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28 March, 10:36

1 kg of oxygen is heated from 20 to 120°C. Determine the amount of heat transfer required when this is done during a (a) constant-volume process and (b) isobaric process.

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  1. 28 March, 14:21
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    (a) At constant-volume, Q = 66.7kJ

    (b) At isobaric condition, Q = 92.7kJ

    Explanation:

    The specific heats of oxygen at the average temperature of (20+120) / 2 = 70°C = 343 K are

    Cp = 0.927 kJ/kg. K

    Cv = 0.667 kJ/kg K

    We take the oxygen as the system. This is a closed system since no mass crosses the boundaries of the system. The energy balance for a constant-volume process can be expressed as

    ΔE (system) = E (in) - E (out)

    and

    Q (in) = ΔH = mCp x (T₂ - T₁)

    since ΔU + Wb = ΔH during a constant pressure quasi-equilibrium

    process. Substituting for both cases,

    (a)

    Qin, V = const = mCv (T2 - T1)

    = (1kg) (0.667 kJ/kg. K) (120 - 20) K

    = 66.7kJ

    (b)

    Qin, P=const = mCp (T2 - T1)

    = (1kg) (0.927 kJ/kg. K) (120 - 20) K

    = 92.7kJ
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