Review
• System
• Property
• State
• Process
• Cycle
• Zeroth Law
Example 2-4
Applied Thermodynamics
Thermodynamics: Energy, Work, Power and Heat
Energy
• Forms of Energy– Kinetic: KE = ½ mv2
– Potential: PE = mgh
• Specific energy:– ke = ½ v2
– pe = gh
• Internal energy, U
• Efficiency, η
Energy
• Total ∆Esystem has three macroscopic quantities:– ∆KE: motion of system– ∆PE: displacement of system in a gravitational
field– ∆U: Internal Energy is an extensive property.
Energy: Forms or Carriers
• Many forms: kinetic, potential, thermal, radiant, elastic, chemical etc….
• Energy is [ex]changed (dynamic) and stored (static)
• It may be better to say energy is carried.
Work: Definition
• Means of energy transfer across a boundary:– Expansion work
Wk = ΣF δx = F ∆x = F (x2 – x1) Wk = Σp A δx = = Σp δV = p ∆V
– Shaft WorkWk = Σ T δ θ = T ∆ θ = T (θ2 – θ1)
P
V
1
2
dV
P
V
1
2
dV
Work: Sign Convention
• W>0: work transfer out of system• W<0: work transfer into system
Caution! Work is path dependent
• dW = p∙dV ----- meaningless because:∫dW = W2 – W1 = ∫p ∙ dV
Implies we can assign values to W1 and W2 .
• Instead we writeδW = p ∙ dV and W = ∫δW = ∫p ∙ dVWhere δW is an inexact differential.
i.e. the left side cannot be integrated and evaluated at the limits.
• Work is not a property.
Example: Work
• CO2 is slowly heated from 50C to 500C in two steps as shown.– p1 = 100 kPa
– p3 = 150 kPa
– T2 = 350C
– m = 0.044kg
• Calculate total Work.
P
V
1
2 3P2=P3
P1
V3V2V1
Example: Work
• Assume quasi-equilibrium• Assume Ideal gas
kJ .J
kPaPam..kPa m..kPa
m .:similarly
m .
kPaPa
kmolkg
kPa
kJJK
KkmolkJ.kg .
m .
kPaPa
kmolkg
kPa
kJJK
KkmolkJ.kg .
33
3
3
3
2022200
1000034500428015002680034502150100
04280
03450
100044150
100027335031480440
02680
100044100
10002735031480440
2
3
2
2
22
1
1
11
23212213
1
W
W
V
V
MpTRm
V
V
MpTRm
V
VVpVVpp
dVpWV
V
P
V
1
2 3P2=P3
P1
V3V2V1
Power
• Energy flow or energy currentPower = dE/dt = IE
• Rate of doing WorkPower = dW/dt = F ∙ dx/dt = F ∙ v
W = ∫F ∙ v dt =∫p ∙ dV
• Involves a flow across a potentialPower = -Δp |dV/dt|
= -Δφ |dq/dt| = V∙Iq
Heat: Definition
• Thermal energy moving across a boundary (not the lay definition)
• Only induced by a temperature difference• Adiabatic process: no transfer of heat• Like work, heat depends on the process, • Heat is not a property• Q>0: heat transfer to system• Q<0: heat transfer from the system
Equivalence of Work and Heat
• Heat and work are both energy transitions• Work can affect a system as if heat had been
transferred. (the opposite is not always true)
Internal Energy
• In a Macroscopic analysis anything not KE or PE is Internal Energy, U.– Specific internal energy, u = U/m, is intensive.– Sensible U – related to temperature – Latent U – associated with phase change
• Microscopically Internal Energy is made of:– Translation, Rotation and Vibration of molecules– Chemical bonds within molecules– Plus: orbital states, nuclear spin and nuclear forces
Work in a Polytropic Process
• pVn = constant
• If n≠1, general polytropic process
• If n = 1, isothermal process
• If n = 0, isobaric process
1
211 V
VVpW ln
nVpVp
W
1
1122
VVpW 2
Example: Polytropic Process
• A gas in a piston–cylinder assembly undergoes a process for which:pVn = constant
Pi = 3 bar, Vi = 0.1 m3, Vf = 0.2 m3
• Determine the Work if a) n=1.5, b) n=1.0, c) n=0
p (b
ar)
V (m3)
1
2a2b
2c3.0
0.1 0.2
pVn=k
Example: Polytropic Process, n=1.5
kJ
mN kJ
bar N/m
.m .bar m .bar .
bar .m .m .bar ,.for
233
.
3
3
617101
110
51110320061
0612010351
11
1
3
5
51
2
112
11221111
1222
11
12
2211
2
1
2
1
.W
VV
ppn
nVpVp
nVVpVVp
W
nVV
kdVVkdVpW
VpVpkpV
n
nnnn
nnV
V n
V
V
nnn
p (b
ar)
V (m3)
1
2a
3.0
0.1 0.2
pVn=k
Example: Polytropic Process, n=1
kJ .mN
kJ bar
mN
m .m .lnm .bar
lnln
2
3
33
.
7920101
110
1020103
3
5
1
211
1
2
221101
2
1
2
1
W
VV
VpVV
kdVVkdVpW
VpVpkpV
V
V
V
V
p (b
ar)
V (m3)
1
2b
3.0
0.1 0.2
pVn=k
Example: Polytropic Process, n=0
kJ mN
kJ bar
mNm .m .bar
233 30
101
110
102033
5
12
210
W
VVpW
ppkpV
pVn=k
p (b
ar)
V (m3)
1
2c3.0
0.1 0.2
Reversibility
• Process are idealized as reversible– The process can be reversed with a return to
the original state.– No dissipative effects– No production of entropy
• Irreversible work– Friction work and viscous work always oppose
mechanical work– Transfer of heat through a finite ∆T
Top Related