????? ????????? ???????? ??????.3
8. ?????? ??? ? ????.39
??????????41
?????? ???????????? ??????????42
?????????? 143
?????????? 246
?????????? 358
?????????????? ???????
r - ??????, ??
S - ???????, ??2
q - ???????????????? ??????? ??????? ??? ??????????? ??????
? - ??????????? ????????
M - ????? ????
t - ??? ???????????
p - ??? ????????
? - ??? ?????????
T* - ??????????? ??????????, ?
T - ??????????? ???????????, ?
p* - ???????? ??????????, ??
p - ??????????? ????????, ??
?* - ????????? ??????????, ??/?3
? - ??????????? ?????????, ??/?3
a?? - ??????????? ???????? ?????, ?/?
a - ??????? ???????? ?????, ?/?
c - ???????? ???????? ??????, ?/?
G - ?????? ???????? ??????, ??/?
� - ??? ????????
p? - ???????? ?? ??????? ?????, ??
? - ??????? ???????? ??????, ?
s? - ??????????? ????????? ???????? ? ?????? ?????? ??????????
s?.?. - ??????????? ????????? ???????? ??? ????????? ??????????
s? - ??????????? ????????? ???????? ??? ??????? ???????
P0-? - ???? ??????????? ???????? ?????? ?? ?????????? ????? ?????, ?
P?-a - ???? ??????????? ???????? ?????? ?? ????????????? ????? ?????, ?
P0-a - ???? ??????????? ???????? ?????? ?? ????? ? ?????, ?
P????. - ?????????? ???????????? ?????? ????, ?
P???. - ???????? ???????????? ?????? ????, ? P - ?????? ???? ?????????, ?
1. ?????????? ??????? ?????? ????????? ?????????.
?????????? ???????? ?????????? ????????? ????????? ? ??????? ???????? ??????:
1) ????? ?????? ????????:
x_k=2�r_y=2�61 ??,
2) ????? ?????????? ????? ?????:
x_y=r_y�v(r_k�(9,25-r_k )-8,25)=61�v(1,7�(9,25-1,7)-8,25)=130,61694,
3) ????? ????????????? ????? ?????:
x_a=x_a�r_y=3,93�61=239,73 ??,
4) ?????? ?????? ????????:
r_k=r_r�r_y=1,7�61=103,7 ??,
5) ?????? ???????? ?????? ??? ????? ? ?????? ????????:
r_0=r_k�v(s_0 )=103,7�v0,3=56,79883 ??,
6) ?????? ????????? ??????? ?????:
r_a=r_a�r_y=1,71�61=104,31 ??
7) ??????????? ?????????? ??????? 1, 2, 3, 4, 5 ??????????????:
1=0.35� x?=0.35�122=42,7 ??;
2=0.5� x?=0.5�130,61694=65,30847 ??;
3=0.2� x?=0.2�130,61694=26,12339 ??;
4=0.2� xa=0.2�239,73 =47,946 ??;
5=0.6� xa=0.6�239,73 =143,838 ??.
?? ???????????? ?????????? ???????? ??????? ?????? ???????? ??. ??????????. ?? ??????? ?????? ?????????? ??????? ????????????? ????????? ??????? r2, r3, r4, r5:
r_2=80,06, r_3=63,6, r_4=74,86, ? r?_5=99,28
???????????? ??????? ???? ??????? ?? ???????:
??? - ?????? ???????????? ???????, ??:
S_0=p�r_0^2=p�?56,799?^2=10135,114
S_(1,k)=p�r_(1,k)^2=p�?103,7?^2=33783,714
S_2=p�r_2^2=p�?80,06?^2=20136,364
S_3=p�r_3^2=p�?63,6?^2=12707,617
S_y=p�r_y^2=p�?61?^2=11689,866
S_4=p�r_4^2=p�?74,86?^2=176,05547
S_5=p�r_5^2=p�?99,28?^2=30965,167
S_a=p�r_a^2=p�?104,31?^2=34182,338
?_? 2. ?????? ??????? ???????? ???????? ??????.
().
?????????? ????????? ?????? ??? ????????????? ????????? ???? ?? ?????.
1)?????????? ????????? ???????? ?????? ??? ??????? "?":
??????????? ?????? ??? ??????? ???????:
q(?_? )=s_y/s_r =11689,866/33783,714=0,2225
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? k ?? ??????? ??????????? ????????? (??. ?????????? 3), ????????, ??? ? ?????? ??????? ?????????? ?????, ?. ?. :
q(?_k )=((k+1)/2)^(1/(k-1))�?_k (1-(k-1)/(k+1) ?_k^2 )^(1/(k-1))
????????; ?_k=0,2225
???????????????? ??????? ?????????? ?? ????????:
t(?_k )=1-(k-1)/(k+1)�?_k^2=1-0,33/2,33�0,2225=0,9929
p(?_k )= ?t(?_k )?^(k/(k-1))=?0,9929?^(1,33/0,33)=0,9717
?(?_k )= ?t(?_k )?^(1/(k-1))=?0,9929?^(1/0,33)=0,9796
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????.
?????? ????? ????:
M_k=?_k�v(2/(k+1))/v(t(?_k ) )=0,2069�v(2/2,33)/v0,9929=0,2225
?^?
??????????? ?????????? ???????? ??????: a_kp=v(2k/(k+1) RT_k^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_k=T_k^*�t(?_k )=2800�0,9929=2780,12 K
a_k=v(kRT_k )=v(1,33�288�2780,12)=1032,1
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c=??_k a?_kp=0,2225�959,48=213,47 ?/? ?M_k a?_k=0,2225�1032,1=213,54 ?/? 2) ?????????? ????????? ???????? ?????? ??? ??????? "0":
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? 0 ?? ??????? ???????????????? ????????? ?????????? ???????? ??? ???? (??. ?????????? 3), ???????????? ? ?????? ???????? ????? ????????? "0" ? "k"), ????????, ??? ? ?????? ??????? ?????????? ?????, ?. ?. :
,
???????? ?_0=0,2311.
???????????????? ??????? ?????????? ?? ????????:
q(?_0 )=((k+1)/2)^(1/(k-1))�?_0 (1-(k-1)/(k+1) ?_0^2 )^(1/(k-1))=(2,33/2)^(1/0,33)�0,2311�(1-0,33/2,33 ?0,2311?^2 )^(1/0,33)=0,3587
t(?_0 )=1-(k-1)/(k+1)�?_0^2=1-0,33/2,33�0,2311=0,9924
p(?_0 )= ?t(?_0 )?^(k/(k-1))=?0,9924?^(1,33/0,33)=0,9697
?(?_0 )= ?t(?_0 )?^(1/(k-1))=?0,9924?^(1/0,33)=0,9771
??? - ???????????????? ??????? ???????, ???????????, ???????? ? ????????? ??????????????.
