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?
[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?
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?