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Файл:Термодинамические циклы теплоэнергетических установок. Учебное пособие
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ȼ. Ⱦ. Ƚɚɥɞɢɧ
ɌȿɊɆɈȾɂɇȺɆɂɑȿɋɄɂȿ ɐɂɄɅɕ
ɌȿɉɅɈɗɇȿɊȽȿɌɂɑȿɋɄɂɏ ɍɋɌȺɇɈȼɈɄ
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ
Ɇɨɫɤɜɚ ȼɨɥɨɝɞɚ
«ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ»
2024
ɍȾɄ 621.311.22
ȻȻɄ 31.37
Ƚ15
Ɋɟɰɟɧɡɟɧɬɵ:
ɞ-ɪ ɬɟɯɧ. ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ (ɈɦȽɍɉɋ) ȼ. Ɋ. ȼɟɞɪɭɱɟɧɤɨ;
ɞ-ɪ ɬɟɯɧ. ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ (ɈɦȽȺɍ) ɉ. Ⱥ. Ʌɢɫɢɧ
Ƚɚɥɞɢɧ, ȼ. Ⱦ.
Ƚ15 Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɰɢɤɥɵ ɬɟɩɥɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɨɤ : ɭɱɟɛ-
ɧɨɟ ɩɨɫɨɛɢɟ / ȼ. Ⱦ. Ƚɚɥɞɢɧ. Ɇɨɫɤɜɚ ; ȼɨɥɨɝɞɚ : ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ, 2024.
116 ɫ. :
ɢɥ
., ɬɚɛɥ.
ISBN 978-5-9729-1611-5
Ɋɚɫɫɦɨɬɪɟɧɵ ɨɫɧɨɜɧɵɟ ɩɨɧɹɬɢɹ ɢ ɡɚɤɨɧɵ ɬɟɪɦɨɞɢɧɚɦɢɤɢ, ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ
ɩɪɨɰɟɫɫɵ ɢɡɦɟɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɜɨɞɵ ɢ ɜɨɞɹɧɨɝɨ ɩɚɪɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ
ɰɢɤɥɵ ɩɚɪɨɫɢɥɨɜɵɯ ɢ ɝɚɡɨɬɭɪɛɢɧɧɵɯ ɭɫɬɚɧɨɜɨɤ, ɩɨɪɲɧɟɜɵɯ ɞɜɢɝɚɬɟɥɟɣ ɜɧɭɬɪɟɧɧɟɝɨ
ɫɝɨɪɚɧɢɹ. ɉɪɢɜɟɞɟɧɵ ɫɯɟɦɵ ɩɚɪɨɝɚɡɨɜɨɣ ɭɫɬɚɧɨɜɤɢ ɢ ɭɫɬɚɧɨɜɤɢ ɞɥɹ ɤɨɦɩɥɟɤɫɧɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ ɬɟɩɥɨɬɵ ɢ ɬɜɟɪɞɨɝɨ ɞɢɨɤɫɢɞɚ ɭɝɥɟɪɨɞɚ. ɉɪɢɜɟɞɟɧɵ ɩɪɢɦɟɪɵ ɪɚɫɱɟɬɚ ɬɟɩɥɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɨɤ ɢ ɢɯ ɷɥɟɦɟɧɬɨɜ.
Ⱦɥɹ ɫɬɭɞɟɧɬɨɜ ɛɚɤɚɥɚɜɪɢɚɬɚ ɢ ɦɚɝɢɫɬɪɚɬɭɪɵ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ «Ɍɟɩɥɨɷɧɟɪɝɟɬɢɤɚ
ɢ ɬɟɩɥɨɬɟɯɧɢɤɚ» ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɩɪɚɤɬɢɱɟɫɤɢɯ ɡɚɧɹɬɢɣ, ɤɭɪɫɨɜɨɝɨ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ
ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɪɚɛɨɬɵ ɩɨ ɞɢɫɰɢɩɥɢɧɟ «Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɰɢɤɥɨɜ ɬɟɩɥɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɨɤ».
ISBN 978-5-9729-1611-5 Ƚɚɥɞɢɧ ȼ. Ⱦ., 2024
ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2024
Ɉɮɨɪɦɥɟɧɢɟ. ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2024
ɍȾɄ 621.311.22
ȻȻɄ 31.37
ɈȽɅȺȼɅȿɇɂȿ
ȼȼȿȾȿɇɂȿ ...................................................................................................... 5
1. ɌȿɊɆɈȾɂɇȺɆɂɄȺ ɗɇȿɊȽȿɌɂɑȿɋɄɂɏ ɍɋɌȺɇɈȼɈɄ ............... 6
1.1. Ɉɫɧɨɜɧɵɟ ɩɨɧɹɬɢɹ ɢ ɡɚɤɨɧɵ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ...................................... 6
1.2. Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɢɡɦɟɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ
ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ .............................................................................................. 9
1.3. Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɜɨɞɵ ɢ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ........................ 13
1.3.1. Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɚɪɨɜ .............................................. 13
1.3.2. ȼɨɞɹɧɨɣ ɩɚɪ. ɉɚɪɨɨɛɪɚɡɨɜɚɧɢɟ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ ......... 14
1.3.3. Ɍɚɛɥɢɰɵ ɢ ɞɢɚɝɪɚɦɦɵ ɞɥɹ ɜɨɞɵ ɢ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ........................ 15
1.3.4. Ɉɫɧɨɜɧɵɟ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ............. 20
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ................................................................................. 23
2. ɉɊɂɇɐɂɉɂȺɅɖɇɕȿ ɋɏȿɆɕ
ɌȿɉɅɈɗɇȿɊȽȿɌɂɑȿɋɄɂɏ ɍɋɌȺɇɈȼɈɄ .......................................... 24
2.1. ɋɯɟɦɚ ɬɟɩɥɨɜɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɫɬɚɧɰɢɢ ............................................ 24
2.2. ɋɯɟɦɚ ɤɨɬɟɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ ................................................................ 27