?????? ????? ????:
M_0=?_0�v(2/(k+1))/v(t(?_0 ) )=0,2311�v(2/2,33)/v0,9924=0,2149
?^?
??????????? ?????????? ???????? ??????:
a_kp=v(2k/(k+1) RT_0^* )=v((2�1,33)/2,33�288�293)=310,38 ?/?
T_0=T_0^*�t(?_0 )=293�0,9924=290,7 K
a_0=v(kRT_0 )=v(1,33�288�290,7)=333,7
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_0=??_0 a?_kp=0,2311�310,38=71,73 ?/? ?M_0 a?_0=0,2149�333,7=213,54 ?/? ?????? ???????? ? ????????? ??????????:
p_0^*=p_0/p(?_0 ) =(5�?10?^6)/0,9697=5,156 ???
?_0^*=(p_0^*)/(RT_0^* )=(5,156�?10?^6)/(288�293)=61,102 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
?_0=?_0?^* ?(?_0 )=61,102 �0,9771=59,722 ??/?^3 G_0=(p_0^* S_0)/v(T_0^* )�q(?_0 )�m_G; ??? m_G=v((2/(k+1))^((k+1)/(k-1))�k/R)=v((2/2,33)^(2,33/0,33)�1,33/288)=0,03964
G_0=(5,156�10135,114)/v293�0,3587�0,03964=43,408
?_0 c_0 S_0=59,722�71,73� 10135,114�?10?^(-6)=43,418
??? 0- ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
3) ???????? ?????????? ????????? ???????? ?????? ? ??????? "k":
?????? ???????? ???????? ?? ???????????????? ????????? ????????????? ??? ????? ??????? "0" ? "k" ???????? ??????: ; p_k=(p_0 c_0 (S_0 ) �T_k)/(T_0 c_k )=(5�?10?^6�71,73�0,3�2780,12)/(290,7�213,47)=4,8189 ???
?????? ???????? ? ????????? ??????????:
p_k^*=p_k/p(?_k ) =(4,8189�?10?^6)/0,9717=4,9549 ???
?_k^*=(p_k^*)/(RT_k^* )=(4,9549�?10?^6)/(288�2800)=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
?_k=?_k^* ?(?_k )=6,1445 �0,9796=6,0186 ??/?^3 G_k=(p_k^* S_k)/v(T_k^* )�q(?_k )�m_G=(4,9549�33783,714)/v293�0,346�0,03964=43,697 ?_k c_k S_k=6,0186�213,47� 33783,714�?10?^(-6)=43,405
???- ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
4) ?????????? ????????? ???????? ?????? ??? ??????? "1":
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? 1 ?? ??????? ???????????????? ????????? ?????????? ???????? ??? ????, ???????????? ? ?????? ???????? ????? ????????? "1" ? "?" (??. ?????????? 3), ????????, ??? ? ?????? ??????? ?????????? ?????, ?. ?. :
, ??? ;
???????? ?_1=0,0689
???????????????? ??????? ?????????? ?? ????????:
q(?_1 )=((k+1)/2)^(1/(k-1))�?_1 (1-(k-1)/(k+1) ?_1^2 )^(1/(k-1))=(2,33/2)^(1/0,33)�0,0689�(1-0,33/2,33 ?0,0689?^2 )^(1/0,33)=0,1092
t(?_1 )=1-(k-1)/(k+1)�?_1^2=1-0,33/2,33�0,0689=0,9993
p(?_1 )= ?t(?_1 )?^(k/(k-1))=?0,9993?^(1,33/0,33)=0,9972
?(?_1 )= ?t(?_1 )?^(1/(k-1))=?0,9993?^(1/0,33)=0,9979
??? - ???????????????? ??????? ???????, ???????????, ???????? ? ????????? ??????????????.
?????? ????? ????:
M_1=?_1�v(2/(k+1))/v(t(?_1 ) )=0,2311�v(2/2,33)/v0,9993=0,06386
??????????? ?????????? ???????? ??????: a_kp=v(2k/(k+1) RT_1^* )=v((2�1,33)/2,33�288�293)=310,38 ?/?
T_1=T_1^*�t(?_1 )=293�0,9993=292,795 K
a_1=v(kRT_1 )=v(1,33�288�292,795)=334,89
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_1=??_1 a?_kp=0,0689�310,38=21,385 ?/? ?M_1 a?_1=0,06386�334,89=21,386 ?/? ?????? ???????? p1 ?? ??????? ???????????????? ????????? ?????????????:
p_1=(p_? c_? T_1)/(T_? c_1 )=(4,8189�?10?^6�213,47�292,795)/(2780,12�21,385)=5,0609 ???
?????? ???????? ? ????????? ??????????:
p_1^*=p_1/p(?_1 ) =(5,0609�?10?^6)/0,9972=5,075 ???
?_1^*=(p_1^*)/(RT_1^* )=(5,075�?10?^6)/(288�293)=60,14 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
?_1=?_1^* ?(?_1 )=60,14 �0,9979=60,017 ??/?^3 G_1=(p_1^* S_1)/v(T_1^* )�q(?_1 )�m_G=(5,075 �33783,714)/v293�0,1092�0,03964=43,257 ?_1 c_1 S_1=60,017�21,385� 33783,714�?10?^(-6)=43,359
??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
5)?????????? ????????? ???????? ?????? ??? ??????? "2":
??????????? ?????? ??? ??????? ???????:
q(?_? )=s_y/s_2 =11689,866/20136,364=0,5805
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? ?? ??????? ??????????? ????????? (??. ?????????? 3), ????????, ??? ? ?????? ??????? ?????????? ?????, ?. ?. :
, ???????? ?_2=0,3905; ???????????????? ??????? ?????????? ?? ????????:
t(?_2 )=1-(k-1)/(k+1)�?_2^2=1-0,33/2,33�0,3905=0,9784
p(?_2 )= ?t(?_2 )?^(k/(k-1))=?0,9784?^(1,33/0,33)=0,9972
?(?_2 )= ?t(?_2 )?^(1/(k-1))=?0,9784?^(1/0,33)=0,9359
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????.
