Thermodynamics Cycle: Gas Temperature and Work Calculation | Homework Solution

[kelvin56484984]

Homework Statement

I.The gas is heated at constant pressure until the volume is 4.4L at point B
II. The gas is cooled at constant volume until the pressure decreases to 1.2 atm
III. The gas undergoes an isothermal compression back to point A

a) Find the temperature at Point A,B,C
b) Find the work done on the gas ,the heat transferred to the gas and the change for each process
c) Find W,Q and delta U for the whole cycle

Homework Equations

[/B]
delta U=Q+W
PV=nRT
1 atm=1.013x10^5 N/m^2
Cp=5/3R+R

The Attempt at a Solution

a)
pv=nRT
Tb=PbVb/nR
Tb=2.4*4.4/(1*8.31) * 0.001* 1.013*10^5
=129K
Ta=129K/2
=64.5K
Tc=129K/2
=64.5K

b)
Wab=pv
=2.4*(4.4-2.2)* 1.013x10^5 *0.001
=535J
Qab=n*Cp*deltaT
=0.32* 8/3*R *(129-64.5K)
=457J
U=Q+W
delta Uab=457+535
=992J

Wbc=0
Since the volume keep unchange
Qbc=n*Cv*deltaT
=0.32*5/3*R*(64.5K-129K)
=-285J
U=Q+W
U=-285J

U=0
Since it is isothermic process
Wca=nRTc *ln(Vc/Va)
=0.32*8.31*64.5K*ln(4.4/2.2)
=118
Q+W=0
Q=-118J

c)
W=Wab+Wbc+Wca
=535+0+118
=653J
Q=Qab+Qbc+Qca
=457-285-118
=54J
deltaU=992-285+0
=707J

 

[Andrew Mason]

Some comments:
1. How many moles of gas are there? You seem to be using 1 and .32 in different places. There has to be more information provided in order to determine this.
2. What is the $\Delta U$ for one complete cycle? (hint: is U a state function?).
3. What kind of gas is this? (e.g monatomic, diatomic etc. Are you given this or given the Cv or Cp?).

AM