PV in a Cylinder Homework: Find W, V, T

[joemama69]

Homework Statement

A vertical cylinder with 500 moles of a monatomic ideal gas is closed with a 50kg piston with an cross-sectional area of 100cm. V_initial = 1 m^3. T = 300K, The Piston is then released and stops at the equilibrium position. Ignore friction.

1) Find the equation for the Work done by the gas in terms of Volume

2) Find the final volume of gas

3) fin dthe final temperature

Homework Equations

The Attempt at a Solution

Part 1)

Work done by the gas...

dW = Pdv from v=1 to v = nRT/P

W = P(nRT/P - 1) = nRT - P <-- Is this correct... I now put it interms of V

W = PV - nRT/V

 

[jbsteele]

<-- Is this correct?Part 2)Since the piston is released, the pressure of the gas = atmospheric pressure. P = PatmTherefore, nRT/V = Patm => V = nRT/PatmPart 3)Tf = Ti (Vf/ Vi)^(γ-1) (γ=1.4 for monatomic ideal gas)Tf = 300(Vf/1)^(1.4-1)