?????? ????? ????:
M_2=?_2�v(2/(k+1))/v(t(?_2 ) )=0,3905�v(2/2,33)/v0,9784=0,3657
??????????? ?????????? ???????? ??????: a_kp2=v(2k/(k+1) RT_2^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_2=T_2^*�t(?_2 )=2800�0,9784=2739,54 K
a_2=v(kRT_2 )=v(1,33�288�2739,54)=1024,4
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_2=??_2 a?_kp2=0,3905�959,48=374,63 ?/? ?M_2 a?_2=0,3657�1024,4=374,62 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_2^*=4,9549 ???
?_2^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
?_2=?_2^* ?(?_2 )=6,1445 �0,9359=5,7915 ??/?^3 G_2=(p_2^* S_2)/v(T_2^* )�q(?_2 )�m_G=(4,9549 �20136,364)/v2800�0,5805�0,03964=43,697 ?_2 c_2 S_2=5,7915�374,63� 20136,364�?10?^(-6)=43,405
??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
6)?????????? ????????? ???????? ?????? ??? ??????? "3":
??????????? ?????? ??? ??????? ???????:
q(?_3 )=s_y/s_3 =11689,866/12707,617=0,9199
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? ?? ??????? ??????????? ????????? (??. ?????????? 3), ????????, ??? ? ?????? ??????? ?????????? ?????, ?. ?. :
,
???????? ?_2=0,7392; ???????????????? ??????? ?????????? ?? ????????:
t(?_3 )=1-(k-1)/(k+1)�?_3^2=1-0,33/2,33�0,7392=0,9226
p(?_3 )= ?t(?_3 )?^(k/(k-1))=?0,9226?^(1,33/0,33)=0,7228
?(?_3 )= ?t(?_3 )?^(1/(k-1))=?0,9226?^(1/0,33)=0,7834
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_3=?_3�v(2/(k+1))/v(t(?_3 ) )=0,7392�v(2/2,33)/v0,9226=0,713
??????????? ?????????? ???????? ??????: a_kp3=v(2k/(k+1) RT_3^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_3=T_3^*�t(?_3 )=2800�0,9226=2583,3 K
a_3=v(kRT_3 )=v(1,33�288�2583,3)=994,74
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_3=??_3 a?_kp3=0,7392�959,48=709,25 ?/? ?M_3 a?_3=0,713�994,74=709,25 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_3^*=4,9549 ???
?_3^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_3=p_3^*� p(?_3 )=4,9549�0,7228=3,5814 ???
?_3=?_3^* ?(?_3 )=6,1445 �0,7834=4,8137 ??/?^3 G_3=(p_3^* S_3)/v(T_3^* )�q(?_3 )�m_G=(4,9549 �12707,617)/v2800�0,9199�0,03964=43,386 5�3
?_3 c_3 S_3=4,8137�709,25 �20136,364�?10?^(-6)=43,386
??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
7)?????????? ????????? ???????? ?????? ??? ??????? "?":
?????? ??????? ???????????, ???????: q(??)=1, ?? =1, M?=1.
???????????????? ??????? ?????????? ?? ????????:
t(?_? )=1-(k-1)/(k+1)�?_?^2=1-0,33/2,33=0,8584
p(?_? )= ?t(?_? )?^(k/(k-1))=?0,8584?^(1,33/0,33)=0,5404
?(?_? )= ?t(?_? )?^(1/(k-1))=?0,8584?^(1/0,33)=0,6295
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
??????????? ?????????? ???????? ??????: a_kp?=v(2k/(k+1) RT_?^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_?=T_?^*�t(?_? )=2800�0,8584=2403,4K
a_?=v(kRT_? )=v(1,33�288�2403,4)=959,48
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_?=??_? a?_kp?=1�959,48=959,48 ?/? ?M_? a?_?=1�959,48=959,48 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_?^*=4,9549 ???
?_?^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_?=p_?^*� p(?_? )=4,9549�0,5404=2,6775 ???
?_?=?_?^* ?(?_? )=6,1445 �0,6295=3,8681 ??/?^3 G_?=(p_?^* S_?)/v(T_?^* )�q(?_? )�m_G=(4,9549 �11689,866)/v2800�1�0,03964=43,386 ?_? c_? S_?=3,8681�959,48 �11689,866�?10?^(-6)=43,386
???- ??????????? ?????????, - ??????????? ????????, ?- ?????? ???????? ??????
8)?????????? ????????? ???????? ?????? ??? ??????? "4":
??????????? ?????? ??? ??????? ???????:
q(?_4 )=s_y/s_4 =11689,866/17605,547=0,6639
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? ?? ??????? ??????????? ????????? (??. ?????????? 3), ????????, ??? ? ?????? ??????? ????????????? ?????, ?. ?. :
,
????????? ??_4=1,5852; ???????????????? ??????? ?????????? ?? ????????:
t(?_4 )=1-(k-1)/(k+1)�?_4^2=1-0,33/2,33�1,5852=0,6441
p(?_4 )= ?t(?_4 )?^(k/(k-1))=?0,6441?^(1,33/0,33)=0,1698
?(?_4 )= ?t(?_4 )?^(1/(k-1))=?0,6441?^(1/0,33)=0,2637
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_4=?_4�v(2/(k+1))/v(t(?_4 ) )=1,5852�v(2/2,33)/v0,6441=1,8299
??????????? ?????????? ???????? ??????: a_kp4=v(2k/(k+1) RT_4^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_4=T_4^*�t(?_4 )=2800�0,6441=1803,5K
a_4=v(kRT_4 )=v(1,33�288�2403,4)=831,1543
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_4=??_4 a?_kp4=1,5852�959,48=1520,95 ?/? ?M_4 a?_4=1,8299�831,1543=1520,95 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_4^*=4,9549 ???
?_4^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_?4=p_4^*� p(?_4 )=4,9549�0,1698=0,84158 ???
