Processes Concerning the Paradox

Consider an apparatus as sketched in Fig. 10.2. We perform now simple experiments with this apparatus. The left chamber we address with a single prime (0 and the right chamber we address with the double prime ( ). Thus, the left chamber has a volume of V and a temperature of T = T. The right chamber has a volume of V and a temperature of T = T. 

We have derived the energy equation of an ideal gas in Eq. (4.8). From there the entropy of a one-component gas can be calculated as 

Suppose the left chamber is filled with a one-component gas of type (1) and the right chamber is empty. The spool valve is closed. Initially the total entropy is 5s = 5 since the right chamber is empty (5 = 0)m 

If we open the spool valve, the gas is distributed between both chambers. At the end we have an entropy of 5  

Now we repeat the experiment if the right chamber is not empty but filled with a certain amount of gas. At the beginning of the experiment the total entropy is 

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