A large power plant heats 1917 kg of water per second to high-temperature steam to run its electrical generators.

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A large power plant heats 1917 kg of water per second to high-temperature steam to run its electrical generators.

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Thông Đạt 2 days 2021-07-22T01:32:29+00:00 1 Answers 0 views 0

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    2021-07-22T01:33:51+00:00

    Complete Question

    A large power plant heats 1917 kg of water per second to high-temperature steam to run its electrical generators.

    (a) How much heat transfer is needed each second to raise the water temperature from 35.0°C to 100°C, boil it, and then raise the resulting steam from 100°C to 450°C? Specific heat of water is 4184 J/(kg · °C), the latent heat of vaporization of water is 2256 kJ/kg, and the specific heat of steam is 1520 J/(kg · °C).

    J

    (b) How much power is needed in megawatts? (Note: In real power plants, this process occurs under high pressure, which alters the boiling point. The results of this problem are only approximate.)

    MW

    Answer:

    The heat transferred is  Q = 5.866 * 10^9 J

    The power is  P = 5866\  MW

    Explanation:

    From the question we are told that

          Mass of the water per second is m = 1917 \ kg

          The initial temperature of the water is T_i  = 35^oC

          The boiling point of water is  T_b = 100^oC

          The final temperature T_f = 450^oC

          The latent heat of vapourization of water is  c__{L}} = 2256*10^3 J/kg

          The specific heat of water c_w = 4184 J/kg^oC

          The specific heat of stem is C_s =1520 \ J/kg ^oC

    Generally the heat needed each second is mathematically represented as

             Q = m[c_w (T_i - T_b) + m* c__{L}}  + m* c__{S}} (T_f - T_b)]

    Then substituting the value

            Q = m[c_w [T_i - T_b] + c__{L}}  + C__{S}} [T_f - T_b]]

             Q = 1917 [(4184) [100 - 35] + [2256 * 10^3]  +[1520]  [450 - 100]]

             Q = 1917 * [3.05996 * 10^6]

             Q = 5.866 * 10^9 J

    The power required is mathematically represented as

             P = \frac{Q}{t}

    From the question t = 1\ s

    So  

            P = \frac{5.866 *10^9}{1}

            P = 5866*10^6 \ W

            P = 5866\  MW

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