?_4=?_4^* ?(?_4 )=6,1445 �0,2637=1,6202 ??/?^3 G_4=(p_4^* S_4)/v(T_4^* )�q(?_4 )�m_G=(4,9549 �11605,547)/v2800�0,6639�0,03964=43,386 ?_4 c_4 S_4=1,6202�1520,95 �11605,547�?10?^(-6)=43,386
??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
9)?????????? ????????? ???????? ?????? ??? ??????? "5":
??????????? ?????? ??? ??????? ???????:
q(?_5 )=s_y/s_5 =11689,866/30965,167=0,3775
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? ?? ??????? ??????????? ????????? (??. ?????????? 3), ????????, ??? ? ?????? ??????? ????????????? ?????, ?. ?. :
, ???????? ? ??_5=1,8666; ???????????????? ??????? ?????????? ?? ????????:
t(?_5 )=1-(k-1)/(k+1)�?_5^2=1-0,33/2,33�1,8666=0,5065
p(?_5 )= ?t(?_5 )?^(k/(k-1))=?0,5065?^(1,33/0,33)=0,0645
?(?_5 )= ?t(?_5 )?^(1/(k-1))=?0,5065?^(1/0,33)=0,1273
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_5=?_5�v(2/(k+1))/v(t(?_5 ) )=1,8666�v(2/2,33)/v0,5065=2,4298
??????????? ?????????? ???????? ??????: a_kp5=v(2k/(k+1) RT_5^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_5=T_5^*�t(?_5 )=2800�0,5065=1418,3K
a_5=v(kRT_5 )=v(1,33�288�1418,3)=737,07
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_5=??_5 a?_kp5=1,8666�959,48=1790,95 ?/? ?M_5 a?_5=2,4298�737,07=1790,95 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_5^*=4,9549 ???
?_5^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_5=p_5^*� p(?_5 )=4,9549�0,0645=0,31957 ???
?_5=?_5^* ?(?_5 )=6,1445 �0,1273=6,1445 ??/?^3 G_5=(p_5^* S_5)/v(T_5^* )�q(?_5 )�m_G=(4,9549 �30965,167)/v2800�0,3775�0,03964=43,386 ?_5 c_5 S_5=6,1445�1790,95 �30965,167�?10?^(-6)=43,386
??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
10)?????????? ????????? ???????? ?????? ??? ??????? "a":
??????????? ?????? ??? ??????? ???????:
q(?_? )=s_y/s_? =11689,866/34182,338=0,342
? ?????????????? ??????????????? ?????? MathCAD ?????????? ???????? ?? ??????? ??????????? ????????? (??. ?????????? 3), ????????, ??? ? ?????? ??????? ????????????? ?????, ?. ?. :
, ???????? ? ??_?=1,9028
???????????????? ??????? ?????????? ?? ????????:
t(?_? )=1-(k-1)/(k+1)�?_?^2=1-0,33/2,33�?1,9028?^2=0,4872
p(?_? )= ?t(?_? )?^(k/(k-1))=?0,4872?^(1,33/0,33)=0,0551
?(?_? )= ?t(?_? )?^(1/(k-1))=?0,4872?^(1/0,33)=0,1131
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_?=?_?�v(2/(k+1))/v(t(?_? ) )=1,9028�v(2/2,33)/v0,4872=2,5258
??????????? ?????????? ???????? ??????: a_kp?=v(2k/(k+1) RT_?^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_?=T_?^*�t(?_? )=2800�0,4872=1364,1K
a_?=v(kRT_? )=v(1,33�288�1364,1)=728,85
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_?=??_? a?_kp?=1,9028�959,48=233,95 ?/? ?M_? a?_?=2,5258�728,85=233,95 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_?^*=4,9549 ???
?_?^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_?=p_?^*� p(?_? )=4,9549�0,0551=0,27118 ???
?_?=?_?^* ?(?_? )=6,1445 �0,1131=0,6952 ??/?^3 G_?=(p_?^* S_?)/v(T_?^* )�q(?_? )�m_G=(4,9549 �34182,338)/v2800�0,342�0,03964=43,386 ?_? c_? S_?=0,6952�233,95 �34182,338�?10?^(-6)=43,386
??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
3. ?????? ??????? ???????? ???????? ??????.
().
?????????? ????????? ?????? ?? ??????? ?????????? ? ???????? ??????? ?????? ????????? ?????????.
?_???=1/?_? =1/1,9028=0,525;
??????????? ?????? ??? ??????? ???????:
q(?_??? )=((k+1)/2)^(1/(k-1))�?_??? (1-(k-1)/(k+1) ?_???^2 )^(1/(k-1))=(2,33/2)^(1/0,33)�0,525�(1-0,33/2,33 ?�0,525?^2 )^(1/0,33)=0,3587
???????????????? ??????? ?????????? ?? ????????:
t(?_??? )=1-(k-1)/(k+1)�?_???^2=1-0,33/2,33�?0,525?^2=0,9609
p(?_??? )= ?t(?_??? )?^(k/(k-1))=?0,9609?^(1,33/0,33)=0,8514
?(?_??? )= ?t(?_??? )?^(1/(k-1))=?0,9609?^(1/0,33)=0,8861
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_???=?_???�v(2/(k+1))/v(t(?_? ) )=0,525�v(2/2,33)/v0,9609=0,4967
??????????? ?????????? ???????? ??????: a_kp???=v(2k/(k+1) RT_???^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_???=T_???^*�t(?_? )=2800�0,9609=2690,52K
a_???=v(kRT_??? )=v(1,33�288�2690,52)=1015,165
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_???=??_??? a?_kp???=0,525�959,48=504,2396 ?/? ?M_??? a?_???=0,4967�1015,165=504,2396 ?/? ????????? ??????????? ????????? ???????? ? ?????? ?????? ?????????? ?? ???????:
s_?=(?_?^2�(1-(k-1)/(k+1)�?_?^2 )^(1/(k-1)))/(1-(k-1)/(k+1)�1/(?_?^2 ))^(1/(k-1)) =(?0,525?^2�(1-(1,33-1)/(1,33+1)�?0,525?^2 )^(1/(1,33-1)))/(1-(1,33-1)/(1,33+1)�1/?0,525?^2 )^(1/(1,33-1)) =0,4623
????????? ??????????? ????????? ???????? ??????:
p_???^*=p_?^*�s_?=4,9549�0,4623=2,291???
?_???^*=(p_???^*)/(RT_???^* )=4,9549/(288�2800)=2,8407 ??/?^3 ??? - ???????? ? ????????? ??????????
p_???=p_???^*� p(?_??? )=2,291�0,8514=1,9504 ???
?_???=?_???^* ?(?_??? )=2,8407�0,8861=2,5171 ??/?^3 G_???=(p_???^* S_???)/v(T_???^* )�q(?_??? )�m_G=(2,291 �34182,338)/v2800�0,3587�0,03964=43,386 ?_??? c_??? S_???=2,5171�504,2396 �34182,338�?10?^(-6)=43,386
??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
4. ?????? ???????? ???????? ???????? ??????.