2.3. Ɍɟɩɥɨɜɵɟ ɫɯɟɦɵ ɬɟɩɥɨɝɟɧɟɪɢɪɭɸɳɢɯ ɭɫɬɚɧɨɜɨɤ ............................. 32
2.3.1. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɬɟɩɥɨɜɚɹ ɫɯɟɦɚ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨ-
ɨɬɨɩɢɬɟɥɶɧɨɣ ɬɟɩɥɨɝɟɧɟɪɢɪɭɸɳɟɣ ɭɫɬɚɧɨɜɤɢ ..................................... 32
2.3.2. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɬɟɩɥɨɜɚɹ ɫɯɟɦɚ ɨɬɨɩɢɬɟɥɶɧɨɣ
ɬɟɩɥɨɝɟɧɟɪɢɪɭɸɳɟɣ ɭɫɬɚɧɨɜɤɢ ɫ ɜɨɞɨɝɪɟɣɧɵɦɢ ɤɨɬɥɚɦɢ .................. 35
2.4. ɉɚɪɨɫɢɥɨɜɵɟ ɭɫɬɚɧɨɜɤɢ ....................................................................... 37
2.4.1. ɐɢɤɥ ɩɚɪɨɫɢɥɨɜɨɣ ɭɫɬɚɧɨɜɤɢ – ɰɢɤɥ Ɋɟɧɤɢɧɚ ............................ 37
2.4.2. ɐɢɤɥ ɩɚɪɨɬɭɪɛɢɧɧɨɣ ɭɫɬɚɧɨɜɤɢ ɫ ɪɟɝɟɧɟɪɚɰɢɟɣ ........................ 41
2.4.3. ɐɢɤɥ ɩɚɪɨɬɭɪɛɢɧɧɨɣ ɭɫɬɚɧɨɜɤɢ ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦ
ɩɟɪɟɝɪɟɜɨɦ ɩɚɪɚ ....................................................................................... 42
2.4.4. Ɍɟɩɥɨɮɢɤɚɰɢɨɧɧɵɣ ɰɢɤɥ ɩɚɪɨɫɢɥɨɜɨɣ ɭɫɬɚɧɨɜɤɢ ..................... 44
2.5. Ƚɚɡɨɬɭɪɛɢɧɧɵɟ ɭɫɬɚɧɨɜɤɢ ................................................................... 45
2.5.1. ɐɢɤɥ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ ................ 46
2.5.2. ɐɢɤɥ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ .................... 47
2.5.3. ɐɢɤɥ ɫ ɪɟɝɟɧɟɪɚɰɢɟɣ ɬɟɩɥɨɬɵ ....................................................... 49
2.6. ɉɨɪɲɧɟɜɵɟ ɞɜɢɝɚɬɟɥɢ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ ................................... 51
2.6.1. ɐɢɤɥ ɞɜɢɝɚɬɟɥɹ ɫ ɢɡɨɯɨɪɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ....................... 52
2.6.2. ɐɢɤɥ ɞɜɢɝɚɬɟɥɹ ɫ ɢɡɨɛɚɪɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ........................ 56
2.6.3. ɐɢɤɥ ɞɜɢɝɚɬɟɥɹ
ɫɨ ɫɦɟɲɚɧɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ .................... 60
2.6.4. ɐɢɤɥ ɬɭɪɛɨɩɨɪɲɧɟɜɨɝɨ ɞɜɢɝɚɬɟɥɹ ............................................... 63
2.7. Ʉɨɦɛɢɧɢɪɨɜɚɧɧɵɟ ɫɢɥɨɜɵɟ ɭɫɬɚɧɨɜɤɢ ............................................... 64
2.7.1. ɉɚɪɨɝɚɡɨɜɚɹ ɭɫɬɚɧɨɜɤɚ .................................................................. 64
2.7.2. ɍɫɬɚɧɨɜɤɚ ɞɥɹ ɤɨɦɩɥɟɤɫɧɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ ɬɟɩɥɨɬɵ
ɢ ɬɜɟɪɞɨɝɨ ɞɢɨɤɫɢɞɚ ɭɝɥɟɪɨɞɚ ................................................................ 65
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ................................................................................. 68
3
3. ɊȺɋɑȿɌ ɌȿɉɅɈȼɕɏ ɋɏȿɆ ɂ ɗɅȿɆȿɇɌɈȼ
ɗɇȿɊȽȿɌɂɑȿɋɄɂɏ ɍɋɌȺɇɈȼɈɄ ........................................................ 69
3.1. Ɋɚɫɱɟɬ ɩɚɪɨɫɢɥɨɜɵɯ ɭɫɬɚɧɨɜɨɤ ........................................................... 69
3.2. Ɋɚɫɱɟɬ ɝɚɡɨɬɭɪɛɢɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ........................................................ 97
3.3. Ɋɚɫɱɟɬ ɩɨɪɲɧɟɜɵɯ ɞɜɢɝɚɬɟɥɟɣ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ ...................... 99
ɄɈɇɌɊɈɅɖɇɕȿ ɁȺȾȺɑɂ ....................................................................... 101
ȻɂȻɅɂɈȽɊȺɎɂɑȿɋɄɂɃ ɋɉɂɋɈɄ .................................................... 107
ɉɊɂɅɈɀȿɇɂȿ .......................................................................................... 108
4
ȼȼȿȾȿɇɂȿ
ɀɢɡɧɶ ɫɨɜɪɟɦɟɧɧɨɝɨ ɱɟɥɨɜɟɤɚ ɧɚ Ɂɟɦɥɟ ɧɟɦɵɫɥɢɦɚ ɛɟɡ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɢ ɬɟɩɥɨɬɵ. Ⱦɥɹ ɢɯ ɩɪɨɢɡɜɨɞɫɬɜɚ ɢɫɩɨɥɶɡɭɸɬɫɹ
ɩɪɢɪɨɞɧɵɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɪɟɫɭɪɫɵ, ɛɨɥɶɲɚɹ ɱɚɫɬɶ ɤɨɬɨɪɵɯ ɫɜɹɡɚɧɚ
ɫ ɫɨɥɧɟɱɧɨɣ ɷɧɟɪɝɢɟɣ. ɋɸɞɚ ɨɬɧɨɫɹɬɫɹ ɯɢɦɢɱɟɫɤɢ ɫɜɹɡɚɧɧɚɹ ɷɧɟɪɝɢɹ ɨɪɝɚɧɢɱɟɫɤɢɯ ɬɨɩɥɢɜ (ɢɫɤɨɩɚɟɦɵɯ ɭɝɥɟɣ, ɧɟɮɬɢ, ɩɪɢɪɨɞɧɨɝɨ ɝɚɡɚ, ɬɨɪɮɚ, ɞɪɨɜ),
ɝɢɞɪɚɜɥɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɩɚɞɚɸɳɟɣ ɜɨɞɵ ɪɟɤ, ɷɧɟɪɝɢɹ ɜɟɬɪɚ
ɢ ɧɟɩɨɫɪɟɞ-
ɫɬɜɟɧɧɨ ɫɨɥɧɟɱɧɨɝɨ ɢɡɥɭɱɟɧɢɹ. Ɇɢɪɨɜɵɟ ɡɚɩɚɫɵ ɨɪɝɚɧɢɱɟɫɤɨɝɨ ɬɨɩɥɢɜɚ
ɨɰɟɧɢɜɚɸɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɭɝɨɥɶ 220330 ɥɟɬ; ɝɚɡ 3560 ɥɟɬ;
ɧɟɮɬɶ 2550 ɥɟɬ.
