A vertical cylinder of cross-sectional area 0.050m^2 is fitted witha tight-fitti

Question

A vertical cylinder of cross-sectional area 0.050m^2 is fitted witha tight-fitting, frictionless piston of mass 5.0 kg. If there are3.0 mol of an ideal gas in the cylinder at 500 K, determine theheight h at which the piston will be in equilibrium under its ownweight.
I tried this problem using the questions that other peopleposted but I get weird answers. Can you please show me how to dothis problem with all of the values? Thank you so much!!
I tried this problem using the questions that other peopleposted but I get weird answers. Can you please show me how to dothis problem with all of the values? Thank you so much!!

Explanation / Answer

The idea is that, for the piston     upward force from pressure ofgas   = weight of piston   +  downward force of air pressure on top            pA    =   mg   + po A Pressure of gas is foundby       p V = n RT   or     p (Ah) = n R T so                 p   =   n R T / A h Now, the original equation          ( n R T / A h) A = m g + po A         n R T / h = m g + po A    h =   n R T / (mg   + poA)   = 3.0* 8.31 * 500 / (5.0 * 9.8   + 101300 *0.05) = 2.437 metres

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