().
?????????? ????????? ?????? ?? ??????? ?????????? ? ??????? "5" ?????? ????????? ?????????.
1) ?????????? ????????? ???????? ?????? ??? ??????? "5??":
?_5??=1/?_5 =1/1,8666=0,5357;
??????????? ?????? ??? ??????? ???????:
q(?_5?? )=((k+1)/2)^(1/(k-1))�?_5?? (1-(k-1)/(k+1) ?_5??^2 )^(1/(k-1))=(2,33/2)^(1/0,33)�0,5357�(1-0,33/2,33 ?�0,5357?^2 )^(1/0,33)=0,7506
???????????????? ??????? ?????????? ?? ????????:
t(?_5?? )=1-(k-1)/(k+1)�?_5??^2=1-0,33/2,33�?0,5357?^2=0,9594
p(?_5?? )= ?t(?_5?? )?^(k/(k-1))=?0,9594?^(1,33/0,33)=0,8462
?(?_5?? )= ?t(?_5?? )?^(1/(k-1))=?0,9594?^(1/0,33)=0,8819
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_5??=?_5??�v(2/(k+1))/v(t(?_5?? ) )=0,5357�v(2/2,33)/v0,9594=0,5067
??????????? ?????????? ???????? ??????: ??????????? ?????????? ?? ??????? ?????????? ???????? ??????????: ?_5^* ?=??^*=2800 ?
a_kp5??=v(2k/(k+1) RT_???^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_5??=T_5??^*�t(?_5 )=2800�0,9594=2686,3 K
a_5??=v(kRT_5?? )=v(1,33�288�2686,3)=1014,38
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_5??=??_5?? a?_kp5??=0,5357�959,48=513,99 ?/? ?M_5?? a?_5??=0,5067�1014,38=513,99 ?/? ????????? ??????????? ????????? ???????? ? ?????? ?????? ?????????? ?? ???????:
s_?=(?_5^2�(1-(k-1)/(k+1)�?_5^2 )^(1/(k-1)))/(1-(k-1)/(k+1)�1/(?_5^2 ))^(1/(k-1)) =(?0,5357?^2�(1-(1,33-1)/(1,33+1)�?0,5357?^2 )^(1/(1,33-1)))/(1-(1,33-1)/(1,33+1)�1/?0,5357?^2 )^(1/(1,33-1)) =0,50305
????????? ??????????? ????????? ???????? ??????:
p_5??^*=p_?^*�s_?=4,9549�0,50305=2,1089???
?_5??^*=(p_5??^*)/(RT_5??^* )=2,1089/(288�2800)=2,6152 ??/?^3 ??? - ???????? ? ????????? ??????????
p_5??=p_5??^*� p(?_5?? )=2,1089�0,8462=2,4923???
?_5??=?_5??^* ?(?_5?? )=2,6152�0,8819=3,2215 ??/?^3 G_5??=(p_5??^* S_5??)/v(T_5??^* )�q(?_5?? )�m_G=(2,1089 �30965,2)/v2800�0,7506�0,03964=43,399 ?_??? c_??? S_???=3,2215�513,99 �30965,2�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
2) ?????????? ????????? ???????? ?????? ??? ??????? "a":
??????????? ?????? ??? ??????? ???????:
q(?_? )=s_5??/s_? �q(?_5?? )=11689,866/34182,338�0,7506=0,6798;
? ?????????????? ??????????????? ?????? MathCAD (??. ?????????? 3, ???. 68) ?????????? ???????? ?? ??????? ??????????? ?????????:
, ???????? ? ??_?=0,4715
???????????????? ??????? ?????????? ?? ????????:
t(?_? )=1-(k-1)/(k+1)�?_?^2=1-0,33/2,33�?0,4715?^2=0,9685
p(?_? )= ?t(?_? )?^(k/(k-1))=?0,9685?^(1,33/0,33)=0,879
?(?_? )= ?t(?_? )?^(1/(k-1))=?0,9685?^(1/0,33)=0,9076
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_?=?_?�v(2/(k+1))/v(t(?_? ) )=0,4715�v(2/2,33)/v0,9685=0,4439
??????????? ?????????? ???????? ??????: a_kp?=v(2k/(k+1) RT_?^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_?=T_?^*�t(?_? )=2800�0,9685=2711,82 K
a_?=v(kRT_? )=v(1,33�288�2711,82)=1019,184
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_?=??_? a?_???=0,4715�959,48=452,439 ?/? ?M_? a?_?=0,4439�1019,184=452,439 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_?^*=2,1089???
?_?^*=2,6152 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_?=p_?^*� p(?_? )=2,1089�0,8462=2,1917???
?_?=?_?^* ?(?_? )=2,6152�0,8819=2,8062 ??/?^3 G_?=(p_?^* S_?)/v(T_?^* )�q(?_? )�m_G=(2,1089 �34182,3)/v2800�0,6798�0,03964=43,399 ?_? c_? S_?=2,8062�452,439 �34182,3�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
5. ?????? ?????????? ???????? ???????? ??????.
().
?????????? ????????? ?????? ?? ??????? ?????????? ? ??????? "4" ?????? ????????? ?????????.
?????????? ????????? ???????? ?????? ??? ??????? "4??":
?_4??=1/?_4 =1/1,5852=0,6308;
??????????? ?????? ??? ??????? ???????:
q(?_4?? )=((k+1)/2)^(1/(k-1))�?_4?? (1-(k-1)/(k+1) ?_4??^2 )^(1/(k-1))=(2,33/2)^(1/0,33)�0,6308�(1-0,33/2,33 ?�0,6308?^2 )^(1/0,33)=0,8405
???????????????? ??????? ?????????? ?? ????????:
t(?_4?? )=1-(k-1)/(k+1)�?_4??^2=1-0,33/2,33�?0,6308?^2=0,9436
p(?_4?? )= ?t(?_4?? )?^(k/(k-1))=?0,9436?^(1,33/0,33)=0,7914
?(?_4?? )= ?t(?_4?? )?^(1/(k-1))=?0,9436?^(1/0,33)=0,8387
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_4??=?_4??�v(2/(k+1))/v(t(?_4?? ) )=0,6308�v(2/2,33)/v0,9436=0,6016
??????????? ?????????? ???????? ??????: ??????????? ?????????? ?? ??????? ?????????? ???????? ??????????: ?_4??^*=?_5^*=?_?^* ?=??^*=2800 ?
a_kp4??=v(2k/(k+1) RT_4??^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_4??=T_4??^*�t(?_4?? )=2800�0,9436=2642,08 K
a_4??=v(kRT_4?? )=v(1,33�288�2642,08 )=1005,99 ?/?
