Energy Conversion in Transformations of Substances

As we have seen in the introduction to the chemical potential (Sect. 4.8), in order to increase the amount n of a substance B, against its own tendency to transform we need an amount of energy equal to 

If we want to obtain the contribution from the change AW of the energy content W of the system, we have to make sure that no other substances, entropy, or similar quantities are added as well. Furthermore, the volume must be kept constant. This can be achieved by fixing the amounts of all other substances, the entropy, the volume, etc., of the body 

This is not different from what we learned in the example of the bathtub (compare Sect. 1.6). The way water flows in and out of the bathtub over various paths is also valid here for energy. The energy content W of the area is a state variable, but the amounts of energy W v, W , W , . .. that are exchanged with the 

The energy current P flowing over path n can be formally described by W if we imagine all other pathways to be blocked, = (W) y. When we use this method to calculate the energy dW flowing in during a short time span df, we obtain the equation we started with  

The following fact is remarkable and important. If entropy Sg is generated (possibly by friction) in an area at temperature T, this costs an additimial amount of energy Wb = T- Sg. The conditicHi that S must be kept constant just means that Sg and therefore cannot remain in the area but must be removed. Whether or not energy is burnt and entropy is generated in the procedure does not affect the result and can, therefore, be ignored. 

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