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

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?

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

Formally: Qin and Wout are positive, Qout and Win are negative Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 3-9 Specifying the directions of heat and work. Formally: Qin and Wout are positive, Qout and Win are negative 3-1

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

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

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

Mechanical Work m

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.

Copyright © The McGraw-Hill Companies, Inc Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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

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

Work of Expansion

Work of Expansion: p-dV work

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

Copyright © The McGraw-Hill Companies, Inc Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 3-20 The area under the process curve on a P-V diagram represents the boundary work. 3-3

Copyright © The McGraw-Hill Companies, Inc Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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. 3-4

PROCESSES INVOLVING IDEAL GASES

Polytropic processes...

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

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

Expression for work: Process equation:

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

For the special case when n = 1:

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

Alternative expressions for W1-2

Constant pressure processes...

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

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:

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