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_4??=??_4?? a?_??4??=0,6308�959,48=605,24 ?/? ?M_4?? a?_4??=0,6016�1005,99 =605,24 ?/? ????????? ??????????? ????????? ???????? ? ?????? ?????? ?????????? ?? ???????:
s_?=(?_4^2�(1-(k-1)/(k+1)�?_4^2 )^(1/(k-1)))/(1-(k-1)/(k+1)�1/(?_4^2 ))^(1/(k-1)) =(?1,5852?^2�(1-(1,33-1)/(1,33+1)�?1,5852?^2 )^(1/(1,33-1)))/(1-(1,33-1)/(1,33+1)�1/?1,5852?^2 )^(1/(1,33-1)) =0,78993
????????? ??????????? ????????? ???????? ??????:
p_4??^*=p_4^*�s_?=4,9549�0,78993=3,9153???
?_4??^*=(p_4??^*)/(RT_4??^* )=3,9153/(288�2800)=4,8553 ??/?^3 ??? - ???????? ? ????????? ??????????
p_4??=p_4??^*� p(?_4?? )=3,9153�0,7914=3,0989???
?_4??=?_4??^* ?(?_4?? )=4,8553�0,8387=4,0725 ??/?^3 G_4??=(p_4??^* S_4??)/v(T_4??^* )�q(?_4?? )�m_G=(3,9153 �17605,5)/v2800�0,8405�0,03964=43,399 ?_4?? c_4?? S_4??=4,0725�605,24 �17605,5�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
2) ?????????? ????????? ???????? ?????? ??? ??????? "5":
??????????? ?????? ??? ??????? ???????:
q(?_5 )=S_4/S_5 �q(?_4?? )=17605,5/30965,2�0,8405=0,4775
? ?????????????? ??????????????? ?????? MathCAD (??. ?????????? 3, ???. 70) ?????????? ???????? ?? ??????? ??????????? ?????????:
, ??????? ? ??_5=0,3118;
???????????????? ??????? ?????????? ?? ????????:
t(?_5 )=1-(k-1)/(k+1)�?_5^2=1-0,33/2,33�?0,3118?^2=0,9862
p(?_5 )= ?t(?_5 )?^(k/(k-1))=?0,9862?^(1,33/0,33)=0,9457
?(?_5 )= ?t(?_4?? )?^(1/(k-1))=?0,9862?^(1/0,33)=0,9587
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_5=?_5�v(2/(k+1))/v(t(?_5 ) )=0,3118�v(2/2,33)/v0,9862=0,2909
??????????? ?????????? ???????? ??????: ??????????? ?????????? ?? ??????? ?????????? ???????? ??????????: a_kp5=v(2k/(k+1) RT_5^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_5=T_5^*�t(?_5 )=2800�0,9862=2761,45 K
a_5=v(kRT_5 )=v(1,33�288�2761,45 )=1028,468 ?/?
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_5=??_5 a?_??5=0,3118�959,48=299,156 ?/? ?M_5 a?_5=0,2909�1028,468 =299,156 ?/? ???????? ? ????????? ?????????? ???????? ???????????: p_5^*=3,9153???
?_5^*=4,8553 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_5=p_5^*� p(?_5 )=3,9153�0,9457=3,7023 ???
?_5=?_5^* ?(?_5 )=4,8553�0,9587=4,6555 ??/?^3 G_5=(p_5^* S_5)/v(T_5^* )�q(?_5 )�m_G=(3,9153 �30965,2)/v2800�0,4779�0,03964=43,399 ?_5 c_5 S_5=4,6555�2999,156 �30965,2�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
3) ?????????? ????????? ???????? ?????? ??? ??????? "a":
??????????? ?????? ??? ??????? ???????:
q(?_? )=S_4/S_? �q(?_4?? )=17605,5/34182,3�0,8405=0,4329
? ?????????????? ??????????????? ?????? MathCAD (??. ?????????? 3, ???. 71) ?????????? ???????? ?? ??????? ??????????? ?????????:
,
??????? ? ??_?=0,2820;
???????????????? ??????? ?????????? ?? ????????:
t(?_? )=1-(k-1)/(k+1)�?_?^2=1-0,33/2,33�?0,2820?^2=0,9887
p(?_? )= ?t(?_? )?^(k/(k-1))=?0,9887?^(1,33/0,33)=0,9554
?(?_? )= ?t(?_? )?^(1/(k-1))=?0,9887?^(1/0,33)=0,9663
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_?=?_?�v(2/(k+1))/v(t(?_? ) )=0,2820�v(2/2,33)/v0,9887=0,2628
??????????? ?????????? ???????? ??????: a_kp?=v(2k/(k+1) RT_?^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_?=T_?^*�t(?_? )=2800�0,9887=2768,5 K
a_?=v(kRT_? )=v(1,33�288�2768,5 )=1029,77 ?/?
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_?=??_? a?_???=0,2820�959,48=270,61 ?/? ?M_? a?_?=0,2628�1029,77 =270,61 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_5^*=3,9153???
?_5^*=4,8553 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_?=p_?^*� p(?_? )=3,9153�0,9554=3,7405 ???
?_?=?_?^* ?(?_? )=4,8553�0,9663=4,6914 ??/?^3 G_?=(p_?^* S_?)/v(T_?^* )�q(?_? )�m_G=(3,9153 �34182,3)/v2800�0,4329�0,03964=43,399 ?_? c_? S_?=4,6914�270,61 �34182,3�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
6. ?????? ?????? ???????? ???????? ??????.
().
?????????? ????????? ?????? ?? ??????? ?????????? ? ??????? "?" ?????? ????????? ?????????.
