Моделирование предохранительных конструкций. Учебное пособие
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ȼɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫɢɫɬɟɦɵ ɢ ɫɪɟɞɵ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɛɦɟɧɟ ɷɧɟɪɝɢɟɣ ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɚɡɥɢɱɧɵɦɢ ɮɨɪɦɚɦɢ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɢ ɢ ɜɢɞɚɦɢ
ɷɧɟɪɝɢɢɫɭɳɟɫɬɜɭɸɬɪɚɡɥɢɱɧɵɟɮɨɪɦɵɨɛɦɟɧɚɢɥɢɩɟɪɟɞɚɱɢɷɧɟɪɝɢɢ ɤɨɬɨɪɵɟ ɩɨɥɭɱɢɥɢ ɧɚɢɦɟɧɨɜɚɧɢɟ ɪɚɛɨɬɵ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɢ ɬ ɩ ɢ ɬɟɩ ɥɨɬɵ Ɉɬɥɢɱɢɟ ɦɟɠɞɭ ɧɢɦɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ
Ɋɚɛɨɬɚ Ɋɚɛɨɬɚ ɹɜɥɹɟɬɫɹ ɮɨɪɦɨɣ ɩɟɪɟɞɚɱɢ ɭɩɨɪɹɞɨɱɟɧɧɨɝɨ ɨɪɝɚɧɢɡɨ ɜɚɧɧɨɝɨɞɜɢɠɟɧɢɹɦɚɬɟɪɢɢ ɢɛɨɩɪɢɫɨɜɟɪɲɟɧɢɢɟɟɱɚɫɬɢɰɵɬɟɥɚɞɜɢɠɭɬɫɹɨɪ ɝɚɧɢɡɨɜɚɧɧɨ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɇɚɩɪɢɦɟɪ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɝɚɡɚ ɩɨɞ ɩɨɪɲɧɟɦ ɬɟɩɥɨɜɨɣ ɦɚɲɢɧɵ
Ɇɟɯɚɧɢɱɟɫɤɚɹ ɪɚɛɨɬɚ ɹɜɥɹɟɬɫɹ ɦɟɪɨɣ ɷɧɟɪɝɢɢ ɩɟɪɟɞɚɜɚɟɦɨɣ ɜ ɦɟɯɚɧɢ ɱɟɫɤɨɣ ɮɨɪɦɟ ɦɟɪɨɣ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɢɫɬɟɦɵ ɢ ɫɪɟɞɵ
Ɍɟɩɥɨɬɚ Ɏɨɪɦɭ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɯɚɨɬɢɱɟɫɤɨɦɭ ɛɟɫɩɨɪɹɞɨɱɧɨɦɭ ɧɟɨɪɝɚɧɢɡɨɜɚɧɧɨɦɭ ɞɜɢɠɟɧɢɸ ɦɢɤɪɨɱɚɫɬɢɰ ɫɨɫɬɚɜɥɹɸɳɢɯ ɫɢɫɬɟɦɭ ɧɚɡɵɜɚɸɬ ɬɟɩɥɨɨɛɦɟɧɨɦ ɚ ɤɨɥɢɱɟɫɬɜɨ ɷɧɟɪɝɢɢ ɩɟɪɟɞɚɧɧɨɟ ɩɪɢ ɬɟɩ ɥɨɨɛɦɟɧɟ ɤɨɥɢɱɟɫɬɜɨɦ ɬɟɩɥɨɬɵ ɢɥɢ ɩɪɨɫɬɨ ɬɟɩɥɨɬɨɣ
Ɍɟɩɥɨɨɛɦɟɧ ɧɟ ɫɜɹɡɚɧ ɫ ɢɡɦɟɧɟɧɢɟɦ ɩɨɥɨɠɟɧɢɹ ɬɟɥ ɫɨɫɬɚɜɥɹɸɳɢɯ ɬɟɪ ɦɨɞɢɧɚɦɢɱɟɫɤɭɸ ɫɢɫɬɟɦɭ ɢ ɫɨɫɬɨɢɬ ɜ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɣ ɩɟɪɟɞɚɱɟ ɷɧɟɪɝɢɢ ɦɨɥɟɤɭɥɚɦɢ ɨɞɧɨɝɨ ɬɟɥɚ ɦɨɥɟɤɭɥɚɦ ɞɪɭɝɨɝɨ ɩɪɢ ɢɯ ɤɨɧɬɚɤɬɟ Ɍɚɤɨɣ ɨɛɦɟɧ ɷɧɟɪɝɢɟɣ ɩɪɨɢɫɯɨɞɢɬ ɦɟɠɞɭ ɬɟɥɚɦɢ ɢɦɟɸɳɢɦɢ ɪɚɡɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ
Ɍɟɩɥɨɨɛɦɟɧ ɢ ɪɚɛɨɬɚ ɹɜɥɹɸɬɫɹ ɮɨɪɦɚɦɢ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ ɚ ɤɨɥɢɱɟ ɫɬɜɨ ɬɟɩɥɨɬɵ ɢ ɤɨɥɢɱɟɫɬɜɨ ɪɚɛɨɬɵ ɦɟɪɚɦɢ ɩɟɪɟɞɚɜɚɟɦɨɣ ɷɧɟɪɝɢɢ
DZȕȕȗȋȏȔȇșȢ ȘȕȘșȕȦȔȏȦ ȄȔșȗȕȖȏȦ ǻȚȔȑȝȏȦ ȘȕȘșȕȦȔȏȦ
ȼ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɨɩɪɟɞɟɥɟɧɵ ɬɟ ɮɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ ɩɨ ɢɡɦɟɧɟɧɢɸ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɫɭɞɢɬɶ ɨ ɧɚɥɢɱɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɫɢɫɬɟɦɨɣ ɢ ɫɪɟɞɨɣ Ʉɚɠɞɨɣ ɮɨɪɦɟ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ ɤɚɠɞɨɣ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ ɜ ɫɢɫɬɟɦɟ ɫɨɨɬɜɟɬ ɫɬɜɭɟɬ ɫɜɨɹ ɫɩɟɰɢɮɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ ɤɨɬɨɪɚɹ ɨɛɹɡɚɬɟɥɶɧɨ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɧɚɥɢɱɢɢ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ ɜ ɞɚɧɧɨɣ ɮɨɪɦɟ ɢ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɩɪɢ ɨɬɫɭɬ ɫɬɜɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɚɧɧɨɝɨ ɪɨɞɚ ɑɪɟɡɜɵɱɚɣɧɨ ɜɚɠɧɨ ɱɬɨ ɷɬɢ ɫɩɟɰɢɮɢɱɟ ɫɤɢɟ ɜɟɥɢɱɢɧɵ ɧɟ ɢɡɦɟɧɹɸɬɫɹ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɞɪɭɝɢɯ ©ɱɭɠɞɵɯªɞɚɧɧɨɣ ɜɟ ɥɢɱɢɧɟ ɮɨɪɦ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ
ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɞɟɥɢɜ ɝɪɭɩɩɵ ɜɟɥɢɱɢɧ ɢ ɧɚɛɥɸɞɚɹ ɡɚ ɢɯ ɩɨɜɟɞɟɧɢɟɦ ɦɨɠɧɨ ɧɟ ɬɨɥɶɤɨ ɭɫɬɚɧɨɜɢɬɶ ɧɚɥɢɱɢɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɫɢɫɬɟɦɵ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ ɧɨ ɢ ɨɩɪɟɞɟɥɢɬɶ ɪɨɞ ɷɬɢɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɬɨ ɟɫɬɶ ɮɨɪɦɭ ɜ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɨɛɦɟɧ ɷɧɟɪɝɢɟɣ ɦɟɠɞɭ ɫɢɫɬɟɦɨɣ ɢ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ
Ɏɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ ɢɡɦɟɧɹɸɳɢɟ ɫɜɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢ ɧɚɥɢɱɢɢ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ ɜ ɨɩɪɟɞɟɥɟɧɧɨɣ ɮɨɪɦɟ ɢ ɫɨɯɪɚɧɹɸɳɢɟ ɫɜɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɷɬɨɣɮɨɪɦɵɨɛɦɟɧɚɷɧɟɪɝɢɟɣ ɞɚɠɟɟɫɥɢɨɛɦɟɧɷɧɟɪɝɢɟɣɜɢɧɵɯɮɨɪɦɚɯɢɩɪɨ
11
ɢɫɯɨɞɢɥ ɧɚɡɵɜɚɸɬɫɹ ɤɨɨɪɞɢɧɚɬɚɦɢ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ ɂɡɦɟɧɟɧɢɟ ɫɨɨɬ ɜɟɬɫɬɜɭɸɳɟɣ ɤɨɨɪɞɢɧɚɬɵ ɫɨɫɬɨɹɧɢɹ ɹɜɥɹɟɬɫɹ ɩɪɢɡɧɚɤɨɦ ɧɚɥɢɱɢɹ ɜɡɚɢɦɨɞɟɣ ɫɬɜɢɹ ɞɚɧɧɨɝɨ ɪɨɞɚ
Ʉɨɨɪɞɢɧɚɬɨɣ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɹɜɥɹɟɬɫɹ ɨɛɴɟɦ V ɯɢɦɢɱɟ ɫɤɨɣ ɤɨɨɪɞɢɧɚɬɨɣ ɫɨɫɬɨɹɧɢɹ ɹɜɥɹɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨ ɜɟɳɟɫɬɜɚ ɤɨɥɢɱɟɫɬɜɨ ɦɨ ɥɟɣ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɯɢɦɢɱɟɫɤɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ ɱɚ ɫɬɹɦɢ ɝɟɬɟɪɨɝɟɧɧɨɣ ɫɢɫɬɟɦɵ ɚ ɧɟ ɫɢɫɬɟɦɵ ɢ ɫɪɟɞɵ
Ʉɨɨɪɞɢɧɚɬɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɹɜɥɹɟɬɫɹ ɡɚɪɹɞ ɋɥɨɠɧɟɟ ɨɛɫɬɨɢɬ ɜɨɩɪɨɫ ɫ ɤɨɨɪɞɢɧɚɬɨɣ ɫɨɫɬɨɹɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ
ɬɟɩɥɨɜɨɦɭ ɜɡɚɢɦɨɞɟɣɫɬɜɢɸ ɗɬɚ ɜɟɥɢɱɢɧɚ ɛɵɥɚ ɧɚɡɜɚɧɚ ɷɧɬɪɨɩɢɟɣ 6
ɉɨɧɢɦɚɧɢɟ ɮɢɡɢɱɟɫɤɨɝɨ ɫɦɵɫɥɚ ɷɧɬɪɨɩɢɢ ɡɚɬɪɭɞɧɟɧɨ ɬɟɦ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨɦ ɱɬɨ ɟɟ ɡɧɚɱɟɧɢɟ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɢɡɦɟɪɟɧɨɧɢɤɚɤɢɦ ɩɪɢɛɨɪɨɦ ȼ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɢɫɩɨɥɶɡɭɸɬ ɢ ɪɹɞ ɞɪɭɝɢɯ ɜɟɥɢɱɢɧ ɧɟ ɩɨɞɞɚɸɳɢɯɫɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɦɭ ɢɡɦɟɪɟɧɢɸ ɩɪɢɛɨɪɚɦɢ Ʉ ɬɚɤɨɜɵɦ ɨɬɧɨɫɢɬɫɹ ɧɚɩɪɢɦɟɪ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ Ȼɨɥɟɟ ɱɟɦ ɥɟɬɧɢɣ ɨɩɵɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨɧɹɬɢɹ ɷɧɬɪɨɩɢɢ ɜ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɩɨɞ ɬɜɟɪɠɞɚɟɬ ɩɪɚɜɢɥɶɧɨɫɬɶ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɧɟɣ ɤɚɤ ɨ ɬɟɩɥɨɜɨɣ ɤɨɨɪɞɢɧɚɬɟ ɫɨɫɬɨɹɧɢɹ ɬɨ ɟɫɬɶ ɤɚɤ ɨ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɟ ɢɡɦɟɧɟɧɢɟ ɤɨɬɨɪɨɣ ɨɞɧɨɡɧɚɱɧɨ ɫɜɹɡɚɧɨ ɫ ɧɚɥɢ ɱɢɟɦ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ ɜ ɮɨɪɦɟ ɬɟɩɥɨɬɵ
ɋɨɫɬɨɹɧɢɟɫɢɫɬɟɦɵ ɬɨɱɤɚɜn ɦɟɪɧɨɦɩɪɨɫɬɪɚɧɫɬɜɟ ɡɚɞɚɜɚɟɦɨɦɤɨɨɪ ɞɢɧɚɬɚɦɢ ɫɨɫɬɨɹɧɢɹ
Ɏɭɧɤɰɢɟɣ ɫɨɫɬɨɹɧɢɹ ɹɜɥɹɟɬɫɹ ɥɸɛɚɹ ɜɟɥɢɱɢɧɚ ɡɧɚɱɟɧɢɟ ɤɨɬɨɪɨɣ ɡɚɜɢ ɫɢɬ ɬɨɥɶɤɨ ɨɬ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ ɬɨ ɟɫɬɶ ɩɪɢɧɢɦɚɟɬ ɨɩɪɟɞɟɥɟɧɧɨɟ ɨɞɢɧɚɤɨ ɜɨɟ ɡɧɚɱɟɧɢɟ ɜɫɹɤɢɣ ɪɚɡ ɤɨɝɞɚ ɫɢɫɬɟɦɚ ɧɚɯɨɞɢɬɫɹ ɜ ɡɚɞɚɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɧɟɡɚ ɜɢɫɢɦɨ ɨɬ ɫɩɨɫɨɛɚ ɤɨɬɨɪɵɦ ɷɬɨ ɫɨɫɬɨɹɧɢɟ ɞɨɫɬɢɝɧɭɬɨ
ǶȕșȌȔȝȏȇȒȢ ȉȎȇȏȓȕȋȌȐȘșȉȏȐ DZȕȒȏȞȌȘșȉȕ ȉȕȎȋȌȐȘșȉȏȦ
ɉɨɬɟɧɰɢɚɥɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɜ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɧɚɡɵɜɚɸɬ ɮɢɡɢɱɟɫɤɭɸ ɜɟɥɢɱɢɧɭ ɪɚɡɥɢɱɢɟ ɡɧɚɱɟɧɢɣ ɤɨɬɨɪɨɣ ɜɧɭɬɪɢ ɫɢɫɬɟɦɵ ɢ ɜ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɟ ɩɪɢɜɨɞɢɬ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣ Ʉɚɠɞɨɣ ɮɨɪɦɟ ɨɛɦɟɧɚ ɷɧɟɪɝɢɟɣɤɚɠɞɨɣ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ ɤɚɠɞɨɣ ɤɨɨɪɞɢɧɚɬɟ ɫɨɫɬɨɹɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɜɨɣ ɩɨɬɟɧɰɢɚɥ
Ɇɟɯɚɧɢɱɟɫɤɢɦ ɩɨɬɟɧɰɢɚɥɨɦ ɹɜɥɹɟɬɫɹ ɞɚɜɥɟɧɢɟ ɪ.
