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PV = RT

Now, if the cylinder were to move with velocity v parallel to the length direction, special relativity requires the length to contract given by:

L' = L √(1-(v^2/c^2))

As the length contracts, the volume must also go down by the same relation:

V' = V√(1-(v^2/c^2))

However, the ideal gas law must continue to hold ( I presume) - which can only be true if the pressure P increases by the same factor. Thus, simply because of it's motion, the pressure experienced the cylinder seems to have gone up by

P' = P /√(1-(v^2/c^2))

if this argument is correct, does this then mean that pressure is not a relativistic invariant but must depend on the frame of reference? A vessel that does not experience any pressure in one frame of reference might be under pressure in another one?

Could anyone confirm or refute this argument? Thanks!!