Will humans swim faste of slower in syrup than in water?

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Will humans swim faste of slower in syrup than in water?
 
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Syrup has a much higher viscosity, so more friction. What are your thoughts on this?
 
It's given a gas of particles all identical which has T fixed and spin S. Let's the density of orbital states and for , zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate and we have...

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