A vertical cylinder of cross-sectional area A is fitted with a tight fitting, fr

Question

A vertical cylinder of cross-sectional area A is fitted with a tight fitting, frictionless piston of mass m. If n moles of an ideal gas are in the cylinder at a temperature T, what is the height H at which the piston is in equilibrium under its own weight?

Explanation / Answer

At Equilibrium, the weight of the piston should be balanced by the pressure force of the gas, i.e Mg = P.A where, M => mass of the piston = 5 kg g => acceleration due to gravity = 9.8 m/s^2 P => Pressure = ? A => Area = p(r)^2 = p(0.046)^2 =0.0066 m^2 substituting the values, 5 x 9.8 = P x 0.0066 P = 7424.24 Pa ============ Now, we know the ideal gas equation, P*V = n*R*T where, P => Pressure = 7424.24 Pa V => Volume = p(r)^2*h = (0.0066)*h n => no. of moles = 3.0 R => Universal Gas Constant = 0.0821 T => Temperature = 420 K substituting values, (7424.24 )*(0.0066)h = (3.0)*(0.0821)*(420) h =103.446 / 48.99 h = 2.11 m ======== ANSWER: therefore, the height of piston at which the system is at equilibrium is 2.11m

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