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21 June, 21:49

A piston-cylinder device initially contains 0.22 kg of steam at 200 kPa and 300°C. Now, the steam is cooled at constant pressure until it is at 150°C. Determine the volume change of the cylinder during this process using the compressibility factor, and compare the result to the actual value.

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  1. 22 June, 00:20
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    Defining compressibility factor (Z), which is also known as the gas deviation factor, is a correction factor which describes the deviation of a real gas from ideal gas behaviour.

    Z = p / (density * Rs * T)

    Where Rs is specific gas constant = R/M

    Deriving the volume values from steam tables,

    At 200kPa and 300°C, V1 = 1.31623 m3/kg

    At 200kPa and 150°C, V2 = 0.95986 m3/kg

    Change in volume, DV = m (V1 - V2)

    = 0.2 * (1.31623 - 0.95986)

    = 0.07128 m3/kg

    Also from steam tables,

    The critical pressure, Pc = 22.06MPa

    The critical temperature, Tc = 647.1K

    Remember, gas constant, R = 0.4615 kPa. m3/kg. K

    Therefore, reduced temperature at initial state, Tr = T1/Tc

    = (360 + 273) / 647.1

    = 0.886

    Also, reduced pressure at initial state, Pr = P1/Pr

    = 200 x 10^-3/22.06

    = 0.0091

    But compressibility factor at initial state, Z1 = 0.9956

    Ideal volume, Vi = m*R*T/P1

    = (0.2*0.4615 * (300+273)) / 200

    = 0.2644m3

    Compressibility volume, Vc = Z1*Vi

    = 0.9956 * 0.2644

    = 0.2633m3

    Reduced temperature at final state, Tr = T2/Tc

    = (150+273) / 647.1

    = 0.65

    Reduced pressure at final state, Pr = P2/Pc

    = 200 x 10^-3/22.06

    = 0.0091

    Compressibility factor at final state, Z2 = 0.9897
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