Ɍɟɩɥɨɜɵɦ ɩɨɬɟɧɰɢɚɥɨɦ ɹɜɥɹɟɬɫɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɬɟɦɩɟɪɚɬɭɪɚ Ɍ.
ɗɥɟɤɬɪɢɱɟɫɤɢɦ ɩɨɬɟɧɰɢɚɥɨɦ ɹɜɥɹɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ȿ ɏɢɦɢɱɟɫɤɢɦ ɩɨɬɟɧɰɢɚɥɨɦ ɹɜɥɹɸɬɫɹ ɫɜɨɣɫɬɜɚ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɝɟɧɬɨɜ
ɨɛɭɫɥɨɜɥɢɜɚɸɳɢɟ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɩɪɨɬɟɤɚɧɢɹ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ Ʉɨɥɢɱɟɫɬɜɨ ɜɨɡɞɟɣɫɬɜɢɹ ɤɨɥɢɱɟɫɬɜɨ ɷɧɟɪɝɢɢ ɩɟɪɟɞɚɧɧɨɟ ɜ ɥɸɛɨɦ
ɜɢɞɟ ɪɚɜɧɨ ɩɪɨɢɡɜɟɞɟɧɢɸ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɢɡɦɟɧɟɧɢɟ ɤɨɨɪɞɢɧɚɬɵ ɫɨɫɬɨɹɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɪɨɞɭ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
12
Ɇɟɯɚɧɢɱɟɫɤɚɹ ɪɚɛɨɬɚ ɫɨɜɟɪɲɚɟɦɚɹ ɡɚɤɪɵɬɨɣ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢ ɫɬɟɦɨɣɩɪɢɢɡɦɟɧɟɧɢɢɨɛɴɟɦɚ ɜɛɟɫɤɨɧɟɱɧɨɦɚɥɨɦɩɪɨɰɟɫɫɟɜɵɪɚɠɚɟɬɫɹɱɟɪɟɡ ɞɚɜɥɟɧɢɟ ɢ ɢɡɦɟɧɟɧɢɟ ɨɛɴɟɦɚ
|
GW = pdV |
|
ɉɪɢ ɤɨɧɟɱɧɨɦ ɩɪɨɰɟɫɫɟ ɤɨɥɢɱɟɫɬɜɨ ɪɚɛɨɬɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɧɬɟɝɪɢɪɨɜɚ ɧɢɟɦ ɷɬɨɝɨ ɜɵɪɚɠɟɧɢɹ
Ɍɟɩɥɨɬɚ Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɹɜɥɹɟɬɫɹ ɦɟɪɨɣ ɨɞɧɨɣ ɢɡ ɮɨɪɦ ɩɟɪɟɞɚɱɢ ɷɧɟɪɝɢɢ ɩɨɷɬɨɦɭ ɟɝɨ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɮɨɪɦɟ ɩɪɨɢɡɜɟɞɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɩɨ ɬɟɧɰɢɚɥɚ ɚɛɫɨɥɸɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ ɧɚ ɢɡɦɟɧɟɧɢɟ ɬɟɩɥɨɜɨɣ ɤɨɨɪɞɢɧɚɬɵ ɫɨɫɬɨɹɧɢɹ ɷɧɬɪɨɩɢɢ S ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɤɨɥɢ ɱɟɫɬɜɚ ɬɟɩɥɨɬɵ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɬɚɤ
|
G4= 7G6 |
|
ɉɨɥɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɜ ɤɚɤɨɦ ɥɢɛɨ ɩɪɨɰɟɫɫɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɧɬɟ ɝɪɚɥɨɦ ɨɬ ɷɬɨɝɨ ɜɵɪɚɠɟɧɢɹ
ɏɢɦɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ȼ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɟ ɩɪɢ ɮɚɡɨɜɵɯ ɢɥɢ ɯɢɦɢɱɟ ɫɤɢɯ ɩɪɟɜɪɚɳɟɧɢɹɯ ɩɪɨɢɫɯɨɞɢɬ ɨɛɦɟɧ ɷɧɟɪɝɢɟɣ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ ɱɚɫɬɹɦɢ ɫɢɫɬɟɦɵ ɩɨɞɫɢɫɬɟɦɚɦɢ ɂɦɟɹ ɜ ɜɢɞɭ ɱɬɨ ɩɨɬɟɧɰɢɚɥɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɹɜɥɹɟɬɫɹ ɯɢɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ȝi ɤɚɠɞɨɣ i ɣ ɩɨɞɫɢɫɬɟɦɵ ɚ ɤɨɨɪɞɢɧɚɬɨɣɫɨɫɬɨɹɧɢɹ ɱɢɫɥɨɦɨɥɟɣQi ɜɞɚɧɧɨɣɩɨɞɫɢɫɬɟɦɟ ɦɨɠɧɨɩɪɟɞɫɬɚ ɜɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɯɢɦɢɱɟɫɤɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɪɚɜɧɨɟ ɢɡɦɟɧɟɧɢɸ ɯɢɦɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɨɞɫɢɫɬɟɦɵ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ
|
GWxi = ȝidQi |
|
ɂɡɦɟɧɟɧɢɟ ɯɢɦɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜɫɟɣ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɵ ɫɨɫɬɨɹɳɟɣ ɢɡ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɦɟɠɞɭ ɫɨɛɨɣ ɩɨɞɫɢɫɬɟɦ ɛɭɞɟɬ ɨɱɟɜɢɞɧɨ ɪɚɜɧɨ ɫɭɦɦɟ ɢɡɦɟɧɟɧɢɣ ɯɢɦɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜɫɟɯ ɩɨɞɫɢɫɬɟɦ
|
dUx = 6GWxi = 6ȝidQi |
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ǩȔȚșȗȌȔȔȦȦ ȤȔȌȗȊȏȦ
Ɉɫɧɨɜɧɵɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɦ ɩɨɧɹɬɢɟɦ ɹɜɥɹɟɬɫɹ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ
ȼɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɷɬɨ ɷɧɟɪɝɢɹ ɜɫɟɯ ɜɢɞɨɜ ɞɜɢɠɟɧɢɹ ɦɢɤɪɨɱɚɫɬɢɰ ɫɨɫɬɚɜɥɹɸɳɢɯ ɫɢɫɬɟɦɭ ɚ ɬɚɤɠɟ ɷɧɟɪɝɢɹ ɢɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɫɨɛɨɣ ȼɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɷɧɟɪɝɢɣ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɜɪɚɳɚɬɟɥɶ ɧɨɝɨ ɢ ɤɨɥɟɛɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɣ ɦɨɥɟɤɭɥ ɷɧɟɪɝɢɢ ɦɟɠɦɨɥɟɤɭɥɹɪɧɨɝɨ ɢ ɜɧɭɬ ɪɢɦɨɥɟɤɭɥɹɪɧɨɝɨ ɜɧɭɬɪɢɚɬɨɦɧɨɝɨ ɢ ɜɧɭɬɪɢɹɞɟɪɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɢ ɞɪ
ɗɧɟɪɝɢɸ ɜɧɭɬɪɢɦɨɥɟɤɭɥɹɪɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɨ ɟɫɬɶ ɷɧɟɪɝɢɸ ɜɡɚɢ ɦɨɞɟɣɫɬɜɢɹ ɚɬɨɦɨɜ ɜ ɦɨɥɟɤɭɥɟ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɯɢɦɢɱɟɫɤɨɣ ɂɡɦɟɧɟɧɢɟ ɷɬɨɣ ɷɧɟɪɝɢɢ ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɢ ɯɢɦɢɱɟɫɤɢɯ ɩɪɟɜɪɚɳɟɧɢɹɯ
13
ȼɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɫɨɫɬɨɹɧɢɹ Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ ɱɬɨ ɢɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɯɚɪɚɤɬɟɪɚ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɡɧɨɫɬɶɸ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɜ ɤɨɧɟɱɧɨɦ U ɢ ɧɚɱɚɥɶɧɨɦ U1 ɫɨɫɬɨɹɧɢɹɯ
