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Mechanical EngineeringQ&A LibraryAt steady state, air at 200 kPa, 51.85°C and a mass flow rate of 4.02 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. At the duct exit, the pressure of the air is 100 kPa, the temperature is 82°C, the velocity is 255 m/s, and the cross-sectional area is 2 x 10-3 m2. Assuming the ideal gas model, determine the rate of entropy production within the duct, in W/K.Question

Asked Dec 2, 2019

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At steady state, air at 200 kPa, 51.85°C and a mass flow rate of 4.02 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. At the duct exit, the pressure of the air is 100 kPa, the temperature is 82°C, the velocity is 255 m/s, and the cross-sectional area is 2 x 10^{-3} m^{2}. Assuming the ideal gas model, determine the rate of entropy production within the duct, in W/K.

Step 1

Given:

Properties of air at the inlet of duct.

Pressure P_{1} = 200 KPa

Temperature T_{1} = 51.85°C

Rate of mass flow m_{1} = 4.02 Kg/s

Properties of air at the outlet of duct.

Pressure P_{2} = 100 KPa

Temperature T_{2} = 82°C

Velocity V_{2} = 255 m/s

Cross-sectional area A_{2} = 2×10^{-3} m^{2}

Step 2

Assumptions:

- The system is steady state.
- For control volume W = 0 and heat transfer can also be ignored thus, Q = 0.
- The air is modeled as an ideal gas.

Step 3

From the entropy rate b...

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