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28 July, 16:03

A cylinder with a piston restrained by a linear spring contains 2 kg of carbon dioxide at 500 kPa and 400°C. It is cooled to 40°C and 300 kPa. Calculate the heat transfer for the process.

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  1. 28 July, 18:44
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    heat transfer for the process is - 643.3 kJ

    Explanation:

    given data

    mass m = 2 kg

    pressure p1 = 500 kPa

    temperature t1 = 400°C = 673.15 K

    temperature t2 = 40°C = 313.15 K

    pressure p2 = 300 kPa

    to find out

    heat transfer for the process

    solution

    we know here mass is constant so

    m1 = m2

    so by energy equation

    m (u2 - u1) = Q - W

    Q is heat transfer

    and in process P = A + N that is linear spring

    so

    W = ∫PdV

    = 0.5 (P1+P2) (V1 - V2)

    so for case 1

    P1V1 = mRT

    put here value

    500 V1 = 2 (0.18892) (673.15)

    V1 = 0.5087 m³

    and

    for case 2

    P2V2 = nRT

    300 V2 = 2 (0.18892) (313.15)

    V2 = 0.3944 m³

    and

    here W will be

    W = 0.5 (500 + 300) (0.3944 - 0.5087)

    W = - 45.72 kJ

    and

    Q is here for Cv = 0.83 from ideal gas table

    Q = mCv (T2-T1) + W

    Q = 2 * 0.83 (40 - 400) - 45.72

    Q = - 643.3 kJ

    heat transfer for the process is - 643.3 kJ
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