# 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 m2. Assuming the ideal gas model, determine the rate of entropy production within the duct, in W/K.

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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 m2. Assuming the ideal gas model, determine the rate of entropy production within the duct, in W/K.

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Step 1

Given:

Properties of air at the inlet of duct.

Pressure P1 = 200 KPa

Temperature T1 = 51.85°C

Rate of mass flow m1 = 4.02 Kg/s

Properties of air at the outlet of duct.

Pressure P2 = 100 KPa

Temperature T2 = 82°C

Velocity V2 = 255 m/s

Cross-sectional area A2 = 2×10-3 m2

Step 2

Assumptions:

1. The system is steady state.
2. For control volume W = 0 and heat transfer can also be ignored thus, Q = 0.
3. The air is modeled as an ideal gas.
Step 3

From the entropy rate b...

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