Homework 10 Solutions

Thermodynamics Homework 10 Solutions 1.

A two-stage compressor is used to compress air. The air is first compressed from 100 kPa to a medium pressure of 600 kPa. Its initial temperature is 15°C. Some of the air (20%) is then fed to a process requiring air at 600 kPa, and the remaining air is further compressed to a high pressure of 800 kPa. The compressor requires 32 kW of power. (a) Draw a process diagram, (b) draw the process on a T-S diagram, (c) determine the temperatures of the medium- and high-pressure air streams, (d) determine the mass flow rate of air into the compressor. The compressor is adiabatic and reversible.

Assumptions: Ideal Gas Constant Heat Capacity Isentropic (reversible, adiabatic) compression

(15+273)*6^(0.375/1.375) = 469 K

Pressure increased by a factor of 8 in high-press ure stream. (15+273)*8^(0.375/1.375) = 508 K

Energy balance around the whole unit:

Define  to be the fraction of air used as medium-pressure air.

32 / (0.8*1.1*(235-15) + 0.2*1.1*(196-15)) = 0.137 kg/s

2.

Steam expands reversibly and adiabatically in a turbine at a rate of  , entering at   and   and leaving at  . After exiting the turbine, it flows through a throttling valve, exiting the process as a saturated vapor at  . Assume kinetic energy changes are negligibly small. a.

Draw the flow diagram.

b. Draw the process on a T-S diagram and a P-H diagram, what phase is the stream exiting the turbine? c.

What is   for the turbine?

d. What is rate of entropy generation for the entire process?

Water 

700

600

500

400    ]    C    °    [    T300

 8000 kPa

200 1000 kPa

100

100 kPa

0 -1.0

0.1

1.2

2.3

3.4

4.5

5.6

6.7

7.8

8.9

10.0

s [kJ/kg-K] 5

10

4

10

1  270°C

  7 .1 200°C

3

10    ]   a    P    k    [    P

2

  K   k g   k J /   7. 8

150°C

110°C

2

3

10

1

10

0.2

0.4

0.6

0.8

0

10

0

500

1000

1500

2000

2500

3000

3500

4000

h [kJ/kg]

The valve is not adiabatic (heat must have been lost from the valve to reduce its enthalpy from 2 to 3).

3.

Air flows into a throttling valve and turbine at a rate of 55 L/s at a temperature of 200°C and a pressure of 5 MPa. It is exhausted from both devices at atmospheric pressure. 20% of the air flows through the throttling valve. The turbine is adiabatic and has an isentropic efficiency of 76%. a.

Throttling Valve

Turbine

    

What is rate of entropy generation for the entire process?

b. Draw the state transitions across the valve and the turbine on a T-S diagram and on a P-H diagram. c.

Determine the power generated by the turbine.

d. Determine the rate entropy is generated by the valve and by the turbine.

valve

turbine

b. c.

(5000*0.055) / (0.2870*(200+273)) = 2.03 kg/s

(200+273.15)*(101.3/5000)^(0.4/1.4) = 155 K 155 -273.15 = -118 C

0.76*0.8*2.03*1.005*(200+118) = 394 kW

-0.2*2.03*0.2870*ln(101.3/5000) = 0.45 kW/K

0.8*2.03*(1.005*ln(231.8/473.15) - 0.2870*ln(101.3/5000)) = 0.65 kW/K

200 - 394 / (0.8*2.03*1.005) = -41.4 C -41.4 + 273.15 = 231.75