1. Energy Transfer by Heat, Work, and Mass
CHAPTER 3
Energy Transfer by Heat, Work, and Mass

2. Heat Transfer Heat, means heat transfer. Adiabatic – no heat transfer
Energy transfer driven by temperature difference
always hotter to cooler
Adiabatic – no heat transfer
same as isothermal?
Symbols used:
Q and q Q
Caloric?

3. Work Energy transfer not driven by a temperature difference. Examples
Rising piston
rotating shaft
electric wire crossing the system boundaries
Symbols used:
W and w W

4. Formally: Qin and Wout are positive, Qout and Win are negative
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FIGURE 3-9 Specifying the directions of heat and work.
Formally:
Qin and Wout
are positive,
Qout and Win
are negative
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5. Heat and Work Both heat and work are boundary phenomena.
Systems possess energy, but not heat or work.
Both are associated with a process, not a state.
Both are path functions
Magnitudes depend on paths as well as end states

6. Processes
Process line, or path
State 1
State 2 P1 P3 P2

7. Electrical Work
We = VI
so We = VIΔt if V and I are constant.

8. Mechanical Work m

9. Work at a system boundary...
Quasi – equilibrium processes,
best case.
Work at a system boundary...
There must be a force acting on the boundary.
The boundary must move.

10. Copyright © The McGraw-Hill Companies, Inc
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FIGURE 3-19 A gas does a differential amount of work dWb as it forces the piston to move by a differential amount ds.
3-2

11. Work transfer at a boundary
System
Surroundings
W > 0
W< 0
System Boundary

12. Work of Expansion

13. Work of Expansion: p-dV work

14. Evaluating a equilibrium expansion process
V = Ax V1 V2 p1 p2

15. Copyright © The McGraw-Hill Companies, Inc
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FIGURE 3-20 The area under the process curve on a P-V diagram represents the boundary work.
3-3

16. Copyright © The McGraw-Hill Companies, Inc
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FIGURE 3-22 The net work done during a cycle is the difference between the work done by the system and the work done on the system.
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17. PROCESSES INVOLVING IDEAL GASES

18. Polytropic processes...

19. The polytropic process: PVn=Const.
State 1
State 2

20. Changes in KE and PE are zero Quasistatic process Polytropic process
Assumptions
Changes in KE and PE are zero
Quasistatic process
Polytropic process
Ideal gas

21. Expression for work:
Process equation:

22. Evaluating the integral:
Note that n cannot equal one, which is the general case.

23. For the special case when n = 1:

24. Polytropic processes p n > 1 V1 V2 V T1 T2
Isothermal Process (n = 1)
n > 1 p1 p2

25. Alternative expressions for W1-2

26. Constant pressure processes...

27. Constant pressure process
Consider as a limiting case of the general polytropic process.
P = Constant
Evaluation of the work integral

28. P V Constant pressure, constant temperature and polytropic processes:1 2 P V
P = Constant
(n = 0)
Isobaric process
Constant pressure, constant temperature
and polytropic processes:

29. Shaft Work Work = F∙d Wsh = T(2πn) or
Replace force with torque, T
Replace distance with angle rotated = 2πn
where n is number of rotations
Wsh = T(2πn) or
Wsh = T(2πn) where n is frequency in Hz