|
'U = U í U1. |
|
ȿɫɥɢ ɫɢɫɬɟɦɚ ɧɟ ɨɛɦɟɧɢɜɚɟɬɫɹ ɷɧɟɪɝɢɟɣ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ ɬɨ ɟɫɬɶ ɹɜɥɹɟɬɫɹ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɬɨ ɢɡɦɟɧɟɧɢɟ ɟɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɪɚɜɧɨ ɧɭɥɸ ɉɪɢ ɧɚɥɢɱɢɢ ɜ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɫɢɫɬɟɦɟ ɯɢɦɢɱɟɫɤɢɯ ɢɥɢ ɮɚɡɨɜɵɯ ɩɪɟɜɪɚɳɟ ɧɢɣ ɜ ɧɟɣ ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɟɜɪɚɳɟɧɢɟ ɨɞɧɨɣ ɮɨɪɦɵ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɢ ɯɢɦɢɱɟ ɫɤɨɣ ɜ ɞɪɭɝɢɟ ɢɥɢ ɨɞɧɨɝɨ ɜɢɞɚ ɷɧɟɪɝɢɢ ɜ ɞɪɭɝɢɟ
ȼ ɨɬɞɟɥɶɧɵɯ ɫɥɭɱɚɹɯ ɩɪɢ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɚɧɚɥɢɡɟ ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɭɱɢɬɵɜɚɬɶɩɨɬɟɧɰɢɚɥɶɧɭɸ ɢ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɫɢɫɬɟɦɵ ɜ ɰɟɥɨɦ ɉɨɬɟɧɰɢɚɥɶ ɧɚɹ ɷɧɟɪɝɢɹ ɨɛɭɫɥɨɜɥɟɧɚ ɩɨɥɨɠɟɧɢɟɦ ɫɢɫɬɟɦɵ ɜ ɩɨɥɟ ɜɧɟɲɧɢɯ ɫɢɥ ɧɚɩɪɢɦɟɪ ɜ ɩɨɥɟ ɫɢɥɵ ɬɹɠɟɫɬɢ Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɞɜɢɠɟɧɢɹ ɫɢ ɫɬɟɦɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɟɥ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɢ ɤɢ ɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɡɚɜɢɫɢɬ ɧɟ ɬɨɥɶɤɨ ɨɬ ɜɧɭɬɪɟɧɧɢɯ ɫɜɨɣɫɬɜ ɫɚɦɨɣ ɫɢɫɬɟɦɵ ɧɨ ɢ ɨɬ ɫɜɨɣɫɬɜ ɬɟɥ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɩɨɷɬɨɦɭ ɨɧɢ ɧɟ ɜɯɨɞɹɬ ɜ ɫɨɫɬɚɜ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ
ǶȌȗȉȢȐ ȎȇȑȕȔ șȌȗȓȕȋȏȔȇȓȏȑȏ
ȼɨɫɧɨɜɟ ɩɟɪɜɨɝɨɡɚɤɨɧɚɬɟɪɦɨɞɢɧɚɦɢɤɢ ɤɚɤɢ ɡɚɤɨɧɚɫɨɯɪɚɧɟɧɢɹ ɢ ɩɪɟ ɜɪɚɳɟɧɢɹ ɷɧɟɪɝɢɢ ɥɟɠɢɬ ɩɪɢɧɰɢɩ ɷɤɜɢɜɚɥɟɧɬɧɨɫɬɢ ɪɚɡɥɢɱɧɵɯ ɮɨɪɦ ɞɜɢɠɟ ɧɢɹ ɦɚɬɟɪɢɢ ɜɢɞɨɜ ɷɧɟɪɝɢɢ ɍɫɬɚɧɨɜɥɟɧɨ ɱɬɨ ɪɚɡɥɢɱɧɵɟ ɮɨɪɦɵ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɢ ɬɟɩɥɨɜɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɯɢɦɢɱɟɫɤɚɹ ɢ ɬ ɩ ɦɟɪɨɣ ɤɨɬɨɪɵɯ ɹɜɥɹɸɬɫɹ ɤɨɥɢɱɟɫɬɜɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɢɞɨɜ ɪɚɛɨɬɵ ɢ ɬɟɩɥɨɬɵ ɦɨ ɝɭɬ ɩɟɪɟɯɨɞɢɬɶ ɜ ɞɪɭɝɢɟ ɮɨɪɦɵ ɜ ɫɬɪɨɝɨ ɨɩɪɟɞɟɥɟɧɧɵɯ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɤɨɥɢ ɱɟɫɬɜɚɯ ɧɟ ɡɚɜɢɫɹɳɢɯ ɧɢ ɨɬ ɯɚɪɚɤɬɟɪɚ ɩɪɨɰɟɫɫɚ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɧɢ ɨɬ ɭɫɥɨ ɜɢɣ ɟɝɨ ɩɪɨɬɟɤɚɧɢɹ
ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɢ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɟ ɤɨ ɬɨɪɵɟ ɨɛɦɟɧɢɜɚɸɬɫɹ ɷɧɟɪɝɢɟɣ ɦɟɠɞɭ ɫɨɛɨɣ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɭɬɜɟɪ ɠɞɚɟɬ ɱɬɨ ɢɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɪɚɜɧɨ ɢɡɦɟɧɟɧɢɸ ɷɧɟɪɝɢɢ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɜɡɹɬɨɦɭ ɫ ɨɛɪɚɬɧɵɦ ɡɧɚɤɨɦ
Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɫɱɢɬɚɸɬ ɩɨɥɨɠɢɬɟɥɶɧɵɦ ɟɫɥɢ ɨɧɨ ɭɜɟɥɢɱɢɜɚɟɬ ɜɧɭɬɪɟɧɧɸɸɷɧɟɪɝɢɸɫɢɫɬɟɦɵ ɬɨɟɫɬɶ ɤɨɝɞɚɬɟɩɥɨɬɚ©ɩɨɞɜɨɞɢɬɫɹªɤɫɢɫɬɟɦɟ Ɋɚɛɨɬɭ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɪɨɞɚ ɩɪɢɧɹɬɨ ɫɱɢɬɚɬɶ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɟɫɥɢ ɨɧɚ ɩɪɢɜɨ ɞɢɬɤɭɦɟɧɶɲɟɧɢɸɜɧɭɬɪɟɧɧɟɣɷɧɟɪɝɢɢɫɢɫɬɟɦɵ ɬɨɟɫɬɶɪɚɛɨɬɚ©ɫɨɜɟɪɲɚɟɬɫɹª ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɨɣ ɧɚɞ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ
ɋ ɭɱɟɬɨɦ ɩɪɚɜɢɥɚ ɡɧɚɤɨɜ ɩɟɪɜɵɣ ɡɚɤɨɧ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɞɥɹ ɢɡɨɥɢɪɨɜɚɧ ɧɨɣ ɫɢɫɬɟɦɵ ɦɨɠɟɬ ɛɵɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɢ ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ
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'8 4 í W í 6Ai |
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14
ɝɞɟ Q ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ
: ɤɨɥɢɱɟɫɬɜɨ ɦɟɯɚɧɢɱɟɫɤɨɣ ɪɚɛɨɬɵ
6Ai ɫɭɦɦɚ ɤɨɥɢɱɟɫɬɜ ɧɟɦɟɯɚɧɢɱɟɫɤɢɯ ɪɚɛɨɬ ɪɚɡɧɨɝɨ ɪɨɞɚ ɷɥɟɤɬɪɢɱɟ ɫɤɨɣ ɯɢɦɢɱɟɫɤɨɣ ɢ ɬ ɩ
ȼ ɩɪɢɦɟɧɟɧɢɢ ɤ ɬɟɪɦɨɦɟɯɚɧɢɱɟɫɤɨɣ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɫɢɫɬɟɦɟ ɩɟɪɜɵɣ ɡɚ
ɤɨɧ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ ɭɪɚɜɧɟɧɢɹ |
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G8 = GQ í G: |
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ɢ ɮɨɪɦɭɥɢɪɭɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ ɢɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɬɟɪɦɨ ɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɪɚɜɧɨ ɪɚɡɧɨɫɬɢ ɦɟɠɞɭ ɤɨɥɢɱɟɫɬɜɨɦ ɬɟɩɥɨɬɵ ɩɨɞɜɟ ɞɟɧɧɨɣ ɤ ɫɢɫɬɟɦɟ ɢ ɤɨɥɢɱɟɫɬɜɨɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɪɚɛɨɬɵ ɫɨɜɟɪɲɟɧɧɨɣ ɫɢɫɬɟ ɦɨɣ