1) ?????????? ????????? ???????? ?????? ??? ??????? "4":
??????????? ?????? ??? ??????? ???????:
q(?_4 )=S_?/S_4 =11689,9/17605,5=0,6639
? ?????????????? ??????????????? ?????? MathCAD (??. ?????????? 3, ???. 72) ?????????? ???????? ?? ??????? ??????????? ?????????:
, ??????? ? ??_4=0,4579;
???????????????? ??????? ?????????? ?? ????????:
t(?_4 )=1-(k-1)/(k+1)�?_4^2=1-0,33/2,33�?0,4579?^2=0,9703
p(?_4 )= ?t(?_4 )?^(k/(k-1))=?0,9703?^(1,33/0,33)=0,8856
?(?_4 )= ?t(?_4 )?^(1/(k-1))=?0,9703?^(1/0,33)=0,9127
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_4=?_4�v(2/(k+1))/v(t(?_4 ) )=0,4579�v(2/2,33)/v0,9703=0,4308
??????????? ?????????? ???????? ??????: ??????????? ?????????? ?? ??????? ?????????? ???????? ??????????: ?_?^*=?_4^* ?=??_5^* ?=??_?^*=?^*=2800 ?
a_kp4=v(2k/(k+1) RT_4^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_4=T_4^*�t(?_4 )=2800�0,9703=2716,8 K
a_4=v(kRT_4 )=v(1,33�288�2716,8 )=1020,12 ?/?
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_4=??_4 a?_??4=0,4579�959,48=439,44 ?/? ?M_4 a?_4=0,4308�1020,12 =439,44 ?/? ???????? ? ????????? ?????????? ???????? ???????????: p_4^*=4,9549???
?_4^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_4=p_4^*� p(?_4 )=4,9549�0,8856=4,389 ???
?_4=?_4^* ?(?_4 )=6,1445�0,9127=4,389 ??/?^3 G_4=(p_4^* S_4)/v(T_4^* )�q(?_4 )�m_G=(3,9153 �17605,5)/v2800�0,6639�0,03964=43,399 ?_4 c_4 S_4=4,389�439,44 �17605,5�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
2) ?????????? ????????? ???????? ?????? ??? ??????? "5":
??????????? ?????? ??? ??????? ???????:
q(?_5 )=S_?/S_5 =11689,9/30965,2=0,3775;
? ?????????????? ??????????????? ?????? MathCAD (??. ?????????? 3, ???. 70) ?????????? ???????? ?? ??????? ??????????? ?????????:
, ??????? ? ??_5=0,2438;
???????????????? ??????? ?????????? ?? ????????:
t(?_5 )=1-(k-1)/(k+1)�?_5^2=1-0,33/2,33�?0,2438?^2=0,9916
p(?_5 )= ?t(?_5 )?^(k/(k-1))=?0,9916?^(1,33/0,33)=0,9665
?(?_5 )= ?t(?_5 )?^(1/(k-1))=?0,9916?^(1/0,33)=0,9747
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_5=?_5�v(2/(k+1))/v(t(?_5 ) )=0,2438�v(2/2,33)/v0,9916=0,2269
??????????? ?????????? ???????? ??????: a_kp5=v(2k/(k+1) RT_5^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_5=T_5^*�t(?_5 )=2800�0,9916=2776,4 K
a_5=v(kRT_5 )=v(1,33�288�2776,4 )=1031,25 ?/?
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_5=??_5 a?_??5=0,2438�959,48=233,95 ?/? ?M_5 a?_5=0,2269�1031,25 =233,95 ?/? ???????? ? ????????? ?????????? ???????? ???????????: p_5^*=4,9549???
?_5^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_5=p_5^*� p(?_5 )=4,9549�0,9665=4,79041 ???
?_5=?_5^* ?(?_5 )=6,1445�0,9747=5,9909 ??/?^3 G_5=(p_5^* S_5)/v(T_5^* )�q(?_4 )�m_G=(3,9153 �30965,2)/v2800�0,3775�0,03964=43,399 ?_5 c_5 S_5=5,9909�233,95 �30965,2�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
3) ?????????? ????????? ???????? ?????? ??? ??????? "a":
??????????? ?????? ??? ??????? ???????:
q(?_? )=S_?/S_? =11689,9/34182,3=0,342;
? ?????????????? ??????????????? ?????? MathCAD (??. ?????????? 3, ???. 71) ?????????? ???????? ?? ??????? ??????????? ?????????:
,
??????? ? ??_?=0,2198;
???????????????? ??????? ?????????? ?? ????????:
t(?_? )=1-(k-1)/(k+1)�?_?^2=1-0,33/2,33�?0,2198?^2=0,9923
p(?_? )= ?t(?_? )?^(k/(k-1))=?0,9923?^(1,33/0,33)=0,9727
?(?_? )= ?t(?_? )?^(1/(k-1))=?0,9923?^(1/0,33)=0,9794
??? - ???????????????? ??????? ???????????, ???????? ? ????????? ??????????????
?????? ????? ????:
M_?=?_?�v(2/(k+1))/v(t(?_? ) )=0,2198�v(2/2,33)/v0,9923=0,2044
??????????? ?????????? ???????? ??????: a_kp?=v(2k/(k+1) RT_?^* )=v((2�1,33)/2,33�288�2800)=959,48 ?/?
T_?=T_?^*�t(?_? )=2800�0,9932=2780,84 K
a_?=v(kRT_? )=v(1,33�288�2780,84 )=1032,07 ?/?
??? - ??????????? ? ??????? ???????? ????? ??????????????, ? - ??????????? ???????????
?????? ???????? ???????? ??????:
c_?=??_? a?_???=0,2198�959,48=210,909 ?/? ?M_? a?_5=0,2269�1031,25 =210,909 ?/? ????? ??????? "k" ???????? ? ????????? ?????????? ???????? ???????????: p_?^*=4,9549???
?_?^*=6,1445 ??/?^3 ????????? ??????????? ????????? ???????? ??????:
p_?=p_?^*� p(?_? )=4,9549�0,9727=4,8212 ???
?_?=?_?^* ?(?_? )=6,1445�0,9794=6,0198 ??/?^3 G_?=(p_?^* S_?)/v(T_?^* )�q(?_? )�m_G=(3,9153 �34182,2)/v2800�0,342�0,03964=43,399 ?_5 c_5 S_5=6,0198�210,99 �34182,2�?10?^(-6)=43,399 ??? - ??????????? ?????????, - ??????????? ????????, ? - ?????? ???????? ??????
7. ?????? ????????? ???????? ??????.
