The assumptions of Clausius

The assumptions of Clausius. In the works of R. Clausius (since 1857)1 we can find a spirit substantially 

Let us take, for instance, a gas at rest, in thermal equilibrium, in the absence of external forces. In this case Clausius, partly tacitly, partly explicitly, bases his calculations on the following statements  

The molecules are distributed with equal density throughout the container. 

The various values of the speed of molecules occur with the same frequencies in the different parts of the container. 

If we take a volume element which contains a sufficiently large number of molecules, all directions of velocity are represented with equal frequency.20 

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