ǵȘȔȕȉȔȕȌ ȚȗȇȉȔȌȔȏȌ ȘȕȘșȕȦȔȏȦ
ȼɵɪɚɠɟɧɢɹ ɫɜɹɡɵɜɚɸɳɢɟɡɧɚɱɟɧɢɹɥɸɛɨɣɢɡɮɭɧɤɰɢɣɫɨɫɬɨɹɧɢɹɫɨɡɧɚ ɱɟɧɢɹɦɢ ɤɨɨɪɞɢɧɚɬ ɫɨɫɬɨɹɧɢɹ ɟɫɬɶ ɨɞɧɨɡɧɚɱɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɬɟɪɦɨ ɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ 8 8 S V … Ɍ 7 S V ɪ = p S V … ɢ ɬ ɩ ȿɫɥɢ ɞɥɹ ɩɪɨɫɬɨɣ ɬɟɪɦɨɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɢɡ ɭɪɚɜɧɟɧɢɹ Ɍ 7 S V ɜɵɪɚɡɢɬɶ ɷɧɬɪɨɩɢɸ ɱɟɪɟɡ ɬɟɦɩɟɪɚɬɭɪɭ ɢ ɨɛɴɟɦ 6 6 T V ɬɨ ɦɨɠɟɦ ɩɨɥɭɱɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɫɜɹɡɵɜɚɸɳɭɸ ɦɟɠɞɭ ɫɨɛɨɣ ɬɟ ɩɚɪɚɦɟɬɪɵ ɫɢɫɬɟɦɵ ɤɨɬɨɪɵɟ ɦɨ
ɝɭɬ ɛɵɬɶ ɢɡɦɟɪɟɧɵ
p S V = p[S T V V] = p T V
ɢɥɢ
f p V T .
ɋɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ ɜ ɬɚɤɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɸɛɨɣ ɩɚɪɨɣ ɩɚɪɚɦɟɬ ɪɨɜ ɬɨ ɟɫɬɶ ɥɸɛɵɟ ɞɜɚ ɩɚɪɚɦɟɬɪɚ ɢɡ ɬɪɟɯ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɜ ɤɚɱɟɫɬɜɟ ɧɟɡɚɜɢɫɢɦɵɯ ɩɟɪɟɦɟɧɧɵɯ
ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɵɦɢ ɫɜɨɣɫɬɜɚɦɢ ɨɛɥɚɞɚɸɬ ɜɟɳɟɫɬɜɚ ɜ ɝɚɡɨɨɛɪɚɡɧɨɦ ɫɨ ɫɬɨɹɧɢɢ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɧɢɡɤɢɯ ɞɚɜɥɟɧɢɹɯ ɢ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɢɯ ɬɟɦɩɟɪɚɬɭ ɪɚɯ ɉɪɢ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɫɜɨɣɫɬɜɚ ɜɫɟɯ ɝɚɡɨɜ ɜɟɫɶɦɚ ɫɯɨɠɢ ɢ ɢɯ ɫɨɫɬɨɹɧɢɟ ɨɩɢ ɫɵɜɚɟɬɫɹ ɨɞɢɧɚɤɨɜɵɦ ɞɥɹ ɜɫɟɯ ɝɚɡɨɜ ɭɪɚɜɧɟɧɢɟɦ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚɭɪɚɜɧɟɧɢɟɦ Ʉɥɚɩɟɣɪɨɧɚ Ɇɟɧɞɟɥɟɟɜɚ
pV = RT
ɝɞɟ V ɨɛɴɟɦ ɤɦɨɥɹ ɜɟɳɟɫɬɜɚ ɦ ɤɦɨɥɶ;
R = ɤȾɠ ɤɦɨɥɶǜɄ ɭɧɢɜɟɪɫɚɥɶɧɚɹɝɚɡɨɜɚɹɩɨɫɬɨɹɧɧɚɹ ɨɞɢɧɚɤɨɜɚɹ ɞɥɹ ɜɫɟɯ ɝɚɡɨɜ
ɍɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɩɪɟɞɥɨɠɟɧɧɵɟ ɞɥɹ ɪɟɚɥɶɧɵɯ ɝɚɡɨɜ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɩɨ ɫɭɳɟɫɬɜɭ ɦɨɞɢɮɢɤɚɰɢɢ ɭɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɧɚɩɪɢɦɟɪ ɭɪɚɜɧɟɧɢɟ ȼɚɧ ɞɟɪ ȼɚɚɥɶɫɚ
15
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a · |
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¨ p |
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V b |
RT |
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© |
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ɂɥɢ ɭɪɚɜɧɟɧɢɟ Ʉɚɦɟɪɥɢɧɝ Ɉɧɧɟɫɚ Ɉɧɨ ɜɵɪɚɠɚɟɬ ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɭɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɜ ɜɢɞɟ ɛɟɫɤɨɧɟɱɧɨɝɨ ɫɬɟɩɟɧɧɨɝɨ ɪɹɞɚ ɩɨ ɩɥɨɬɧɨɫɬɢ
RT Bp Cp Dp
ɝɞɟ ȼ ɋ D ... ɜɬɨɪɨɣ ɬɪɟɬɢɣ ɱɟɬɜɟɪɬɵɣ ɢ ɬ ɞ ɤɨɷɮɮɢɰɢɟɧɬɵ ɡɚɜɢɫɹɳɢɟ ɨɬ ɬɟɦ ɩɟɪɚɬɭɪɵ ɢ ɩɪɢɪɨɞɵ ɝɚɡɚ ɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ
ȼ ɯɢɦɢɱɟɫɤɨɣ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɤ ɝɚɡɨɨɛɪɚɡɧɵɦ ɜɟɳɟɫɬɜɚɦ ɨɛɵɱɧɨ ɩɪɢ ɦɟɧɹɸɬ ɡɚɤɨɧɵ ɢɞɟɚɥɶɧɵɯ ɝɚɡɨɜ ɗɬɨ ɭɩɪɨɳɚɟɬ ɪɚɫɱɟɬɵ ɢ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɨɥɭ ɱɟɧɢɟ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ
ɉɨɫɤɨɥɶɤɭ ɢɡɦɟɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɵ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɢɡ ɦɟɧɟɧɢɟɦ ɤɨɥɢɱɟɫɬɜɚ ɦɚɫɫɵ ɜɟɳɟɫɬɜɚ ɜ ɨɬɞɟɥɶɧɵɯ ɟɟ ɫɨɫɬɚɜɥɹɸɳɢɯ ɬɨ ɞɥɹ ɩɨɥɧɨɣɯɚɪɚɤɬɟɪɢɫɬɢɤɢɫɨɫɬɨɹɧɢɹɫɢɫɬɟɦɵɧɟɨɛɯɨɞɢɦɨɩɨɦɢɦɨɬɟɪɦɨɦɟɯɚɧɢ ɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬ S ɢ V ɭɤɚɡɵɜɚɬɶ ɬɚɤɠɟ ɜɫɟ ɯɢɦɢɱɟɫɤɢɟ ɤɨɨɪɞɢɧɚɬɵ ɫɨɫɬɨ ɹɧɢɹ
ɋɨɫɬɚɜ ɫɥɨɠɧɨɣ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧ ɪɚɡ ɥɢɱɧɵɦɢ ɫɩɨɫɨɛɚɦɢ ɨɫɧɨɜɧɵɦ ɢɡ ɤɨɬɨɪɵɯ ɩɪɢɧɹɬɨ ɨɩɪɟɞɟɥɟɧɢɟ ɫɨɫɬɚɜɚ ɫɢ ɫɬɟɦɵ ɩɨ ɱɢɫɥɭ ɦɨɥɟɣ ɫɨɫɬɚɜɥɹɸɳɢɯ ɫɢɫɬɟɦɵ Qi.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɭɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɵ ɫɜɹɡɵɜɚɟɬ ɮɭɧɤ ɰɢɸ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ ɧɟ ɬɨɥɶɤɨ ɫ ɞɜɭɦɹ ɬɟɪɦɨɦɟɯɚɧɢɱɟɫɤɢɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɨɩɪɟɞɟɥɹɸɳɢɦɢ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ ɜ ɩɪɨɰɟɫɫɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɟɟ ɫ ɨɤɪɭɠɚ ɸɳɟɣ ɫɪɟɞɨɣ ɧɨ ɢ ɫɨ ɡɧɚɱɟɧɢɹɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɨɫɬɚɜɚ ɞɥɹ ɜɫɟɯ ɫɨɫɬɚɜɥɹ ɸɳɢɯ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɸɳɢɯ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ ɩɪɢ ɮɚɡɨɜɨɦ ɢɥɢ ɯɢɦɢɱɟɫɤɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɦɟɠɞɭ ɟɟ ɫɨɫɬɚɜɥɹɸɳɢɦɢ ɜɧɭɬɪɢ ɫɢɫɬɟɦɵ ɧɚɩɪɢɦɟɪ
