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## Homework Statement

A thermally insulated cylinder, closed at both ends, is fitted with a frictionless heat-conducting piston that divides the cylinder into two parts. Initially, the piston is clamped in the center with 1 liter of air at 300 K and 2 atm pressure on one side and 1 liter of air at 300K at 1 atm pressure on the other side. The piston is released and reaches equilibrium in pressure and temperature at a new position. Compute the final pressure and temperature and increase of entropy if air is assumed to be the ideal gas. What irreversible process has taken place?

## Homework Equations

[tex]\Delta[/tex]S = [tex]\Delta[/tex]Q/T

## The Attempt at a Solution

This is an isothermal free expansion. So temperature remains constant. I know the final pressure will be 1.5 atm (intuitively, (1+2)/2), but how can I compute this out by ideal gas law?

By PV=nRT,

(101325)(1000/1000000)=n (8.31)(300)

n1(the compartment with 1atm)=0.040643802

n2(the compartment with 2atm) = 0.081828

TOTAL number of moles = 0.12193

When I search through the Internet, I find this equation

[tex]\Delta[/tex]S=nRln(Vf/Vi) = 0.12193(8.31)ln2 = 0.702323.........

but the answer is 0.0566, what's wrong with my calculation???