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17 February, 08:45

Propellants enter a rocket combustion chamber with a volume of 1.20 m3 at a constant rate of 45.0 kg/s. After they burn, their temperature rises to 2600 K and the molecular weight of the burned products is 9.42 kg/kmol. The nozzle downstream of the combustion chamber limits the exiting mass flowrate to p·8.20 * 10-6 kg / (Pa·s), where p is the pressure in the combustion chamber. If the combustion chamber is at a pressure of 44.0 bar, what is the density of the combustion products in the combustion chamber? You can assume that the products are ideal gases at these high temperature conditions.

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  1. 17 February, 10:14
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    Answer: 1942.32kg/m3

    Explanation: pressure in CC (combustion chamber) = 44bar = 44x1.013x10^5 = 4457200pa

    Volume of cc = 1.2m3

    Temperature of cc = 2600k

    molar mass of burnt product = 9.42kg/kmol

    Using PV = nRT

    n = PV/RT

    where R = 8.314 j/mol/k, a constant

    n = (4457200x1.2) / (8.314x2600)

    n = 247.43mol = no of moles of product in cc

    n = m/mm

    Where m is the mass of the cc product

    M = n*mm = 247.43x9.42 = 2330.79kg

    Density = m/V

    = 2330.79/1.2 = 1942.32kg/m3

    NB: we assumed that the product behave as an ideal gas hence the formula pv = nRT was used.
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