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pV = nRT |
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n 6Qi – ɤɨɥɢɱɟɫɬɜɨ ɦɨɥɟɣ ɜɟɳɟɫɬɜɚ ɜ ɫɢɫɬɟɦɟ
ǹȌȗȓȕȋȏȔȇȓȏȞȌȘȑȏȐ ȖȗȕȝȌȘȘ
ɋ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɜ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɫɢɫɬɟɦɟ ɩɪɟɤɪɚɳɚɸɬɫɹ ɜɫɹɤɢɟ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɟ ɢɡɦɟɧɟɧɢɹ ɢ ɡɧɚɱɟɧɢɟ ɥɸɛɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ ɜ ɤɚɠ ɞɨɣ ɬɨɱɤɟ ɫɢɫɬɟɦɵ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ Ɍɚɤɨɟ ɫɨɫɬɨɹɧɢɟ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɫɢ ɫɬɟɦɵ ɧɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɜɟɫɧɵɦ
Ɇɚɬɟɦɚɬɢɱɟɫɤɢɣ ɚɩɩɚɪɚɬ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɨɫɧɨɜɵɜɚɟɬɫɹ ɧɚ ɪɚɫɫɦɨɬɪɟ ɧɢɢ ɬɨɥɶɤɨ ɫɢɫɬɟɦ ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɪɚɜɧɨɜɟɫɧɵɯ ɫɨɫɬɨɹɧɢɹɯ ɩɪɢ ɤɨɬɨɪɵɯ ɡɧɚ ɱɟɧɢɹ ɥɸɛɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ ɞɚɜɥɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɚ ɢ ɬ ɩ ɨɞɢɧɚɤɨɜɨ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɫɢɫɬɟɦɵ ɗɬɨ ɨɛɭɫɥɚɜɥɢɜɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɡ ɦɟɪɟɧɧɵɯ ɡɧɚɱɟɧɢɣ
16
Ɋɚɜɧɨɜɟɫɧɵɦ ɢɥɢ ɨɛɪɚɬɢɦɵɦ ɧɚɡɵɜɚɟɬɫɹ ɩɪɨɰɟɫɫ ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣɧɟɩɪɟɪɵɜɧɭɸɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɪɚɜɧɨɜɟɫɧɵɯɫɨɫɬɨɹɧɢɣ ɩɪɢɤɨɬɨɪɨɦ ɫɢɫɬɟɦɚ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɧɚɯɨɞɢɬɫɹ ɜ ɪɚɜɧɨɜɟɫɧɨɦ ɫɨɫɬɨɹɧɢɢ
Ɋɚɜɧɨɜɟɫɧɵɣ ɩɪɨɰɟɫɫ ɩɪɨɬɟɤɚɟɬ ɛɟɫɤɨɧɟɱɧɨ ɦɟɞɥɟɧɧɨ ɂɡɦɟɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɪɚɜɧɨɜɟɫɧɨɣ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɜ ɪɟ
ɡɭɥɶɬɚɬɟɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɟɟɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɧɚɷɥɟɦɟɧ ɬɚɪɧɨɦ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ ɢ ɧɚɡɵɜɚɟɬɫɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɦ ɩɪɨɰɟɫɫɨɦ
ȼ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɜ ɬɟɱɟɧɢɟ ɩɪɨɰɟɫɫɚ ɩɚɪɚɦɟɬɪɵ ɫɨɫɬɨɹɧɢɣ ɩɪɨɫɬɨɣ ɬɟɪɦɨɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɭɪɚɜɧɟɧɢɸ ɫɨɫɬɨɹɧɢɹ
ǵȘȔȕȉȔȕȌ ȚȗȇȉȔȌȔȏȌ ȖȗȕȝȌȘȘȇ
ȼɵɪɚɠɚɹ ɤɨɥɢɱɟɫɬɜɚ ɪɚɛɨɬɵ ɢ ɬɟɩɥɨɬɵ ɱɟɪɟɡ ɩɚɪɚɦɟɬɪɵ ɫɨɫɬɨɹɧɢɹ ɜ ɭɪɚɜɧɟɧɢɢ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɞɥɹ ɩɪɨɫɬɨɣ ɬɟɪɦɨɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜ ɩɪɢɦɟɧɟɧɢɢ ɤ ɪɚɜɧɨɜɟɫɧɵɦ ɩɪɨɰɟɫɫɚɦ ɭɪɚɜɧɟɧɢɟ ɜ ɜɢɞɟ
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dU = TdS í pdV. |
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ɗɬɨ ɜɵɪɚɠɟɧɢɟ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɩɪɨɰɟɫɫɚ ȼ ɥɢɬɟɪɚɬɭɪɟ ɩɨ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɨɧɨ ɧɟɪɟɞɤɨ ɧɚɡɵɜɚɟɬɫɹ ɨɫɧɨɜɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɬɟɪɦɨɞɢɧɚ ɦɢɤɢ
ȼ ɫɥɨɠɧɨɣ ɬɟɪɦɨɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɩɨɦɢɦɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɟɟ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ ɢɦɟɸɬ ɦɟɫɬɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ ɫɨɫɬɚɜɥɹɸɳɢɦɢ ɫɢɫɬɟɦɵ ɩɨɞɫɢɫɬɟɦɚɦɢ ɫɥɟɞɫɬɜɢɟɦ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɢɡɦɟɧɟɧɢɟ ɯɢɦɢɱɟɫɤɨɣ ɢɥɢ ɮɚɡɨɜɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ
ȄȔșȇȒȣȖȏȦ
ȼ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɟɳɟ ɨɞɧɚ ɮɭɧɤɰɢɹ ɫɨɫɬɨɹɧɢɹ – ɷɧɬɚɥɶ ɩɢɹ ɪɨɥɶ ɤɨɬɨɪɨɣ ɨɫɨɛɟɧɧɨ ɜɚɠɧɚ ɩɪɢ ɚɧɚɥɢɡɟ ɨɬɤɪɵɬɵɯ ɫɢɫɬɟɦ
ɗɧɬɚɥɶɩɢɟɣ ɧɚɡɵɜɚɟɬɫɹ ɜɟɥɢɱɢɧɚ ɪɚɜɧɚɹ ɫɭɦɦɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɫɢ ɫɬɟɦɵ ɢ ɩɪɨɢɡɜɟɞɟɧɢɹ ɞɚɜɥɟɧɢɹ ɧɚ ɭɞɟɥɶɧɵɣ ɨɛɴɟɦ
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H = U + pV. |
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ɂɡɦɟɧɟɧɢɟ ɷɧɬɚɥɶɩɢɢ ɜɵɪɚɠɚɟɬ ɫɨɛɨɣ ɢɡɦɟɧɟɧɢɟ ɷɧɟɪɝɢɢ ɨɬɤɪɵɬɨɣ ɫɢɫɬɟɦɵ ɩɪɢ ɜɜɨɞɟ ɜɵɜɨɞɟ ɜ ɧɟɟ ɟɞɢɧɢɰɵ ɦɚɫɫɵ ɛɟɡ ɭɱɟɬɚ ɜɧɟɲɧɟɣ ɷɧɟɪɝɢɢ ɜɜɨɞɢɦɨɣ ɦɚɫɫɵɤɢɧɟɬɢɱɟɫɤɨɣ ɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣ
ɉɪɨɞɢɮɮɟɪɟɧɰɢɪɭɟɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɷɧɬɚɥɶɩɢɢ ɢ ɩɨɞɫɬɚɜɢɦ dU ɢɡ ɨɫ ɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɬɟɪɦɨɞɢɧɚɦɢɤɢ
dH = dU + d pV TdS í pdV + pdV + Vdp = TdS + Vdp. |
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17