Ɉɞɧɨɣ ɢɡ ɨɫɧɨɜɧɵɯ ɬɟɧɞɟɧɰɢɣ ɦɢɪɨɜɨɝɨ ɬɨɩɥɢɜɧɨ-ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ
ɛɚɥɚɧɫɚ ɹɜɥɹɟɬɫɹ ɫɧɢɠɟɧɢɟ ɞɨɥɢ ɧɟɮɬɢ ɞɥɹ ɝɟɧɟɪɚɰɢɢ ɬɟɩɥɨɜɨɣ ɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, ɫɜɹɡɚɧɧɨɟ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɝɥɭɛɢɧɵ ɟɟ ɩɟɪɟɪɚɛɨɬɤɢ.
ȼ ɬɨ
ɠɟ ɜɪɟɦɹ ɧɚɛɥɸɞɚɟɬɫɹ ɫɧɢɠɟɧɢɟ ɬɟɦɩɨɜ ɪɨɫɬɚ ɞɨɥɢ ɚɬɨɦɧɨɣ ɷɧɟɪɝɟɬɢɤɢ ɜ ɦɢɪɨɜɨɦ ɛɚɥɚɧɫɟ.
ȼ ɰɟɥɨɦ, ɜ ɩɟɪɫɩɟɤɬɢɜɟ ɛɥɢɠɚɣɲɢɯ 4050 ɥɟɬ ɩɪɢɪɨɫɬ ɝɟɧɟɪɢɪɭɸɳɢɯ
ɦɨɳɧɨɫɬɟɣ ɜ ɦɢɪɟ ɛɭɞɟɬ ɨɛɟɫɩɟɱɢɜɚɬɶɫɹ ɜ ɧɟɦɚɥɨɣ ɫɬɟɩɟɧɢ ɡɚ ɫɱɟɬ ɬɟɩɥɨɜɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɬɚɧɰɢɣ (Ɍɗɋ) ɧɚ ɨɪɝɚɧɢɱɟɫɤɨɦ ɬɨɩɥɢɜɟ, ɜ ɬɨɦ ɱɢɫɥɟ
ɢ ɡɚ ɫɱɟɬ ɛɨɥɟɟ ɲɢɪɨɤɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɧɢɡɤɨɫɨɪɬɧɵɯ
ɬɨɩɥɢɜ.
ɇɚɢɛɨɥɶɲɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜ ɷɧɟɪɝɟɬɢɤɟ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɩɨɥɭɱɢɥɢ
Ɍɗɋ, ɧɚ ɤɨɬɨɪɵɯ ɬɟɩɥɨɜɚɹ ɷɧɟɪɝɢɹ, ɜɵɞɟɥɹɸɳɚɹɫɹ ɩɪɢ ɫɠɢɝɚɧɢɢ ɨɪɝɚɧɢɱɟɫɤɢɯ ɬɨɩɥɢɜ, ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ. ɇɚ ɢɯ ɞɨɥɸ ɩɪɢɯɨɞɢɬɫɹ ɨɤɨɥɨ 75 % ɜɵɪɚɛɚɬɵɜɚɟɦɨɣ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɧɚ Ɂɟɦɥɟ ɢ ɨɤɨɥɨ 80 % ɩɪɨɢɡɜɨɞɢɦɨɣ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɜ Ɋɨɫɫɢɢ. Ɉɫɧɨɜɧɵɦ ɧɚɡɧɚɱɟɧɢɟɦ Ɍɗɋ ɹɜɥɹɟɬɫɹ ɜɵɪɚɛɨɬɤɚ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɞɥɹ ɨɫɜɟɳɟɧɢɹ, ɬɪɚɧɫɩɨɪɬɚ, ɤɨɦɦɭɧɚɥɶɧɨɝɨ
ɯɨɡɹɣɫɬɜɚ ɢ ɛɵɬɨɜɵɯ ɧɭɠɞ, ɚ ɬɚɤɠɟ ɫɧɚɛɠɟɧɢɟ ɠɢɥɵɯ ɞɨɦɨɜ, ɭɱɪɟɠɞɟɧɢɣ
ɢ ɩɪɟɞɩɪɢɹɬɢɣ ɬɟɩɥɨɦ ɞɥɹ ɨɬɨɩɥɟɧɢɹ ɡɢɦɨɣ ɢ ɝɨɪɹɱɟɣ ɜɨɞɨɣ ɞɥɹ ɤɨɦɦɭɧɚɥɶɧɵɯ ɢ ɛɵɬɨɜɵɯ ɰɟɥɟɣ ɢɥɢ ɩɚɪɨɦ ɞɥɹ ɩɪɨɢɡɜɨɞɫɬɜɚ.
