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Pressure in a closed system

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Lets say we have a bioreactor (closed system) with cells floating in it. If we are to introduce a stir rod, which would increase the velocity of the cells within the system, would the pressure of the system increase as well?

I believe the pressure will increase: the particles are moving faster -> this means that KE goes up (since KE is directly related to velocity) -> this means that T is higher -> this means that P is higher (since volume remained constant)!

Right or wrong?

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