Solving Air Pressure Concepts in Torricelli Experiment

[Pedro Lemos]

Well, I'm trying to grasp the concepts behind the following problem :

"A guy puts some air in a vassel, the air's temperature was t0 the vessel's basis area is 50 cm³ and the height is 20. Afterwards the vassel was set onto a container full of water at 300k (Similar to Torricelli experiment), part of the water entered the tube reaching 4 cm of height and then the system acquires equilibrium. The Change in pressure is asked"

The awser is : ΔP = μ(water).g.h ->I don`t understand what formula is that nor that creepy μ.
=-1.10³.10.4.10^-2
=-4,0.10² N/m²
There is a change in temperature as well, so shouldn't this change to be considered as a factor of pressure through Clapayron's Equation p.v=R.n.T?

 

[dE_logics]

Apperently I find there's something IS wrong with the solution given.

How is the change in pressure related to μ(water).g.h...the upthrust?

 

[ericgrau]

That first number should be the density of water. Normally I see it written as the greek letter rho (looks like a rounded lowercase p). P1 - P2 = ΔP = dgΔh.

It looks like in this situation the pressure difference is negative, as the hot expanded air is being used to suck water into the tube as it contracts. Heat transfer in water is fairly rapid, so the air in the tube should change to match the temperature of the water, thus causing it to cool and contract by Pv=nRT.