Ⱦɥɹ ɜɵɪɚɛɨɬɤɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɢ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɬɟɩɥɨɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɭɫɬɚɧɨɜɤɢ ɧɚ ɨɫɧɨɜɟ ɩɚɪɨɫɢɥɨɜɵɯ ɢ ɝɚɡɨɬɭɪɛɢɧɧɵɯ
ɰɢɤɥɨɜ, ɩɨɪɲɧɟɜɵɯ ɞɜɢɝɚɬɟɥɟɣ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ ɢ ɤɨɦɛɢɧɢɪɨɜɚɧɧɵɯ
(ɤɨɝɟɧɟɪɚɰɢɨɧɧɵɯ) ɭɫɬɚɧɨɜɨɤ.
Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɰɢɤɥɨɜ ɬɟɩɥɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɨɤ
ɨɫɧɨɜɵɜɚɟɬɫɹ ɧɚ ɩɟɪɜɨɦ ɢ ɜɬɨɪɨɦ ɡɚɤɨɧɚɯ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɢ ɩɨɡɜɨɥɹɟɬ ɜɵɹɫɧɢɬɶ ɩɪɟɞɟɥɶɧɭɸ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɭɫɬɚɧɨɜɤɢ ɢ ɧɚɦɟɬɢɬɶ ɩɭɬɢ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɷɥɟɦɟɧɬɨɜ ɭɫɬɚɧɨɜɤɢ, ɭɥɭɱɲɟɧɢɟ ɤɨɬɨɪɵɯ ɫɩɨɫɨɛɧɨ ɩɨɜɥɢɹɬɶ
ɧɚ ɪɨɫɬ ɨɛɳɟɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ.
5
1. ɌȿɊɆɈȾɂɇȺɆɂɄȺ ɗɇȿɊȽȿɌɂɑȿɋɄɂɏ ɍɋɌȺɇɈȼɈɄ
1.1. Ɉɫɧɨɜɧɵɟ ɩɨɧɹɬɢɹ ɢ ɡɚɤɨɧɵ ɬɟɪɦɨɞɢɧɚɦɢɤɢ
Ɏɨɪɦɭɥɢɪɨɜɤɚ ɢ ɨɛɳɟɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ. ɉɟɪɜɵɦ ɡɚɤɨɧɨɦ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɧɚɡɵɜɚɸɬ ɡɚɤɨɧ
ɫɨɯɪɚɧɟɧɢɹ ɢ ɩɪɟɜɪɚɳɟɧɢɹ ɷɧɟɪɝɢɢ – ɷɧɟɪɝɢɹ ɧɟ ɜɨɡɧɢɤɚɟɬ ɢɡ ɧɢɱɟɝɨ ɢ ɧɟ
ɢɫɱɟɡɚɟɬ, ɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɨɞɧɨɝɨ ɜɢɞɚ ɜ ɞɪɭɝɨɣ.
Ɍɟɩɥɨɬɚ q (Q) ɩɟɪɟɯɨɞɚ ɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ ɪɚɫɯɨɞɭɟɬɫɹ
ɧɚ ɢɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ
'
u ('U) ɢ ɫɨɜɟɪɲɟɧɢɟ ɪɚɛɨɬɵ w (W).
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɜ ɭɞɟɥɶɧɵɯ (Ⱦɠ/ɤɝ) ɢ ɚɛɫɨɥɸɬɧɵɯ (Ⱦɠ) ɜɟɥɢɱɢɧɚɯ:
q = 'u + w ɢɥɢ Q = 'U + W,
ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɮɨɪɦɚɯ:
dq = du + dw; dq = du + pdX; dQ = dU + dW.
ȼɵɪɚɠɟɧɢɟ pdX ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɪɚɛɨɬɭ ɢɡɦɟɧɟɧɢɹ ɨɛɴɟɦɚ.
ȼɬɨɪɚɹ ɮɨɪɦɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɜɵɪɚɠɟɧɢɹ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ:
dq = dh + dl; dq = dh Xdp; q = h + l,
ɬ. ɟ. ɬɟɩɥɨɬɚ ɩɟɪɟɯɨɞɚ ɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɨɜɵɲɟɧɢɟ ɷɧɬɚɥɶɩɢɢ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ h ɢ ɫɨɜɟɪɲɟɧɢɟ ɪɚɛɨɬɵ l. ȼɵɪɚɠɟɧɢɟ
X
dp ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɬɟɯɧɢɱɟɫɤɭɸ ɪɚɛɨɬɭ (ɪɚɛɨɬɭ ɧɚ ɜɚɥɭ).
ɉɨɧɹɬɢɟ ɨɛ ɨɫɧɨɜɧɵɯ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɚɯ. Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ ɷɬɨ ɧɟɩɪɟɪɵɜɧɨɟ ɢɡɦɟɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ, ɯɚɪɚɤɬɟɪɢɡɭɟɦɨɟ ɢɡɦɟɧɟɧɢɟɦ ɱɢɫɥɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ ɫɨɫɬɨɹɧɢɹ. ȿɝɨ ɦɨɠɧɨ ɢɡɨɛɪɚɡɢɬɶ ɝɪɚɮɢɱɟɫɤɢ ɜ ɤɨɨɪɞɢɧɚɬɚɯ ɩɚɪɚɦɟɬɪɨɜ ɫɨɫɬɨɹɧɢɹ, ɧɚɩɪɢɦɟɪ ɪ ɢ X (V) (ɪɢɫ. 1.1). ɇɚ ɞɢɚɝɪɚɦɦɟ ɫɨɫɬɨɹɧɢɹ ɦɨɝɭɬ ɛɵɬɶ
ɢɡɨɛɪɚɠɟɧɵ ɬɨɥɶɤɨ ɨɛɪɚɬɢɦɵɟ ɩɪɨɰɟɫɫɵ. Ɉɞɧɚɤɨ ɜ ɬɟɯ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ
ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɫɪɚɜɧɢɬɶ ɨɛɪɚɬɢɦɨɟ ɢ ɧɟɨɛɪɚɬɢɦɨɟ ɩɪɨɬɟɤɚɧɢɟ
ɩɪɨɰɟɫɫɚ, ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɭɧɤɬɢɪ.
