AGUS HARYANTO

1

• AGUS HARYANTO
• 01 March 2010

2
Objectives

• Examine the moving boundary work or P.dV work.
• Identify the first law of thermodynamics for
  closed (fixed mass) systems.
• Develop the general energy balance for closed
  systems.
• Define the specific heat at constant volume and
  at constant pressure.
• Relate the specific heats to the changes in
  internal energy and enthalpy of ideal gases.
• Changes in internal energy and enthalpy for
  incompressible substances.
• Solve energy balance problems for closed (fixed
  mass) systems that involve heat and work
  interactions.

3
MOVING BOUNDARY WORK

• Wb F.s
• ?Wb F.ds
• ?Wb PA.ds
• ?Wb P.dV

4
Wb A under the curve

• The area under the process curve on a P-V diagram
  is equal, in magnitude, to the work done during a
  quasi-equilibrium expansion or compression
  process of a closed system.
• On the P-v diagram, it represents the Wb done per
  unit mass.)

5
Wb depends on path
6
Wb for systems undergo cycle
7
Car Engine

• In a car engine, the boundary work done by the
  expanding hot gases is used to overcome friction
  between the piston and the cylinder, to push
  atmospheric air out of the way, and to rotate the
  crankshaft.

8
EX. 41 Wb _at_ Constant Volume

• A rigid tank contains air at 500 kPa and 150C.
  As a result of heat transfer to the surroundings,
  the temperature and pressure inside the tank drop
  to 65C and 400 kPa, respectively. Determine the
  boundary work done during this process.

9
EX. 41 Wb _at_ Constant Volume

• Analysis
• P-V diagram of the process is shown.
• The boundary work can be determined

10
EX. 41 Wb _at_ Constant Pressure

• A frictionless pistoncylinder device contains 10
  lbm of steam at 60 psia and 320F. Heat is now
  transferred to the steam until the temperature
  reaches 400F. If the piston is not attached to a
  shaft and its mass is constant, determine the
  work done by the steam during this process.

11
Sketch
12
EX. 41 Wb _at_ Constant Pressure

• Analysis The pressure of the steam remains
  constant during this process since both the
  atmospheric pressure and the weight of the piston
  remain constant. For a constant-pressure process
  (Mind that V mv)

13
Calculation

• From the superheated vapor table (Table A6E),
  the specific volumes are determined to be v1
  7.4863 ft3/lbm at state 1 (60 psia, 320oF), v2
  8.3548 ft3/lbm at state 2 (60 psia, 400oF).
  Substituting these values yields

14
EXAMPLE 43 Isothermal Compression

• A pistoncylinder device initially contains 0.4
  m3 of air at 100 kPa and 80C. The air is now
  compressed to 0.1 m3 in such a way that the
  temperature inside the cylinder remains constant.
  Determine the work done during this process.

15
Sketch
16
Solution
17
Polytropic Process

• Pressure and volume are often related by PVn C,
  where n and C are constants.

18
Polytropic Process

• For ideal gas (PV mRT), then
• Special cases (n 1), then (isothermal)

19
EXAMPLE 44

• A pistoncylinder device contains 0.05 m3 of a
  gas initially at 200 kPa. At this state, a linear
  spring that has a spring constant of 150 kN/m is
  touching the piston but exerting no force on it.
  Now heat is transferred to the gas, causing the
  piston to rise and to compress the spring until
  the volume inside the cylinder doubles. If the
  cross-sectional area of the piston is 0.25 m2,
  determine (a) the final pressure inside the
  cylinder, (b) the total work done by the gas, and
  (c) the fraction of this work done against the
  spring to compress it.

20
Sketch
21
Calculation

• Final pressure 200 120 320 kPa

22
Calculation
23
ENERGY BALANCE FOR CLOSED SYSTEMS

• From Ch. 2
• In the rate form
• For constant rate

24
ENERGY BALANCE

• Differential form
• Closed system undergo cycle
• Esystem E2 - E1 0
• Ein - Eout 0
• Ein Eout.
• No mass flow (closed system)

25
Energy balance (first-law) relations Summary

• where
• Q Qnet,in
• Qin - Qout
• (is the net heat input)
• W Wnet,out
• Wout - Win
• (is the net work output)

26
EXAMPLE 45 Heating gas _at_ P

• A pistoncylinder device contains 25 g of
  saturated water vapor that is maintained at a
  constant pressure of 300 kPa. A resistance heater
  within the cylinder is turned on and passes a
  current of 0.2 A for 5 min from a 120-V source.
  At the same time, a heat loss of 3.7 kJ occurs.
  (a) Show that for a closed system the boundary
  work Wb and the change in internal energy U in
  the first-law relation can be combined into one
  term, H, for a constant pressure process. (b)
  Determine the final temperature of the steam.

27
Sketch
28
Calculation

• (a)

29
Calculation

• (b) To find T2 we need other property. Work is
  only electrical work, which is determined from
• Apply the Equation resulted in (a)

30
Calculation (Contd)

• Finally, from Table A-6

31
EXAMPLE 46 Unrestrained Expansion of Water

• A rigid tank is divided into two equal parts by a
  partition. Initially, one side of the tank
  contains 5 kg of water at 200 kPa and 25C, and
  the other side is evacuated. The partition is
  then removed, and the water expands into the
  entire tank. The water is allowed to exchange
  heat with its surroundings until the temperature
  in the tank returns to the initial value of 25C.
  Determine (a) the volume of the tank, (b) the
  final pressure, and (c) the heat transfer for
  this process.

32
Sketch
33
Calculation
34
Calculation
(c) Under stated assumptions and observations,
the energy balance on the system can be expressed
as
35
Calculation