Thermodynamics Homework 7 Solutions

1. An adiabatic piston-cylinder device supports two bricks. It contains saturated liquid water at 200°C. One

brick is removed. How many times bigger is the new volume? What is the new temperature? Atmospheric

pressure is negligible. Draw the state transition on P-V and T-V diagrams (use the button in EES to

make them).

The problem is that you don’t know or ̂ ., and it is very difficult to use the water tables for this type

of problem. EES will iterate on the two equations and solve for the volume ratio and .

2. Steam enters a nozzle with a speed of 80 m/s, a temperature of 498°C and an absolute pressure of 4.1 MPa. The

steam leaves the nozzle at 2150 kPa and 295°C. The inlet diameter of the nozzle is 8.5 cm. Heat is lost from the

nozzle at a rate of 7.25 kW. Determine (1) the mass flow rate of the steam, (2) the exit speed of the steam, and (3)

the exit area of the nozzle.

10-3 10-2 10-1 100102

103

104

105

v [m3/kg]

P [

kP

a]

200°C

169.2°C

0.05 0.1 0.2 0.5

1

2

10-3 10-2 10-1 1000

100

200

300

400

v [m3/kg]

T [

°C]

1555 kPa

777.5 kPa

1

2

3. A diagram for a steam power plant is shown. The following data are known for each location.

The flow rate of steam around the loop is 47 kg/s. The shaft work entering the pump is 350 kW. The diameter of the pipe

from the steam generator to the turbine is 375 mm and the diameter of the pipes between the condenser to the steam

generator is 95 mm. The pipe diameter between the turbine and condenser is unknown. The temperature of the cooling

water increases from 15°C to 25°C in the condenser.

Determine (1) the power output of the turbine, the heat transfer rates in the (2) condenser, (3) economizer, and (4)

steam generator, and (5) the flow rate of cooling water through the condenser. (6) make a graph of the cycle on a P-V

diagram (use the button on EES to make a quantitative one). (7) Graph the mass flow rate of cooling water as a

function of the cooling water output temperature, ranging from 16°C to 50°C.

Turbine

Condenser CoolingWater

Pump

SteamGenerator

Economizer

12

3

45

6

7

Location ( ) ( ) ( )

1 9.8

2 9.7

3 9.4 250

4 9.1 725

5 9.0 715

6 0.01 0.97 150

7 0.009 40

energy balance around the turbine:

energy balance around the condenser:

energy balance around the economizer:

energy balance around the steam generator:

cooling water flow:

Note that the area inside this cycle is the net amount of work the power plant generates per kilogram of steam

flowing through it (kW/kg).

10-4 10-3 10-2 10-1 100 101 10210

0

101

102

103

104

105

v [m3/kg]

P [

kP

a]

725°C

250°C

40°C

0.05 0.1 0.2 0.5

1

23

45

67

20 30 40 500

5000

10000

15000

20000

25000

TCW,O [C]

mC

W

[kg

/s]