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مثـال دالة هاميلتون (Info)


في الميكانيكا نستنبط معادلة هاميلتون من معادلة لاغرانج عن طريق استخدام تحويل ليجاندر:

وفي الترموديناميكا يمكننا عن طريق تحويل ليجاندر استنباط الجهد الترمويناميكي من المعادلات الأساسية للترموديناميكا. عندئذ يمكن الانتقال من الطاقة الداخلية U (وهي تعتمد على الإنتروبيا) S إلى طاقة هيلمهولتز F التي تعتمد على درجة الحرارة T:

وهنا يختص تفاضل المعادلة (U(S,V,N بانسبة لإنتروبيا S, حيث نضع كلا من V و N كثوابت .

بالمثل نستخدمها عند دراسة جهد ترموديناميكي وتحوله إلى جهد آخر، مثلما يحدث عند الانتقال من الإنثالبي H إلى طاقة جيبس G:

وبالمثل نستطيع الحصول على جهود ترموديناميكية أخرى أننا عن طريق تحويل ليجاندر نستطيع الانتقال إلى إحداثيات معممة والتي عن طريقها يمكننا استبدالها بالقوة الترموديناميكية المقترنة.

Source: wikipedia.org
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Mustafa Mahmoud The Words Of God Almighty Ibrahim AlFiqi Muhammad Bin Saleh AlUthaymeen Ibn Qayyim Al-Jawziyya Ahmed Khaled Tawfiq Fahad Amer AlAhmadi Muhammad Metwally AlShaarawi Ali Bin Jaber AlFifi Dale Carnegie Islam Gamal Sayed Qutb Muhammad AlGhazali Omar AlHourani Agatha Christie Muhammad Bin Ismail AlBukhari Abbas AlAkkad Abu Hamid AlGhazali Najib Mahfouz Jalal AlDin AlSuyuti Fyodor Dostoevsky Bin Taymiyyah Ismail Bin Omar Bin Katheer AlQurashi Aldamashqiu Ibrahim Al-Sukran Mustafa AlAdawi More of Authors of books