ȼ ɞɚɥɶɧɟɣɲɟɦ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɮɨɪɦɭɥɭ ɫɜɹɡɵɜɚɸɳɭɸ ɷɧɬɚɥɶɩɢɸ ɢ ɜɧɭɬɪɟɧɧɸɸ ɷɧɟɪɝɢɸ
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dH = dU + d pV |
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ɢ ɫ ɭɱɟɬɨɦ ɭɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ |
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' pV 'Q RT ɢ 'H 'U RT 'Q |
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ɝɞɟ 'Q ɢɡɦɟɧɟɧɢɟ ɫɨɫɬɚɜɚ ɫɢɫɬɟɦɵ ɢɡɦɟɧɟɧɢɟ ɱɢɫɥɚ ɦɨɥɟɣ ɜ ɯɨɞɟ ɯɢɦɢɱɟ ɫɤɨɣ ɪɟɚɤɰɢɢ .
ǹȌȖȒȕȌȓȑȕȘșȣ
Ɍɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɱɬɨ ɷɧɬɪɨɩɢɹ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡɦɟ ɪɟɧɚ ɫɨɡɞɚɟɬ ɜ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɧɟɤɨɬɨɪɵɟ ɨɫɥɨɠɧɟɧɢɹ
ȼɨ ɩɟɪɜɵɯ ɩɪɢɯɨɞɢɬɫɹ ɨɬɤɚɡɚɬɶɫɹ ɨɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɧɬɪɨɩɢɢ ɜ ɤɚɱɟ ɫɬɜɟɧɟɡɚɜɢɫɢɦɨɣɩɟɪɟɦɟɧɧɨɣ ɧɟɫɦɨɬɪɹɧɚɬɨ ɱɬɨɨɧɚɩɨɫɜɨɟɦɭɮɢɡɢɱɟɫɤɨɦɭ ɫɦɵɫɥɭ ɬɟɩɥɨɜɚɹ ɤɨɨɪɞɢɧɚɬɚ ɫɨɫɬɨɹɧɢɹ ɜɦɟɫɬɟ ɫ ɞɪɭɝɢɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ ɫɨ ɫɬɨɹɧɢɹ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ
ȼɨ ɜɬɨɪɵɯ ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɤɨɥɢɱɟɫɬɜɚ ɬɟɩ ɥɨɬɵ ɛɟɡ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɧɬɪɨɩɢɢ
Ȼɵɥɨ ɜɜɟɞɟɧɨ ɜɵɪɚɠɟɧɢɟ ɫɜɹɡɵɜɚɸɳɟɟ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɫ ɢɡɦɟɧɟ ɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ
įQ = CdT. |
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Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɋ ɜ ɷɬɨɦ ɜɵɪɚɠɟɧɢɢ ɩɨɥɭɱɢɥ ɧɚɡɜɚ ɧɢɟ ɬɟɩɥɨɟɦɤɨɫɬɢ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɬɟɩɥɨɟɦɤɨɫɬɶ ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɤɚɤ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɤɨɬɨɪɨɟ ɧɟɨɛɯɨɞɢɦɨ ɫɨɨɛɳɢɬɶ ɬɟɥɭ ɱɬɨɛɵ ɢɡɦɟɧɢɬɶ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɭ ɧɚ Ʉ Ɍɟɩɥɨɟɦɤɨɫɬɶ ɟɞɢɧɢɰɵ ɤɨɥɢɱɟɫɬɜɚ ɜɟɳɟɫɬɜɚ ɧɚɡɵɜɚɟɬɫɹ ɭɞɟɥɶɧɨɣ ɬɟɩɥɨɟɦɤɨɫɬɶɸ ȼ ɯɢɦɢɱɟɫɤɨɣ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɸɬ ɭɞɟɥɶɧɭɸɦɨɥɹɪɧɭɸɬɟɩɥɨɟɦɤɨɫɬɶ ɟɞɢɧɢɰɚɢɡɦɟɪɟɧɢɹɤɨɬɨɪɨɣȾɠ ɤɦɨɥɶ·Ʉ
Ɋɚɡɥɢɱɚɸɬ ɢɫɬɢɧɧɭɸ ɬɟɩɥɨɟɦɤɨɫɬɶ ɩɪɟɞɫɬɚɜɥɹɸɳɭɸ ɫɨɛɨɣ ɨɬɧɨɲɟ ɧɢɟ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɬɟɩɥɨɬɵ ɤ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɨɦɭ ɢɡɦɟɧɟɧɢɸ ɬɟɦ ɩɟɪɚɬɭɪɵ
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C = GQ dT |
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ɢ ɫɪɟɞɧɸɸ ɬɟɩɥɨɟɦɤɨɫɬɶ ɨɬɧɨɲɟɧɢɟ ɩɨɥɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɬɟɩɥɨɬɵ ɤ ɩɨɥɧɨɦɭ ɢɡɦɟɧɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɛɥɸɞɚɟɦɨɦɭ ɜ ɞɚɧɧɨɦ ɩɪɨɰɟɫɫɟ
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Q |
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C |
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'T |
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ɋɜɹɡɶ ɦɟɠɞɭ ɢɫɬɢɧɧɨɣ ɢ ɫɪɟɞɧɟɣ ɭɞɟɥɶɧɨɣ ɬɟɩɥɨɟɦɤɨɫɬɶɸ ɭɫɬɚɧɚɜɥɢɜɚ ɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ
18
T
³ɋ G7
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T1 |
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ɋ |
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'T |
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Ɉɫɨɛɭɸ ɪɨɥɶ ɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɚɧɚɥɢɡɟ ɜɵɩɨɥɧɹɸɬ ɬɟɩɥɨɟɦɤɨɫɬɢ ɫɢɫɬɟɦ ɜ ɩɪɨɰɟɫɫɚɯ ɩɪɨɢɫɯɨɞɹɳɢɯ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ ɋv ɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ ɋɪ Ɍɟɩɥɨɟɦɤɨɫɬɢ ɋv ɢ ɋɪ ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɹɦɢ ɫɨɫɬɨɹɧɢɹ
ɗɬɨ ɥɟɝɤɨ ɩɨɤɚɡɚɬɶ ɧɚ ɩɪɢɦɟɪɟ ɋv ȼɵɪɚɠɚɹ ɢɡ ɭɪɚɜɧɟɧɢɹ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢ ɧɚɦɢɤɢ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ
dQv G8 S G9 v G8v
ɢ ɩɨɞɫɬɚɜɥɹɹ ɟɝɨ ɜ ɢɫɯɨɞɧɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɬɟɩɥɨɟɦɤɨɫɬɢ ɩɨɥɭɱɚɟɦ
Cv |
dQv |
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dUv |
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dTv |
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dTv |
