Chap 4. Energy Analysis of
Closed Systems I
Objectives
1. Examine the moving boundary work or PdV work commonly
encountered in reciprocating devices such as automotive engines and compressors
2. Identify the first law of thermodynamics as simply a statement of the conservation of energy principle for closed (fixed mass) systems
3. Develop the general energy balance applied to closed systems
1 st law of Thermodynamics
Control mass (Closed System)
Control volume (Opened System)
W Q U KE P E
∆ + ∆ = ∆ + ∆ + ∆ W Q
massKE PE
W Q KE P
E
E U
H
∆ + ∆ + = + ∆ + ∆
∆ + ∆ = ∆ + ∆ + ∆
∆
∆
If your system is a stationary system
U W Q
∆ + ∆ = ∆ W Q E
mass(
boundary) U
H W
E Q
∆ + ∆ + =
∆
∆ + ∆
∆
= ∆
∆
Emass=PV
Moving boundary (closed System)
Moving Boundary Work
Moving boundary work: the expansion and compression work
2
1
(kJ)
b
b
W Fds PAds PdV
W PdV
δ = = =
= ∫
dV > 0 : expansion ⇒ W > 0 dV < 0 : compression ⇒ W<0
(kJ)
Area
21 2
1
dA PdV
A = ∫ = ∫
=
• The area under the process curve on a P-v diagram represents the boundary work
Summary
- Work
+ Work
Moving Boundary Work II
• Quasi-equilibrium (Quasi-static) process
- a process during which the system remains nearly in equilibrium at all times
- reversible process
- idealized process and is not a true representation of actual process
• The work output of a device is maximum and the work input to a device is minimum when quasi-equilibrium processes are used
• The boundary work done during a process depends on the path followed as well as the end states
Quasi-equilibrium vs. Non-quasi equilibrium (Compression)
Fast change
Slow change
Quasi-equilibrium vs. Non-quasi equilibrium (Expansion)
Fast change
Slow change
Ex. 1) Boundary Work for a Constant-Volume Process
Ex. 2) Boundary Work for a Constant-Pressure Process
Polytropic Process
• Work is dependent on detailed process
• In polytropic process, Pvn=constant
n=1 ; isothermal process (T=const.)
n=0 ; isobaric process (P=const.)
n=∞; isovolumetric process (V=const.)
n=κ=Cp/Cv; isentropic process (s=const.)
Ex. 3) Isothermal Compression of an Ideal Gas
Summary
Here is a tip!
1) Check your system (A piston-cylinder device vs. a rigid tank) - A piston-cylinder device moving boundary (Wb)
- A rigid tank fixed boundary (No Wb )
2) Note the type of fluid (Water, steam, R-134 vs. Other gases) - Water, steam, R-134 Use property table
- Other gases, air Use an ideal gas equation
Ex. 4) Expansion of a Gas against a Spring
Energy Balance for Closed Systems
• Energy balance (or the first law)
• The rate form
• For a closed system undergoing a cycle
•The energy balance in terms of heat and work interactions = (kJ)
= (kW)
in out system
in out system
E E E
E E dE dt
− ∆
ɺ − ɺ
, ,
, ,
= or =
where ,
net in net out system
net in in out net out out in
Q W E Q W E
Q Q Q W W W
− ∆ − ∆
= − = −
= = 0
in out system
in out
E E E
E E
− ∆
=
