[osker246]

Ok so I'm not sure if I am doing this problem correctly, I was hoping somebody could help me out here.

Question:

Five moles of  an ideal monatomic gas contract adiabatically and irreversibly
when subjected to a constant external pressure of 1 atm from an initial volume
V1=200L and initial pressure P1=0.50 atm. Assume the contraction ceases when
the system reaches equilibrium. Calculate ∆Ssys.
 
My attempt:

Ok So my first step was to find the initial temperature using pv=nRT

T(initial)=[(50662.5Pa)(0.2 m^3)]/[(5mol)(8.314)]=243.7k

Using the realtionship P(initial)V(initial)^gamma=P(final)V(final)^gamma, where gamma=5/3. I find the final volume.

V(final)= 0.132 m³

So from here I used the equation Delta(S)= nRln(V_f/V_i)+nC_v,mln(T_f/T_i)

Plugging in values gives me Delta(S)=0.0418 J/K

Did I use the proper equation for this answer?