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17 December, 15:00

A 0.8-m³ rigid tank contains carbon dioxide (CO₂) gas at 250 K and 100 kPa. A 500-W electric resistance heater placed in the tank is now turned on and kept on for 40 min after which the pressure of CO₂ is measured to be 175 kPa. Assuming the surroundings to be at 300 K and using constant specific heats, determine (a) the final temperature of CO₂, (b) the net amount of heat transfer from the tank, and (c) the entropy generation during this process.

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  1. 17 December, 15:49
    0
    Given:

    Power, p = 500 W

    Time, t = 40 min

    = 2400 s

    Volume, V = 0.8 m^3

    Temperature, T = 250 K

    Pressure, P = 100 kPa

    Temperature of surroundings, Ts = 300 K

    Using ideal gas equation,

    PV = nRT

    n = (100 * 10^3 * 0.8) / (8.3145 * 250)

    = 38.49 mole

    Mass = number of moles * molar mass

    Molar mass = 12 + (16 * 2)

    = 44 g/mol

    Mass = 44 * 38.49

    = 1693.43 g

    = 1.693 kg.

    A.

    P2 = 175 kPa

    Using pressure law,

    P1/T1 = P2/T2

    T2 = (175 * 250) / 100

    = 437.5 K

    B.

    Cvco2 = 0.706 kJ/kg. K

    Total energy, U = Qin - Qout

    Qout = (p * t) - (m * cv * delta T)

    = (500 * 2400) - (1.693 * 0.706 * (437.5 - 250))

    = 1200 kJ - 224.11 kJ

    = 975.889 kJ

    = 975.9 kJ

    C.

    Cpco2 = 0.895 kJ/kg. K

    Gas constant, Rc = R/molar mass of CO2

    = 8.3145/44

    = 0.189

    Using the formula,

    Entropy, S = (m * (Cpco2 * ln (T2/T1) - Rc * ln (P2/P1)) + Qout/Ts

    Inputting values,

    = (1.693 * (0.895 * ln (437.5/250) - 0.189 * ln (175/100)) + 975.9/300

    = 3.922 kJ/K.
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