How Does Constant Temperature Affect Heat Transfer in a Piston-Cylinder Device?

[CRich]

Homework Statement

T1=300K
P1=100kPa
V1=1m^3

T1=T2=T3
P2=P3=200kPa
V3=0.1m^3

Q: Air initially at 300kpa is contained inside a piston-cylinder device with a volume of 1m^3. The cylinder is equiped with a check valve allowing air to escape when the air pressure reaches 200kPa. An extrernal force pushes the frictionless piston slowly until the final volume reaches 0.1m^3. Durring this entire process, the air temp is maintained at 300K by heat transfer. To determine the heat transfer answer the following questions. Air is assumed to be an ideal gas with constant specefic heats, cp=1 kJ/kg-K, cv=0.713 kJ/kg-K.

(a) skecth (p-V) (T-V) diagrams [no problem I got those]
(b) find the heat transfer amount by the time when the valve opens so...Q1-2?
(c)Write down the energy conservation equation after the valve opens [I got this one too]
(d)Fing the inital and final mass of air
(e)Find the heat transfer amount after the valve opens until the final state so...Q2-3?

Homework Equations

W={intergral}Pdv
Q-W=0 ===> Q=W
b/c it is frictionless it is an isotropic process
s1=s2
k=Cp/Cv
PV=RT

The Attempt at a Solution

(b)for Q1-2 I tried
Q1-2=mT(s2-s1)=mT(Cpln (T2/T1)-Rln(P2/P1)) = -69.29 ... since s1=s2 I'm unsure if this equation is correct
I also tried Q1-2=mP(V2-V1) ... however I have 2 different Ps
So I also tried Q=W={the intergral from 1-2}pdv = m{the intergral from 1-2}C/V^k

(d)m=PV/RT => m1=1.161 m3=0.232 does m1=m2? ... I alos found? v2= (RT2)/P2=.4305?

(e) Q2-3=m2P(V3-V2) ... I think this equation is correct but I think I'm missing something...

 

[CRich]

anyone please... Just point me in a different direction...I'm horribly stuck and frustrated ... any direction any idea I'll try it!