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Thermodynamics; Temperature in cylinder after combustion

  1. Aug 6, 2013 #1
    1. The problem statement, all variables and given/known data
    I have an assignment to calculate the temperature, T1, after combustion in a cylinder. The combustion itself happens at constant pressure. I also know the average molar mass, M, of the gases after combustion and that the specific heat capacity is constant and can be calculated with use of the molar mass and that the specific heat ratio K.

    M = 28.71 kg/kmol
    K = 1.40
    Q1 = 1890 J (the heat that comes from the fuel due to combustion
    V0 = 0.002 m^3 (the volume of the cylinder)
    p0 = 1.013*10^-5 Pa (pressure in cylinder before compression
    T0 = 293.15 K (temperature of the air before compression)
    m_fuel = 45.0*10^3 kg (fuel in cylinder)
    m_air = 2.40*10^-3 kg (air in cylinder)

    2. Relevant equations
    My assumption is, considering that it is stated in the task that the combustion happens at constant pressure, that this is an isobaric process.

    This yields that p0 = p1 and that V1/V0 = T1/T0.

    q_r = c_p*(T1-T0).

    c_p = K*8314.3/(M*(K-1))

    Here I don't know q_r (what is that?) and V1.

    Another equation from which I can get T1 is: Q1 = n*c_p*T_delta, where n is that number of moles.


    3. The attempt at a solution

    Using the equations above: c_p = 1013.53 => T_delta = Q1/(n*c_p) = 1890/(n*c_p).

    Here I'm not sure about n. Is it the moles of fuel (C4H10) or fuel and air?

    Using moles of fuel: T_delta = 1890/(7.76*10^-4*1013.53) = 777.29 K.

    I'm really lost here. Is then T1 = T_delta-T0 = 777.29-293.15 (= 484.14 degree Celsius)?

    Is my assumption of isobaric process correct? And can I really use the temperature T0 since that is before compression?

    I would really appriciate some help with this!

    Best regards
    Christopher
     
    Last edited: Aug 6, 2013
  2. jcsd
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