Ɋɚɡɥɢɱɚɸɬ ɱɟɬɵɪɟ ɨɫɧɨɜɧɵɯ ɩɪɨɰɟɫɫɚ:
– ɢɡɨɬɟɪɦɢɱɟɫɤɢɣ – ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ (Ɍ = const);
– ɢɡɨɛɚɪɧɵɣ – ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ (ɪ = const);
X
– ɢɡɨɯɨɪɧɵɣ – ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ (
– ɚɞɢɚɛɚɬɧɵɣ – ɛɟɡ ɬɟɩɥɨɨɛɦɟɧɚ ɫ ɜɧɟɲɧɟɣ ɫɪɟɞɨɣ (dq = 0).
= const);
Ƚɪɚɮɢɤɢ ɷɬɢɯ ɩɪɨɰɟɫɫɨɜ ɞɥɹ ɪɚɫɲɢɪɟɧɢɹ ɝɚɡɚ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 1.1.
Ɂɚɦɤɧɭɬɵɣ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ 1-ɚ-2-b-1, ɬ. ɟ. ɩɪɨɰɟɫɫ, ɩɪɢ
ɤɨɬɨɪɨɦ ɪɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ, ɩɪɨɣɞɹ ɱɟɪɟɡ ɪɹɞ ɫɨɫɬɨɹɧɢɣ, ɜɨɡɜɪɚɳɚɟɬɫɹ
6
ɜ ɩɟɪɜɨɧɚɱɚɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɧɚɡɵɜɚɟɬɫɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɦ ɰɢɤɥɨɦ.
X
Ⱦɥɹ ɰɢɤɥɚ ɢɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ 'u = 0 ɢ ɭɪɚɜɧɟɧɢɟ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ q = w, ɬ. ɟ. ɬɟɩɥɨɬɚ q, ɢɫɩɨɥɶɡɨɜɚɧɧɚɹ
ɜ ɰɢɤɥɟ, ɰɟɥɢɤɨɦ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɪɚɛɨɬɭ, ɚ ɩɪɢ ɨɛɪɚɬɧɨɦ ɩɪɨɬɟɤɚɧɢɢ ɰɢɤɥɚ, ɧɚɨɛɨɪɨɬ, ɪɚɛɨɬɚ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɬɟɩɥɨɬɭ.
p
Ɋɢɫ. 1.1. Ɉɫɧɨɜɧɵɟ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ
ɩɪɨɰɟɫɫɵ ɢ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɰɢɤɥ
p = const
= const
T = const
dq = 0
a
1
2
b
V
ɉɚɪɚɦɟɬɪɵ ɢ ɭɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ. Ⱦɥɹ ɩɪɟɜɪɚɳɟɧɢɹ ɪɚɡɥɢɱɧɵɯ ɜɢɞɨɜ ɷɧɟɪɝɢɢ ɧɭɠɧɵ ɢ ɪɚɡɥɢɱɧɵɟ ɪɚɛɨɱɢɟ ɜɟɳɟɫɬɜɚ. ɂɡɦɟɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ ɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ ɮɢɤɫɢɪɭɟɬɫɹ ɧɟɡɚɜɢɫɢɦɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ, ɱɢɫɥɨ ɤɨɬɨɪɵɯ ɨɩɪɟɞɟɥɹɟɬɫɹ ɯɚɪɚɤɬɟɪɨɦ ɫɢɫɬɟɦɵ.
Ɍɟɦɩɟɪɚɬɭɪɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚ-
ɫɬɢɰ ɜ ɫɢɫɬɟɦɟ.
ɒɤɚɥɚ ɬɟɦɩɟɪɚɬɭɪ, ɨɬɫɱɟɬ ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɨɬ ɬɨɱɤɢ ɚɛɫɨɥɸɬɧɨɝɨ
ɧɭɥɹ ɬɟɦɩɟɪɚɬɭɪɵ, ɧɚɡɵɜɚɟɬɫɹ ɚɛɫɨɥɸɬɧɨɣ ɲɤɚɥɨɣ, ɟɞɢɧɢɰɚ ɢɡɦɟɪɟɧɢɹ
ɬɟɦɩɟɪɚɬɭɪɵ – ɤɟɥɶɜɢɧ (Ʉ).
ȼ ɩɪɚɤɬɢɱɟɫɤɨɣ ɲɤɚɥɟ (ɫɬɨɝɪɚɞɭɫɧɨɣ) ɬɟɦɩɟɪɚɬɭɪɚ 0 °ɋ ɫɨɨɬɜɟɬɫɬɜɭɟɬ
ɩɨɫɬɨɹɧɧɨɣ ɬɨɱɤɟ ɩɥɚɜɥɟɧɢɹ ɯɢɦɢɱɟɫɤɢ ɱɢɫɬɨɝɨ ɥɶɞɚ, ɚ 100 °ɋ ɩɨɫɬɨɹɧɧɨɣ
ɬɨɱɤɟ ɤɢɩɟɧɢɹ ɜɨɞɵ ɩɪɢ ɧɨɪɦɚɥɶɧɨɦ ɚɬɦɨɫɮɟɪɧɨɦ ɞɚɜɥɟɧɢɢ (760 ɦɦ ɪɬ. ɫɬ).
ɋɨɨɬɧɨɲɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪ ɩɨ ɩɪɚɤɬɢɱɟɫɤɨɣ t ɢ ɚɛɫɨɥɸɬɧɨɣ Ɍ ɲɤɚɥɚɦ:
Ɍ = 273,16 + t.
Ⱦɚɜɥɟɧɢɟ ɝɚɡɚ ɧɚ ɫɬɟɧɤɢ ɫɨɫɭɞɚ ɟɫɬɶ ɪɟɡɭɥɶɬɚɬ ɭɞɚɪɨɜ ɨ ɧɢɯ ɦɨɥɟɤɭɥ.
Ⱦɚɜɥɟɧɢɟ ɢɡɦɟɪɹɟɬɫɹ ɜ ɩɚɫɤɚɥɹɯ (ɉɚ = ɇ/ɦ
2
(1 ɤɝɫ/ɫɦ
ɢ 1 Ɇɉɚ = 10
= 1 ɚɬɦ = 0,98ā105 ɉɚ), ɭɞɨɛɧɟɟ ɢɫɩɨɥɶɡɨɜɚɬɶ 1 ɤɉɚ = 1000 ɉɚ
6
ɉɚ. ɋɬɚɪɵɟ ɟɞɢɧɢɰɵ ɫɜɹɡɚɧɵ ɫ ɩɚɫɤɚɥɟɦ ɫɨɨɬɧɨɲɟɧɢɹ-
ɦɢ 1 ɛɚɪ = 750 ɦɦ ɪɬ. ɫɬ. = 1,02 ɚɬɦ = 10
2
). ɉɨɫɤɨɥɶɤɭ ɷɬɚ ɟɞɢɧɢɰɚ ɦɚɥɚ
5
ɉɚ.
ɉɪɭɠɢɧɧɵɟ ɢ ɠɢɞɤɨɫɬɧɵɟ ɦɚɧɨɦɟɬɪɵ ɨɛɵɱɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɢɡɦɟɪɹɸɬ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɩɨɥɧɵɦ (ɚɛɫɨɥɸɬɧɵɦ) ɞɚɜɥɟɧɢɟɦ ɫɪɟɞɵ ɪɚ ɢ ɚɬɦɨɫɮɟɪɧɵɦ (ɛɚɪɨɦɟɬɪɢɱɟɫɤɢɦ) ɞɚɜɥɟɧɢɟɦ ɪ
. ɗɬɚ ɪɚɡɧɨɫɬɶ ɧɚɡɵɜɚɟɬɫɹ ɢɡ-
ɛ
7
ɛɵɬɨɱɧɵɦ ɞɚɜɥɟɧɢɟɦ: ɪɢ = ɪɚ – ɪɛ. ȿɫɥɢ ɞɚɜɥɟɧɢɟ ɜ ɟɦɤɨɫɬɢ ɧɢɠɟ ɚɬɦɨɫɮɟɪɧɨɝɨ, ɬɨ ɝɨɜɨɪɹɬ, ɱɬɨ ɜ ɧɟɦ ɜɚɤɭɭɦ.
ɍɞɟɥɶɧɵɣ ɨɛɴɟɦ
ɠɚɟɬɫɹ ɜ ɦ
3
ɉɥɨɬɧɨɫɬɶ
/ɤɝ.
X
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɨɛɴɟɦ ɟɞɢɧɢɰɵ ɦɚɫɫɵ ɢ ɜɵɪɚ-
U
– ɦɚɫɫɚ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ, ɤɝ/ɦ3, U = 1/X.
ɍɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ Ʉɥɚɩɟɣɪɨɧɚ Ɇɟɧɞɟɥɟɟɜɚ ɞɥɹ m
ɤɝ ɝɚɡɚ:
ɪV = mRT,
ɝɞɟ V – ɨɛɴɟɦ, ɡɚɧɢɦɚɟɦɵɣ ɝɚɡɨɦ;
Ɍ – ɬɟɦɩɟɪɚɬɭɪɚ;
R = R
R
P
ɍɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɝɚɡɚ ɞɥɹ 1 ɤɝ ɝɚɡɚ:
/P ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ, Ⱦɠ/(ɤɝāɄ);
P
= 8314, 41 Ⱦɠ/(ɤɦɨɥɶāɄ) – ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ;
P
– ɦɨɥɟɤɭɥɹɪɧɚɹ ɦɚɫɫɚ ɝɚɡɚ, ɤɝ/ɤɦɨɥɶ.
ɪX = RT.
ɍɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɦɨɠɧɨ ɩɪɢɦɟɧɹɬɶ ɜ ɪɚɫɱɟɬɚɯ
ɞɥɹ ɪɟɚɥɶɧɵɯ ɝɚɡɨɜ ɩɪɢ ɧɢɡɤɢɯ ɞɚɜɥɟɧɢɹɯ ɢ ɜɵɫɨɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ.
ɍɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɪɟɚɥɶɧɵɯ ɝɚɡɨɜ, ɭɱɢɬɵɜɚɸɳɢɟ ɪɚɡɦɟɪ ɦɨɥɟɤɭɥ,
ɫɢɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɧɢɦɢ, ɨɛɪɚɡɨɜɚɧɢɟ ɤɨɦɩɥɟɤɫɨɜ ɦɨɥɟɤɭɥ ɚɫɫɨɰɢɚɰɢɣ (ɩɪɢ ɜɵɫɨɤɢɯ ɞɚɜɥɟɧɢɹɯ) ɢ ɩɪ. ɢɦɟɸɬ ɫɥɨɠɧɵɣ ɜɢɞ ɢ ɜ ɩɪɚɤɬɢɤɟ
ɪɚɫɱɟɬɨɜ ɨɛɵɱɧɨ ɧɟ ɩɪɢɦɟɧɹɸɬɫɹ – ɧɚ ɢɯ
ɨɫɧɨɜɚɧɢɢ ɫɨɡɞɚɸɬɫɹ ɬɚɛɥɢɰɵ.
