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11 November, 16:28

A compressor brings nitrogen from 100 kPa, 290 K to 2000 kPa. The process has a specific work input of 450 kJ / kg and the exit temperature is 450 K. Find the specific heat transfer using constant specific heats

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Answers (2)
  1. 11 November, 18:47
    0
    Given Information:

    Gas = Nitrogen

    Inlet temperature = T₁ = 290 K

    Exit temperature = T₂ = 450 K

    Inlet Pressure = P₁ = 100 kPa

    Exit Pressure = P₂ = 2000 kPa

    Work input = W = - 450 kJ/kg

    Required Information:

    specific heat transfer = Q = ?

    Answer:

    specific heat transfer = - 282.64 KJ/kg

    Explanation:

    The specific heat transfer can be found using the equation

    Q - W = ΔU

    Q = ΔU + W eq. 1

    Where W is the work input and ΔU is the change in internal energy.

    The change in specific internal energy is given by

    ΔU = h₂ - h₁ = Cp (T₂ - T₁)

    Where Cp is the specific heat capacity.

    The specific heat capacity is the amount of heat required to increase the temperature of one gram of a substance by one degree K.

    The Cp of Nitrogen gas is equal to 1.046 KJ/kg. K

    Therefore, equation 1 becomes

    Q = ΔU + W

    Q = Cp (T₂ - T₁) + W

    Q = 1.046 (450 - 290) + (-450)

    Q = 1.046 (160) - 450

    Q = 167.36 - 450

    Q = - 282.64 KJ/kg

    The negative sign indicates that the heat energy was transferred from the system (leaving the system) rather than transferred to the system (entering the system).
  2. 11 November, 18:51
    0
    The specific heat transfer is 687.5 kJ/kg.

    Explanation:

    Specific heat transfer = specific work input + specific internal energy

    specific work input = 450 kJ/kg

    specific internal energy = Cv (T2 - T1)

    Cv is specific heat at constant volume = 20.785 kJ/kmol. K

    T1 is initial temperature = 290 K

    T2 is exit temperature = 450 K

    specific internal energy = 20.785 (450 - 290) = 20.785*160 = 3325.6 kJ/kmol = 3325.6 kJ/kmol * 1 kmol/14 kg = 237.5 kJ/kg

    specific heat transfer = 450 kJ/kg + 237.5 kJ/kg = 687.5 kJ/kg
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