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    Power Cycle for a Piston-Cylinder Device

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    A power cycle for a piston-cylinder device is described by the following four processes:

    1→2 Isothermal compression from T1 = 300K, P1 = 100 kPa to P2 = 600 kPa.
    2→3 Constant pressure heat addition until the temperature is T3 = 800K.
    3→4 Isentropic expansion until the volume at state 4 equals the volume at state 1.
    4→1 Constant volume heat rejection until the temperature is 300K.

    Assume the working fluid is an ideal gas with constant specific heats and has properties as follows: CV = 0.600 kJ/(kg-K), CP = 0.900 kJ/(kg-K), R = 0.300 kJ/(kg-K), k = 1.500.

    (a) Sketch the P-v diagram for this cycle
    (b) Sketch the T-s diagram for this cycle
    (c) Determine the heat rejected during process 1→2, in kJ/kg.
    (d) Determine the heat added during process 2→3, in kJ/kg.
    (e) Determine the total cycle expansion work done by the gas, in kJ/kg.

    Could you please fill in this table, this will help organize all of the processes.
    State P (kPa) T (K) V (m3/kg)
    1 100 300
    2 600 300
    3 600 800
    4

    © BrainMass Inc. brainmass.com May 20, 2020, 2:57 pm ad1c9bdddf
    https://brainmass.com/physics/power/power-cycle-piston-cylinder-device-108728

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    SOLUTION

    For an ideal gas following equations are applicable :

    i) PV = nRT where n = quantity of gas in moles, P = Pressure, V = Volume, T = Absolute temperature, R = Universal gas constant = 8.31 J/mole/K ..........(1)

    Or PV = m(R/M)T where m = mass of gas, P = Pressure, V = Volume, T = Absolute temperature, M = Molecular mass of the gas, R/M = Gas constant for unit mass of the given gas (different for different gases) ............(2)

    ii) For adiabatic expansion or compression, PVk = Constant where k = Cp/Cv ......(3)

    iii) From the first law of thermodynamics we have : dQ = dU + dW where dQ = Quantity of heat given to the system, dU = Change in the internal energy of the system(gas), dW = External work done by the gas. .............(4)

    iv) Work done by the gas at constant pressure : dW = PdV .........(5)

    v) Work done by the gas at constant volume = 0

    vi) Heat transferred to/from the gas at constant volume = mcvdT where cv= specific heat of the gas at constant volume ......(6)

    vii) Heat transferred to/from the gas at constant pressure = mcpdT where cp= specific heat of the gas at constant pressure ......(7)

    viii) Cp - Cv = R where Cp = Molar specific heat of the gas at constant pressure (i.e. specific heat for one mole), Cv = Molar specific heat of the gas at constant volume ......(8)

    Cp = Mcp and Cv = Mcv

    Substituting in (8) we get : Mcp - Mcv = R or cp - cv = R/M .......(9)

    (a) Sketch the P-v diagram for this cycle

    1→2 Isothermal compression from T1 = 300K, P1 = 100 kPa to P2 = 600 kPa.

    Assuming 1 kg of gas, m = 1 kg.

    From (9) R/M = cp - cv = (0.9 - 0.6) kJ/(kg-K) = 0.3 kJ/(kg-K) = 0.3x103 J/(kg-K)

    Substituting ...

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