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Answer :
The intermediate pressure, Px, in the two-stage reciprocating compressor is approximately 11.4 kPa.
The intermediate pressure, Px, in the two-stage reciprocating compressor can be determined using the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
First, let's convert the mass flow rate of 8.0 kg/min to the number of moles. We can use the equation n = m/M, where n is the number of moles, m is the mass, and M is the molar mass. The molar mass of air is approximately 28.97 g/mol.
So, n = (8.0 kg/min * 1000 g/kg) / 28.97 g/mol = 276.3 mol/min.
Next, we need to determine the volume. We can use the equation V = m/d, where V is the volume, m is the mass, and d is the density. The density of air is given as 1.1 kg/m3.
So, V = (8.0 kg/min * 1000 g/kg) / (1.1 kg/m3) = 7272.7 m3/min.
Now, let's calculate the initial pressure, P1, and temperature, T1, using the equation PV = nRT.
P1 * V = n * R * T1
(100.2 kPa) * (7272.7 m3/min) = (276.3 mol/min) * (8.314 J/(mol·K)) * T1
Simplifying the equation, we can solve for T1:
T1 = (100.2 kPa * 7272.7 m3/min) / (276.3 mol/min * 8.314 J/(mol·K)) = 316.4 K
Now, we can determine the final pressure, P2, using the equation PV = nRT, where V is the volume of the compressed air.
(Px) * (V) = (276.3 mol/min) * (8.314 J/(mol·K)) * (T1)
Simplifying the equation, we can solve for Px:
Px = (276.3 mol/min * 8.314 J/(mol·K) * T1) / V
Given that V is equal to (7272.7 m3/min), we can substitute the values and solve for Px.
Px = (276.3 mol/min * 8.314 J/(mol·K) * 316.4 K) / (7272.7 m3/min)
After performing the calculation, the intermediate pressure, Px, is found to be approximately 11.4 kPa.
In summary, the intermediate pressure, Px, in the two-stage reciprocating compressor is approximately 11.4 kPa.
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