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10 April, 04:43

Calculate the energy required to change the temperature of 1.00 kg of ethane (C2H6) from 25.0"C to 73.4"C in a rigid vessel. (Cv for C2H6 is 44.60 J K%1 mol%1.) Calculate the energy required for this same temperature

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  1. 10 April, 04:53
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    Question:

    Calculate the energy required to change the temperature of 1.00 kg of ethane (C2H6) from 25.0"C to 73.4"C in a rigid vessel. (Cv for C2H6 is 44.60 J K%1 mol%1.)

    Calculate the energy required for this same temperature change at constant pressure.

    Calculate the change in internal energy of the gas in each of these processes.

    Answer:

    The answers are

    qv = 71787.16 J

    qp = 85169.99 J

    ΔE = 71787 J for both constant volume and constant pressure processes

    Explanation:

    Mass of ethane gas, m = 1.00 kg = 1000 g

    Cv = 44.60 J / (K·mol)

    The temperature change is given by

    ΔT T₂ - T₁ = 73.4 °C - 25 °C = 48.4 °C

    The molar mass of ethane = 30.07 g/mol

    Number of moles, n of ethane = mass / (molar mass) = 1000/30.07

    = 33.26 moles

    Therefore the energy required at constant volume to change the temperature of 1.00 kg of ethane (C₂H₆) from 25.0 °C to 73.4 °C

    is given by H qv = n ·Cv·ΔT = 33.26 * 44.60*48.4 = 71787.16 J

    b) At constant pressure we have Cp - Cv = R

    ∴ Cp = R + Cv

    = 8.3145 + 44.6 = 52.9145 J / (K·mol)

    Therefore we have H, qp = n ·Cp·ΔT = 33.26*52.9145*48.4

    = 85169.99 J

    For constant volume process, we have

    q = U

    Therefore ΔU = Δq = 71787 J

    For constant pressure process, we have

    ΔU = n*Cv*dT = 71787 J
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