Forums Assignment Help Numerical on molar concept

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  • #895

    ahwriter
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    A piston cylinder device contains 1 kg of oxygen at 150 kPa, 30°C. The cross-sectional area of the piston is 0.1 m2. Heat is now added causing gas to expand. When the volume reaches 0.2 m3, the piston reaches a linear spring with a spring constant of 120 kN/m. More heat is added until the piston rises another 25 cm. Determine the final pressure, temperature and the energy transfers.

    #9460

    Aakanksha
    Participant

    Solution :

    Since O2 is a diaatomic gas

    CP=7R/2,CV=5R/2

    Molecular mass=32 gm

    Intial state

    Intial volume of gas

    V=nRT/P

    n=1*103/32

    T=303K

    R=8.3

    P0=500*103 N/m2

    so V=.157 m3

    Second state ( when piston reaches the spring)

    v=.2 m3

    P=500*103 N/m2

    As per ideal gas equation

    Temperature becomes=385.5 K

    So heat tranfer till that point=nCP(T2 -T1)

    =1*103 *7*8.3*82.5/32*2

    =74.8 KJ

    Third state ( when it compresses the spring)V=.2+0.1*0.25=0.225 m3

    P=500*103 + kx/A

    =500*103 + 120*103*25*10-2/.1

    =800*103 N/m2

    As per ideal equation

    Temperature becomes=694K

    Change in Internal energy=nCV(T3 -T2)=5nR(T3 -T2)/2

    =5*1*103*8.3*308.5/32*2

    =200 KJ

    Workdone by the gas =P0Ax + kx2/2

    =500*103*.1*.25 + 120*103*.25*.25/2

    =16.25 KJ

    Total heat supplied in this Process=200+16.25=216.25KJ

    So net Heat transfer=291.05 KJ

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