Các nguyên tắc cơ bản của nhiệt động lực học đã được phát triển trong thế kỷ 19 trên nền tảng của hai tiên đề chủ yếu, bổ sung một số lượng nhỏ của các định nghĩa, và cân bằng vật lý mà không cần sử dụng bất kỳ mô hình đơn giản hóa hoặc đào sâu vào lý thuyết về cấu trúc phân tử. | Again consider a system constrained to constant total volume and to have a uniform temperature. Then as before we can write the total change in entropy that might result from a change in volume of either part in the form T V dS 1 dV1 dV1 dV1 1 dV1 1 and because total volume is constant dV1 - dV2. Substitution of equation 12 gives5 P P dS T - Tl dVi 0 13 yT T2j This proves that two bodies in equilibrium must have not only the same temperature but also the same pressure. It also proves that when two bodies in contact at the same temperature have different pressures the body at the higher pressure will tend to expand and compress the body at the lower pressure. ISOTHERMAL ENTROPY CHANGES. Entropy changes at a single temperature follow directly from equation 5. Calculations involving a temperature difference or temperature change will be treated later. A change of phase under equilibrium conditions will be at constant temperature and constant pressure. The thermal energy transfer Q Q v. will be AH. Therefore AS AH 14 For example the entropy change for the melting of ice was found to be J g-K or J mol-K. The entropy of vaporization of water at 100oC is 40 657 J mol A S 108 .96 J mol K vap K More typical liquids not involving such strong intermolecular forces have ASvap values of about 92 J molK at their normal boiling points. This is known as Trouton s rule. The work done in a reversible isothermal expansion of an ideal gas was found to be equation 10 Chapter 1 Wrev - nRT ln V2 V1. For an ideal gas at constant temperature AE 0 and therefore Qrev -Wrev. The entropy change is thus 5 It is assumed that T1 T2 and thus the total entropy is unchanged by a transfer of thermal energy between the two parts. The constant-energy restriction of equation 12 is satisfied because any work done by one part on the other can be compensated by such a transfer of thermal energy. 7 10 07 2- 40 ĩ . rev FIGURE 2 The ras initially in the left-hand container of volume Ki at