?????????? ???????? ???????????????? ??????? "f" ? ?????????? ???????? ???????? ?????? "?" ?? ????????:
f=(1+?^2 )�e ?=p^*�S�f
f_0=(1+?_0^2 )�e(?_0 )=(1+?0,2311?^2 )�0,9771=1,029 ?_0=p^*�S�f=5,156�10135,14�1,029=53,78
f_?=(1+?_?^2 )�e(?_? )=(1+?0,2225?^2 )�0,9796=1,027 ?_?=p^*�S�f=4,9549�33783,7�1,027=172,03
f_?=(1+?_?^2 )�e(?_? )=(1+1^2 )�0,6295=1,26 ?_?=p^*�S�f=4,9549�11689,9�1,26=72,98
?????? ???????:
f_?=(1+?_?^2 )�e(?_? )=(1+?1,9028?^2 )�0,1131=0,52 ?_?=p^*�S�f=4,9549�34182,3�0,52=88,6
?????? ???????:
f_?=(1+?_?^2 )�e(?_? )=(1+?0,525?^2 )�0,8861=1,1308 ?_?=p^*�S�f=4,9549�34182,3�1,1308=88,57 ?????? ???????:
f_?=(1+?_?^2 )�e(?_? )=(1+?0,4715?^2 )�0,9076=1,109 ?_?=p^*�S�f=2,1089�34182,3�1,109=94,55
????????? ???????:
f_?=(1+?_?^2 )�e(?_? )=(1+?0,2820?^2 )�0,9663=1,043 ?_?=p^*�S�f=3,9153�34182,3�1,043=139,6
????? ???????:
f_?=(1+?_?^2 )�e(?_? )=(1+?0,2198?^2 )�0,9794=1,027 ?_?=p^*�S�f=4,9549�34182,3�1,027=173,95
8. ?????? ??? ? ????.
?????????? ???????????? ???????? ?????????? ??? ????????? ?????? ?????? ???????? 1-5:
s_(?.?)=s_(0-1)=(p_1^*)/(p_0^* )=5,075/5,156=0,985
s_?=s_(1-?)=(p_?^*)/(p_1^* )=4,9549/5,075=0,9759
???????????? ???????? ?????????? s? ???? ???????? ?????.
?????????? ???????? pH ?? ???????, ??? ? ????? ?????????? ?????? ??? ????????? ?? ??????? ????? ???????? ????? pH:
p_(H_1 )=p_a=0,2732 ???
p_(H_2 )=p_???=1,951???
p_(H_3 )=p_3a=2,192???
p_(H_4 )=p_4a=3,741 ???
p_(H_5 )=p_5a=4,821 ??? ???????? ??? P0-k ? Pk-y ??? ???? ????????? ????????? ? ?????:
?_(0-?)=?_?-?_0=118,243 ??
?_(?-?)=?_?-?_?=-99,08 ??
????????? ???? ?????? ?? ????????:
?_(?-?)=?_?-?_?
?_(0-?)=?_?-?_0
?_?????=?_?
?_???=?-p?_(H_i ) S_?
?=?_?????+?_???
?_(?-1?)=?_1?-?_?=88,6-72,98=15,625 ??
?_(?-2?)=?_2?-?_?=88,57-72,98=15,625 ??
?_(?-3?)=?_3?-?_?=94,55-72,98=21,602 ??
?_(?-4?)=?_4?-?_?=139,6-72,98=66,65 ??
?_(?-5?)=?_5?-?_?=173,95-72,98=101,603 ??
?_(0-1?)=?_1?-?_0=88,6-53,78=34,786 ??
?_(0-2?)=?_2?-?_0=88,57-53,78=34,786 ??
?_(0-3?)=?_3?-?_0=94,55-53,78=40,763 ??
?_(0-4?)=?_4?-?_0=139,6-53,78=85,815 ??
?_(0-5?)=?_5?-?_0=173,95-53,78=120,164 ??
?_?????1=?_1?=88,6 ??
?_?????2=?_2?=88,57 ??
?_?????3=?_3?=94,55 ??
?_?????4=?_4?=139,6 ??
?_?????5=?_5?=173,95 ??
?_???1=?-p?_(H_1 ) S_?=-0,2732� 34182,3=-9,339 ??
?_???2=?-p?_(H_2 ) S_?=-1,951� 34182,3=-66,69 ??
?_???3=?-p?_(H_3 ) S_?=-2,192� 34182,3=-74,92 ??
?_???4=?-p?_(H_4 ) S_?=-3,741� 34182,3=-127,86 ??
?_???5=?-p?_(H_5 ) S_?=-4,821� 34182,3=-164,799 ??
?=?_?????1+?_???1=88,6-9,339=79,24
?=?_?????2+?_???2=88,57-66,69=21,88
?=?_?????3+?_???3=94,55-74,92=19,66 ?=?_?????4+?_???4=139,6-127,86=11,74
?=?_?????5+?_???5=173,95 -164,799=9,153
??????????
? ?????? ??????????? ????????? ???? ? ?????? ??????????? ??????? ?? ????????????? ? ?????????? ???????, ?? ???????? ?????????? ? ??? ???. ????????? ??????? ??????. ? ?????????? ?????? ????? ???????? ???????? ?????????? ???????? ??????, ???????? ??????? ?? ???????? ??????, ???????? ????????? ??????? ?????, ???????? ??? ?????????????? ?????? ?? ???????? ?????. ??? ?????? ???????? ? ???????. ????????? ??????? ???????????? ???????? ????????????? ?????? ?? ???????, ? ????? ??????? ???????????? ???????? ?????? ? ???????? ??????? ? ??? ?????????????? ?????? ?? ???????? ??????.
??? ????? ?? ????????, ?? ????????? ?????? ??????????? ???????????? ?????????? ???????? ?????? ?? ?????????? ????? ??????. ?????? ? ??????????? ????????, ??????????? ????????, ?????????, ??????????? ? ???????? ????? ? ????, ????????? ?????????? ???????? ???????????.
?? ?????????????? ???????? ????? ?????? ????????? ?????????? ?????? ?? ??????????? ??????? ??? ??????? ??????? ?????????? ? ?? ?????????? ???????: ???????????? ???????? ???????? ??????, ?????????? ????????, ?????????, ??????????? ? ???????? ????? ? ????, ?????????? ????????? ??????????. ?????????? ????? ????? ??????????? ????. ??????? ??????????? ?????? ???????? ?????????????? ? ???? ????????????? ??? ?????????????? ?????.
?????? ???????????? ??????????
1. ???????? ?. ?., ????????? ?. ?. ? ??. ?????? ?????????? ???????? ?????? ? ?????? ????????? ?????????. - ??????: ???? 2002.
2. ????????? ?. ?. ?????????? ??????? ????????. ?. ?????, 1976.
3. ??????? ?. ?. ?????????? ?????????????????. ???, ?., 1968.
2
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