ɗɧɬɚɥɶɩɢɹ – ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ, ɢɦɟɸɳɚɹ ɫɦɵɫɥ ɩɨɥɧɨɣ
ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ. Ɉɧɚ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ u ɢ ɷɧɟɪɝɢɢ
ɪX, ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɧɚɥɢɱɢɟɦ ɜɧɟɲɧɟɝɨ ɞɚɜɥɟɧɢɹ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɪ:
h = u + pX.
Ɍɟɩɥɨɟɦɤɨɫɬɶ ɢ ɟɟ ɜɢɞɵ. Ɍɟɩɥɨɟɦɤɨɫɬɶɸ ɫ ɧɚɡɵɜɚɸɬ ɤɨɥɢɱɟɫɬɜɨ
ɬɟɩɥɨɬɵ q, ɤɨɬɨɪɨɟ ɧɭɠɧɨ ɩɨɞɜɟɫɬɢ ɤ 1 ɤɝ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ ɞɥɹ ɢɡɦɟɧɟɧɢɹ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ 1 ɝɪɚɞɭɫ:
ɫm = q /'T, c = dq / dT.
ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɩɨɫɨɛɚ ɢɡɦɟɪɟɧɢɹ ɟɞɢɧɢɰɵ ɤɨɥɢɱɟɫɬɜɚ ɜɟɳɟɫɬɜɚ,
ɯɚɪɚɤɬɟɪɚ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɢ ɜɟɥɢɱɢɧɵ ɢɧɬɟɪɜɚɥɚ ɬɟɦɩɟɪɚɬɭɪ ɪɚɡɥɢɱɚɸɬ:
ɬɟɩɥɨɟɦɤɨɫɬɢ ɦɚɫɫɨɜɭɸ ɫ, [Ⱦɠ/(ɤɝāɄ)] ɢ ɨɛɴɟɦɧɭɸ ɫ', [Ⱦɠ/(ɦ3āɄ)];
ɬɟɩɥɨɟɦɤɨɫɬɶ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ (ɢɡɨɛɚɪɧɭɸ) ɫ
ɤɨɫɬɶ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ ɫ
ɧɢɟ ɤ = c
/ ɫX ɧɚɡɵɜɚɸɬ ɩɨɤɚɡɚɬɟɥɟɦ ɚɞɢɚɛɚɬɵ;
p
. ɍɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɫɪ – ɫX = R. Ɉɬɧɨɲɟ-
X
ɢ ɬɟɩɥɨɟɦ-
ɪ
8
ɢɫɬɢɧɧɭɸ ɬɟɩɥɨɟɦɤɨɫɬɶ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɨɦɭ ɢɧ-
ɬɟɪɜɚɥɭ ɬɟɦɩɟɪɚɬɭɪ: ɫ = dq
ɳɭɸ ɤɨɧɟɱɧɨɦɭ ɢɧɬɟɪɜɚɥɭ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ: ɫ
/ dT ɢ ɫɪɟɞɧɸɸ ɬɟɩɥɨɟɦɤɨɫɬɶ, ɫɨɨɬɜɟɬɫɬɜɭɸ-
= q / (T2 – T1).
m
Ɏɨɪɦɭɥɢɪɨɜɤɚ ɢ ɨɛɳɟɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɜɬɨɪɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ. ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɩɨɥɨɠɟɧɢɣ ɜɬɨɪɨɝɨ ɡɚɤɨɧɚ ɬɟɪ-
ɦɨɞɢɧɚɦɢɤɢ ɱɚɳɟ ɜɫɟɝɨ ɢɫɯɨɞɹɬ ɢɡ ɩɨɫɬɭɥɚɬɨɜ (ɚɤɫɢɨɦ), ɨɫɧɨɜɚɧɧɵɯ ɧɚ
ɱɚɫɬɧɵɯ ɫɨɨɛɪɚɠɟɧɢɹɯ ɨ ɪɚɛɨɬɟ ɬɟɩɥɨɜɵɯ ɞɜɢɝɚɬɟɥɟɣ.
ɋɭɳɟɫɬɜɭɟɬ ɦɧɨɝɨ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɞɪɭɝ ɞɪɭɝɭ ɮɨɪɦɭɥɢɪɨɜɨɤ ɜɬɨɪɨɝɨ
ɡɚɤɨɧɚ, ɧɚɩɪɢɦɟɪ:
«Ɍɟɩɥɨɬɚ ɦɨɠɟɬ ɩɟɪɟɯɨɞɢɬɶ ɫɚɦɚ ɫɨɛɨɣ ɬɨɥɶɤɨ ɨɬ ɝɨɪɹɱɟɝɨ ɬɟɥɚ ɤ
ɯɨɥɨɞɧɨɦɭ
; ɞɥɹ ɨɛɪɚɬɧɨɝɨ ɩɟɪɟɯɨɞɚ ɧɚɞɨ ɡɚɬɪɚɬɢɬɶ ɪɚɛɨɬɭ» (Ɋ. Ʉɥɚɭɡɢɭɫ,
1850 ɝ.);
«ȼɫɟ ɟɫɬɟɫɬɜɟɧɧɵɟ ɩɪɨɰɟɫɫɵ ɹɜɥɹɸɬɫɹ ɩɟɪɟɯɨɞɨɦ ɨɬ ɦɟɧɟɟ ɜɟɪɨɹɬɧɵɯ ɤ ɛɨɥɟɟ ɜɟɪɨɹɬɧɵɦ ɫɨɫɬɨɹɧɢɹɦ» (Ʌ. Ȼɨɥɶɰɦɚɧ, 18701876 ɝɝ.).
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɜɬɨɪɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɞɥɹ ɨɛɪɚɬɢɦɵɯ ɩɪɨɰɟɫɫɨɜ ɢɦɟɟɬ ɜɢɞ:
dq = T ds,
ɞɥɹ ɧɟɨɛɪɚɬɢɦɵɯ ɩɪɨɰɟɫɫɨɜ:
dq < T ds.
