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A vertical cylinder of cross-sectional area 0.045m2 is fitted with a tight-fitting, frictionless piston of mass 6.5kg. The acceleration of gravity is 9.8 m/s2, andthe universal gas constant is 8.31451 J/Kmol.

If there are 4.4mol of an ideal gas in the cylinder at 412 K, determine the height h at which the position is in equilibrium under its own weight (in units of m).

The work I have so far is the following:

Pressure=f x area=(6.5kgx9.81)x(0.045m2)

=2.869N/m2

using PV=nRT I isolated my Volume

V = (4.4mol x 8.3145 x 412K) / 2.869N/m2

= 5253.58 m3

Using this volume inside the cylinder I want to find the height:

h = volume/area

= 5253.58m3 / 0.045m2

= 116 746.22m (this seems kind of high for a height, no?)

I also tried this

Area of cylinder = 2 x pie x r2

isolated my radius then plugged that into V = pie x r2 x h

the height I calculated was 334688.55m (once again pretty high)

I'm assuming my first calculation h= volume/area is a more reliable answer but I just need some assurance as to my answer...it seems pretty high for a cylinder/piston

Thanks

Sergio