1. 4
CHAPTER
The First Law of Thermodynamics: Control Volumes

2. Velocity Profiles for Flow in a Pipe
4-1
Velocity Profiles for Flow in a Pipe
(fig. 4-6)
© The McGraw-Hill Companies, Inc.,1998

3. 4-2
Volume Flow Rate
Volume flow rate is the volume of fluid flowing through a cross section per unit of time

4. Mass Flow, Heat, and Work Affect Energy Content
4-3
Mass Flow, Heat, and Work Affect Energy Content
The energy content of a control volume can be changed by mass flow as well as heat and work interactions

5. Control Volume May Involve Boundary, Electrical, and Shaft Work
4-4
Control Volume May Involve Boundary, Electrical, and Shaft Work
(Fig. 4-9)

6. Schematic for Flow Work
4-5
Schematic for Flow Work
(Fig. 4-10)

7. 4-6
During Steady Flow Process, Volume Flow Rates are not Necessarily Conserved
(Fig. 4-19)

8. A Water Heater Under Steady Operation
4-7
A Water Heater Under Steady Operation
(Fig. 4-21) .

9. Steady-Flow Devices Operate Steadily for Long Periods
4-8
Steady-Flow Devices Operate Steadily for Long Periods
(Fig. 4-25)

10. Nozzle and Diffuser Shapes Cause Large Changes in Fluid Velocities
4-9
Nozzle and Diffuser Shapes Cause Large Changes in Fluid Velocities
Nozzles and Diffusers are shaped so that they cause large changes in fluid velocities and thus kinetic energies
(Fig. 4-27)

11. Schematic for Example 4-2
4-10
Schematic for Example 4-2

12. Schematic for Example 4-4
4-11
Schematic for Example 4-4

13. Throttling Valve Devices Cause Large Pressure Drops in Fluid
4-12
Throttling Valve Devices Cause Large Pressure Drops in Fluid
(Fig.4-32)

14. Ideal Gas Temperature Does Not Change During a Throttling
4-13
Ideal Gas Temperature Does Not Change During a Throttling
The temperature of an ideal gas does not change during
a throttling(h =constant) process since h = h (T)

15. T-Elbow Serves as Mixing Chamber for Hot and Cold Water Steams
4-14
T-Elbow Serves as Mixing Chamber for Hot and Cold Water Steams
The T-ebow of an ordinary shower serves as the mixing chamber
for hot- and cold-water streams.
(Fig. 4-35)

16. Heat Transfer Via Heat Exchanger Depends on System Selection
4-15
Heat Transfer Via Heat Exchanger Depends on System Selection
The heat transfer associated with a heat exchanger may be zero or nonzero
depending on how the system is selected

17. Schematic for Example 4-9
4-16
Schematic for Example 4-9 .

18. Rigid Tank Charging From a Supply Line is an Unsteady-Flow Process
4-17
Rigid Tank Charging From a Supply Line is an Unsteady-Flow Process
Charging of a rigid tank from a supply line is an unsteady-flow process since it involves changes within the control volume
(Fig. 4-47)

19. 4-18
Temperature of Steam Rises Entering Tank, Flow Energy Converts to Internal Energy
(Fig. 4-54)
The Temperature of Steam rises from 300 to 456°C as it enters a tank as a result of flow energy being converted to internal energy o

20. Enthalpy of a Saturated Vapor at a Given Pressure
4-19
Enthalpy of a Saturated Vapor at a Given Pressure
In a pressure cooker, the enthalpy of the existing steam is
(enthalpy of the saturated vapor at the given pressure)

21. 4-20
Chapter Summary
A control volume differs from a closed system in that it involves mass transfer. Mass carries energy with it, and thus the mass and energy content of a system change when mass enters or leaves.

22. 4-21
Chapter Summary
The mass and energy balances for any system undergoing any process can be expressed as

23. 4-22
Chapter Summary
The mass and energy balances for any system undergoing any process can be expressed in the rate form as

24. 4-23
Chapter Summary
Mass flow through a cross section per unit time is called the mass flow rate and is denoted m. It is expressed as where  = density, kg/m3 (= 1/v) = average fluid velocity normal to A, m/s A = cross-sectional area, m2 .

25. 4-24
Chapter Summary
The fluid volume flowing through a cross section per unit time is called the volume flow rate V. It is given by .

26. 4-25
Chapter Summary
The mass and volume flow rates are related by

27. 4-26
Chapter Summary
Thermodynamic processes involving control volumes can be considered in two groups: steady-flow processes and unsteady-flow processes. During a steady-flow process, the fluid flows through the control volume steadily, experiencing no change with time at a fixed position. The mass and energy content of the control volume remain constant during a steady-flow process.

28. 4-27
Chapter Summary
Taking heat transfer to the system and work done by the system to be positive quantities, the conservation of mass and energy equations for steady-flow processes are expressed as where the subscript i stands for inlet and e for exit. These are the most general forms of the equations for steady-flow processes.
for each exit
for each inlet

29. 4-28
Chapter Summary
For single-stream (one-inlet--one-exit) systems such as nozzles, diffusers, turbines, compressors, and pumps, the steady flow equations simplify to In the above relations, subscripts 1 and 2 denote the inlet and exit states, respectively.

30. 4-29
Chapter Summary
During a uniform-flow process, the state of the control volume may change with time, but it may do so uniformly. Also, the fluid properties at the inlets and the exits are assumed to remain constant during the entire process. The conservation of energy equation for a uniform-flow process reduces to

31. 4-30
Chapter Summary
When the kinetic and potential energy changes associated with the control volume and the fluid streams are negligible, the conservation of energy equation for a uniform-flow process simplifies to