【正文】
),( nVSUU ? 且 dnnUdVVUdSSUdU VSnSnV , ?????? ????????? ????????? ??? ( ) 得到 VSnU,?????? ???? ( ) 也就是說(shuō),化學(xué)勢(shì)被定義為 恒定熵和體積下的每千摩爾的內(nèi)能增量。 這可以通過(guò)歐拉定理 來(lái)求得齊次函數(shù) 。 然后廣延量 U 將隨著 ? 產(chǎn)生改變,并且所有獨(dú)立的廣延量都將 隨 因 子 ? 的變化而變化 。 最后我們采用差分方程( ) ,得到 jj jj jj dndnV dPP dVSdTT dSdU ?? ?? ?????? ( ) 方程( )和( )等同,我們得到 01 ??? ?? jmj j dnV dPSdT ? ( ) 吉布斯 迪昂方程的一個(gè)關(guān)系式。 因此,如果我們讓某個(gè)過(guò)程在恒定的溫度和壓強(qiáng)下發(fā)生,( )式成立的前兩項(xiàng)為零,所以和隨之為零。 r is the distance between the molecule and its neighbor, at ??r , 0?? and 0?V so 0?E everywhere. At orr? , ? ? 0?? orVK , so 0)( ?? orVK Figure Schematic diagram of a potential well due to intermolecular forces. Energy is conserved, but a conversion from potential energy to kiic energy takes place. The kiic energy is added to the internal energy of the system. It is reasonable to ask what the magnitude of ? is. In a standard laboratory experiment, sulfuric acid is added to water , producing an increase in temperature. Imagine that 510? kilomoles of acid at room temperature are added to a liter of water ? ?kilomo ?? , also at room temperature. the temperature is observed to rise C? . we wish to determine the chemical potential of acid in water. We shall assume that the interaction among the acid molecules is small pared with their interaction with the water molecules (both acid and water molecules are electrically polarized.) the specific heat capacity of water is ?? ?? Jkilo m o le. thus the heat gained by the water through the addition of the acid is .418))()(( 42 JTmcQ p ?????? ? Since the mass of the water is more than 310 times the mass of the acid, we can ignore the heat capacity of the latter. The chemical potential then ,is JnQ 75 ??????? ?? 1?kilomole The sign is negative because heat is transferred from the acid to the water. We are interested in the chemical en