ɗɧɬɪɨɩɢɹ s – ɩɚɪɚɦɟɬɪ ɫɨɫɬɨɹɧɢɹ ɬɚɤɨɣ ɠɟ, ɤɚɤ ɢ ɞɚɜɥɟɧɢɟ ɪ, ɬɟɦɩɟɪɚɬɭɪɚ Ɍ, ɩɥɨɬɧɨɫɬɶ U, ɷɧɬɚɥɶɩɢɹ h ɢ ɬ. ɞ. ɗɧɬɪɨɩɢɸ ɧɟɥɶɡɹ ɢɡɦɟɪɢɬɶ, ɟɟ
ɫɦɵɫɥ ɡɚɬɪɭɞɧɢɬɟɥɶɧɨ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɬɶ ɫ ɩɨɦɨɳɶɸ ɧɚɝɥɹɞɧɵɯ ɩɨɫɨɛɢɣ, ɧɨ ɦɨɠɧɨ ɩɨɧɹɬɶ ɩɨ ɪɹɞɭ ɢɧɬɟɪɩɪɟɬɚɰɢɣ.
1.2. Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɢɡɦɟɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ
ȼɫɟ ɜɨɡɦɨɠɧɵɟ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɢɡɦɟɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ
ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɜ ɤɨɬɨɪɵɯ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɝɚɡɚ ɩɪɟɧɟɛɪɟɠɢɬɟɥɶɧɨ ɦɚɥɚ, ɦɨɝɭɬ ɛɵɬɶ ɨɩɢɫɚɧɵ ɨɞɧɢɦ ɭɪɚɜɧɟɧɢɟɦ ɩɪɢ ɞɨɩɭɳɟɧɢɢ, ɱɬɨ ɩɪɨɰɟɫɫɵ
ɨɛɪɚɬɢɦɵ ɢ ɬɟɩɥɨɟɦɤɨɫɬɶ ɩɪɢ ɢɯ ɩɪɨɬɟɤɚɧɢɢ ɩɨɫɬɨɹɧɧɚ.
Ɉɛɨɛɳɟɧɧɵɣ ɩɪɨɰɟɫɫ ɧɚɡɵɜɚɟɬɫɹ ɩɨɥɢɬɪɨɩɧɵɦ:
ɝɞɟ n – ɩɨɤɚɡɚɬɟɥɶ ɩɨɥɢɬɪɨɩɵ.
Ⱥɧɚɥɢɡ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɨɛɵɱɧɨ ɫ ɰɟɥɶɸ ɭɫɬɚɧɨɜɥɟɧɢɹ ɫɜɹɡɢ ɦɟɠɞɭ ɩɚɪɚɦɟɬɪɚɦɢ ɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɥɢɱɟɫɬɜ
ɪɚɛɨɬɵ, ɬɟɩɥɨɬɵ, ɢɡɦɟɧɟɧɢɹ ɷɧɬɚɥɶɩɢɢ, ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ, ɷɧɬɪɨɩɢɢ.
ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ
n
p
X
,const
(1.1)
9
Ⱦɥɹ ɷɬɨɝɨ ɢɫɩɨɥɶɡɭɸɬ ɭɪɚɜɧɟɧɢɹ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ, ɫɨɫɬɨɹ-
X
X
X
ɧɢɹ ɢ ɩɪɨɰɟɫɫɚ.
Ɋɚɫɫɦɨɬɪɢɦ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɩɨɥɢɬɪɨɩɧɨɝɨ ɩɪɨɰɟɫɫɚ.
1. ɍɪɚɜɧɟɧɢɟ ɩɨɥɢɬɪɨɩɧɨɝɨ ɩɪɨɰɟɫɫɚ:
2. ɋɜɹɡɶ ɦɟɠɞɭ ɩɚɪɚɦɟɬɪɚɦɢ:
ɂɫɩɨɥɶɡɭɹ ɭɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ
T
1
T
2
n
const
p
X
p
1
p
2
1
n
§
·
X
2
¨
¸
;
¨
©
¸
X
1
¹
.
n
§
·
X
2
¨
¸
.
¨
¸
X
1
©
¹
RTp
, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ:
1
n
n
·
§
p
T
T
1
1
2
¸
¨
¨
©
.
¸
p
2
¹
3. ɉɨɤɚɡɚɬɟɥɶ ɩɨɥɢɬɪɨɩɵ, ɟɫɥɢ ɢɡɜɟɫɬɧɵ ɩɚɪɚɦɟɬɪɵ ɫɨɫɬɨɹɧɢɹ ɞɜɭɯ
ɬɨɱɟɤ ɩɪɨɰɟɫɫɚ, ɢɡ (1.1):
ppn
4. ɂɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɜ ɥɸɛɨɦ ɩɪɨɰɟɫɫɟ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ:
Tcu ddX
ɢɥɢ
5. ɂɡɦɟɧɟɧɢɟ ɷɧɬɚɥɶɩɢɢ:
Tchpdd
ɢɥɢ
6. Ɋɚɛɨɬɚ ɪɚɫɲɢɪɟɧɢɹ:
7. Ɍɟɩɥɨɟɦɤɨɫɬɶ ɩɨɥɢɬɪɨɩɧɨɝɨ ɩɪɨɰɟɫɫɚ:
8. Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɜ ɩɪɨɰɟɫɫɟ:
X
2
X
1
X
n
2
X
p
X
pw
11
n
³³
X
2
X
1
n
X
Tcq ddX
ɢɥɢ
1
dd
n
./lg//lg
1221
X
p
1
X
.12TTcu '
.12TTch
'
.
XXX
pp
1122
.1/ nkncc
.12TTcq
9. ɂɡɦɟɧɟɧɢɟ ɷɧɬɪɨɩɢɢ:
T
2
Tqs /dd
ɢɥɢ
10
³
T
1
'
nn
./ln/d
TTcTTcs
12
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