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A horizontal tube of length L closed at both ends contains He gas.The tube is rotated at a constant angular velocity W about a vertical axis passing through an end. Assuming temperature is uniform and constant, which of the following is correct? (1)p1>p2 (2)p2>p1 (3)p1>p2 (4)Cannot say A horizontal tube of length L closed at both ends contains He gas.The tube is rotated at a constant angular velocity W about a vertical axis passing through an end. Assuming temperature is uniform and constant, which of the following is correct? (1)p1>p2 (2)p2>p1 (3)p1>p2 (4)Cannot say
let r be distance from axis of rotation. the acceleration is (W^2)r,directed radially outward. This acceleration exerts a force on the gas away from the axis, at each point in the tube. let P(r) be pressure(r is distance fron axis), and let ρ(r) be density. dP(r)=ρW2rdr, from this equation it is clear that pressure increases as the distance from the axis increases. PV=nRT, density ρ is directly proportional to n/V =P/RT, T is uniform and constant. and P increases as r increases, therefore ρ(r) also increases as r increases
let r be distance from axis of rotation. the acceleration is (W^2)r,directed radially outward. This acceleration exerts a force on the gas away from the axis, at each point in the tube. let P(r) be pressure(r is distance fron axis), and let ρ(r) be density.
dP(r)=ρW2rdr, from this equation it is clear that pressure increases as the distance from the axis increases.
PV=nRT, density ρ is directly proportional to n/V =P/RT, T is uniform and constant. and P increases as r increases, therefore ρ(r) also increases as r increases
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