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ɇɨ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɫɨɫɬɨɹɧɢɹ ɢ ɜ ɩɪɨɫɬɨɣ ɬɟɪɦɨɦɟɯɚɧɢɱɟ ɫɤɨɣ ɫɢɫɬɟɦɟ ɮɭɧɤɰɢɟɣ ɞɜɭɯ ɧɟɡɚɜɢɫɢɦɵɯ ɩɟɪɟɦɟɧɧɵɯ ɨɩɪɟɞɟɥɹɸɳɢɯ ɟɟ ɫɨɫɬɨɹ ɧɢɟ ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɬɟɩɥɨɟɦɤɨɫɬɶ ɋv ɬɨɠɟ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɫɨɫɬɨɹɧɢɹ
Ɍɟɩɥɨɟɦɤɨɫɬɢ ɋɪ ɢ ɋv ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɤɚɤ ɢ ɟɝɨ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɡɚ ɜɢɫɹɬ ɬɨɥɶɤɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɗɬɢ ɡɚɜɢɫɢɦɨɫɬɢ ɧɚɣɞɟɧɧɵɟ ɨɩɵɬɧɵɦ ɩɭɬɟɦ ɩɪɟɞɫɬɚɜɥɹɸɬɫɹ ɜ ɜɢɞɟ ɦɧɨɝɨɱɥɟɧɨɜ ɧɚɡɵɜɚɟɦɵɯ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɟ ɭɪɚɜ ɧɟɧɢɹ
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C = D + ET + JTx + GTy |
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ɝɞɟ Į ȕ Ȗ į ɩɨɫɬɨɹɧɧɵɟɤɨɷɮɮɢɰɢɟɧɬɵ ɢɦɟɸɳɢɟɪɚɡɧɵɟɡɧɚɱɟɧɢɹɞɥɹɪɚɡ ɥɢɱɧɵɯ ɝɚɡɨɜ;
ɯ ɭ ɩɨɤɚɡɚɬɟɥɢ ɫɬɟɩɟɧɢ
ɂɫɩɨɥɶɡɭɹ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɞɢɮɮɟɪɟɧɰɢɚɥɚ ɷɧɬɪɨɩɢɢ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɭɪɚɜɧɟɧɢɟ ɨɩɪɟɞɟɥɹɸɳɟɟɬɟɩɥɨɟɦɤɨɫɬɶɜɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦɩɪɨɰɟɫɫɟ ɉɨɞ ɫɬɚɜɢɜ ɜ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɬɟɩɥɨɟɦɤɨɫɬɢ
ɋ GdTQ TdSdT
ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɹ ɜ ɧɟɡɚɜɢɫɢɦɵɯ ɩɟɪɟɦɟɧɧɵɯ T ɢ V
T § wp · dV ɋ ɋv ¨©wT ¸¹v dT
ɢ ɜ ɧɟɡɚɜɢɫɢɦɵɯ ɩɟɪɟɦɟɧɧɵɯ Ɍ ɢ ɪ
§ wV · dp ɋ ɋp 7¨© wT ¸¹p dT
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ɨɬɤɭɞɚ |
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§ wp · |
§wV · |
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ɋp ɋv |
T ¨ |
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¸ |
¨ |
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¸ . |
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©wT ¹v © wT ¹p |
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ɂɡ ɭɪɚɜɧɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ pV = RT ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ
Ɇɚɣɟɪɚ |
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ɋp ɋv R. |
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ǩȢȗȇȍȌȔȏȌ ȏȎȓȌȔȌȔȏȐ ©U ȏ ©H ȞȌȗȌȎ șȌȖȒȕȌȓȑȕȘșȏ
Ɋɚɫɫɦɨɬɪɢɦ ɨɫɧɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɞɥɹ ɡɚɤɪɵɬɨɣ ɢ ɨɬɤɪɵ
ɬɨɣ ɫɢɫɬɟɦ: |
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dU = TdS í pdV = dQ í pdV |
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dH = TdS + Vdp = dQ í Vdp. |
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ɉɪɢ V = const ɞɥɹ ɡɚɦɤɧɭɬɨɣ ɫɢɫɬɟɦɵ ɢɦɟɟɦ |
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Cv |
dU |
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dT |
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ɢ ɩɪɢ p = const ɞɥɹ ɨɬɤɪɵɬɨɣ ɫɢɫɬɟɦɵ |
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Cp |
dH |
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ɨɬɤɭɞɚ |
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dU = CvdT |
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dH = CpdT |
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ɢ ɞɥɹ ɤɨɧɟɱɧɵɯ ɢɧɬɟɪɜɚɥɨɜ ɫɪɟɞɧɢɯ ɬɟɩɥɨɟɦɤɨɫɬɟɣ ɢ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ |
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'U |
'T ¦ Q |
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v i |
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C |
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i |
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'H |
'T ¦ Q |
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p i |
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C |
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i |
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DZ ȗȇȘȞȌșȚ șȌȖȒȕȌȓȑȕȘșȌȐ |
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Ⱦɥɹ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ ɢ ɧɟɤɨɬɨɪɵɯ ɝɨɪɸɱɢɯ ɷɦɩɢɪɢɱɟɫɤɚɹ ɮɨɪɦɭɥɚ |
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ɞɥɹ ɪɚɫɱɟɬɚ ɬɟɩɥɨɟɦɤɨɫɬɢ ɢɦɟɟɬ ɜɢɞ |
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Cɪ = a + bT + c T . |
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20 |
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