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Thermodynamics cycle

  1. May 5, 2016 #1
    1. The problem statement, all variables and given/known data
    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


    2. Relevant equations

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

    3. 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
     

    Attached Files:

  2. jcsd
  3. May 6, 2016 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    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
     
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