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.

Question

Engineering

Noemi Ruiz

28 December, 19:06

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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Christine Horton · Answer 1

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.