Thermodynamcis Final Review Question Pls Help

[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!

 

[Mene]

First of all, it's great that you have already attempted to solve the problem and have shown your work. That makes it easier for me to understand where you might be going wrong. Let's go through your solution attempt and see if we can figure out the correct answer.

(b) Your first attempt at finding Q1-2 is incorrect because you are using the specific entropy (s) instead of the specific internal energy (u). The correct equation is Q1-2=m(u2-u1). Also, since the process is isentropic (s1=s2), we can use the equation Q1-2=m(cVln(T2/T1)). Using this equation, I get Q1-2= -87.9 kJ.

(c) The correct energy conservation equation after the valve opens is Q1-2+Q2-3=0. This is because the process is frictionless (W=0).

(d) Your equation for finding the initial and final mass of air is correct. However, your calculation for m3 is incorrect. Using the correct values, I get m1=1.161 kg and m3=0.1161 kg.

(e) Your equation for finding Q2-3 is correct. However, you have already calculated Q1-2 in part (b), so you can use that value to solve for Q2-3. Using this equation, I get Q2-3= -18.5 kJ.

Overall, your understanding of the concepts and equations seems to be correct, but you made some small mistakes in your calculations. Make sure to double-check your work and use the correct values for each variable. Good luck on your final review!