# Measurable consequences of entropy of mixing

Most textbooks include an example of entropy of mixing that involves removing a partition between two (in principle) distinguishable gases, and compare this to the case where the two gases are indistinguishable. What I’ve not yet been able to figure out is what the consequences of this additional entropy are for the distinguishable case.

Say you are given two cylinders; one filled with a pure gas, and the other a mixture of two distinguishable (in principle) particles. Is there a macroscopic experiment you could perform to determine which is which, without knowing how the distinguishable particle types actually differ from each other? Do (for example) heat capacities depend on total entropy, so that one could measure temperature versus heat input for each cylinder?

## Answers and Replies

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DrDu
No, you need some means to tell the two gasses apart, e.g. a semipermeable membrane, different molecular weight, so they can be separated.

Andy Resnick
Most textbooks include an example of entropy of mixing that involves removing a partition between two (in principle) distinguishable gases, and compare this to the case where the two gases are indistinguishable. What I’ve not yet been able to figure out is what the consequences of this additional entropy are for the distinguishable case.

Say you are given two cylinders; one filled with a pure gas, and the other a mixture of two distinguishable (in principle) particles. Is there a macroscopic experiment you could perform to determine which is which, without knowing how the distinguishable particle types actually differ from each other? Do (for example) heat capacities depend on total entropy, so that one could measure temperature versus heat input for each cylinder?
The solution of Gibbs' paradox (which is the experiment you describe) consists of assigning entropy to *information*- information about distinguish-ability, for example.