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6 October, 13:12

A well-insulated, rigid vessel contains 3 kg of saturated liquid water at 40°C. The vessel also contains an electrical resistor that draws 10 A when 50 V are applied. Determine the final temperature in the vessel after the resistor has been operating for 30 min. (Solve this problem using appropriate software.)

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  1. 6 October, 14:23
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    The final temperature in the vessel after the resistor has been operating for 30 min is 111.67°C

    Explanation:

    given information:

    mass, m = 3 kg

    initial temperature, T₁ = 40°C

    current, I = 10 A

    voltage, V = 50 V

    time, t = 30 min = 1800 s

    Heat for the system because of the resistance is

    Q = V I t

    where

    V = voltage (V)

    I = current (A)

    t = time (s)

    Q = heat transfer to the system (J)

    so,

    Q = V x I x t

    = 50 x 10 x 1800

    = 900000

    = 9 x 10⁵ J

    the heat transfer in the closed system is

    Q = ΔU + W

    where

    U = internal energy

    W = work done by the system

    thus,

    Q = ΔU + W

    9 x 10⁵ = ΔU + 0, W = 0 because the tank is a well-insulated and rigid.

    ΔU = 9 x 10⁵ J = 900 kJ

    then, the energy change in the system is

    ΔU = m c ΔT

    ΔT = ΔU / m c, c = 4.186 J/g°C

    = 900 / (3 x 4.186)

    = 71.67°C

    so, the final temperature (T₂)

    ΔT = T₂ - T₁

    T₂ = ΔT + T₁

    = 71.67°C + 40°C

    = 111.67°C
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