1. LECTURE UNIT 009
3. Second Law of Thermodynamics is concerned with the availability of energy from a thermodynamic
cycle and shows the impossibility of a perpetual motion machine.
A. Kelvin-Plank Statement (Concept of thermal efficiency)
It is impossible to operate an engine in a cycle that will have no other effect than to extract heat from a
reservoir and produce an equivalent amount
ILLUSTRATION: Rankine Cycle Steam Power Plant
STEAM
. TURBINE
ms
1 Pi
QA
2
QR
BOILER BOILER FEED PUMP CONDENSER
3
B . .
ms ms
WP
Thermal Efficiency, e:
WNET
e= QA * 100%
B. Reeves Statement
Heat flows readily from a region of high temperature to region of lower temperature.
C. Clausius statement
It is impossible for a self-acting machine, unaided by an external agency to convey heat from one body
to another at a higher temperature.
ILLUSTRATION: Refrigeration Cycle
QR
.
mR
. CONDENSER
mR COMPRESSOR
EXPANSION
VALVE
WC
. EVAPORATOR .
mR mR
QA ROOM
4. Third Law of Thermodynamics states that the entropy of any pure substance in thermodynamic equilibrium tends to approach
zero as the absolute temperature approaches zero.
T2
S2 - S1 = dQ
T T
1
CYCLE ANALYSIS
is a series of processes that a system undergoes, whereby the system’s starting state is also its final state.
1. Use Pv and Ts diagram to illustrate the cycle.
2. PVT relationship
a.) PV = mRT (for any ideal gas processes)
P1V1 P2V2
b.) = (for P=C, V=C or T=C only)
T1 T2
k-1 k-1
k
T2 P2 V1
c.) = = (for PVk=C or S=C)
T1 P1 V2
Note: Change k to n for Special polytropic process (PVn=C)
“God gives us the ingredients for our daily bread, but He expects us to do the baking.”

2. 3. Heat Added, QA
QA = +Q
CYCLE
4. Heat Rejected, QR
QR = -Q CYCLE
5. Net Work, WNET
WNET = QA - QR = WNF = P dV
6. Cycle thermal efficiency, e
WNET
e = * 100% (for any cycle)
QA
7. Cycle mean effective pressure, Pm
Network
Pm =
Volumetric displacement
WNET e QA
Pm = =
VD (Vmax - Vmin)
CARNOT CYCLE
The most efficient cycle and basis of comparison for Rankine Cycle.
ILLUSTRATION: QA
Heat Source
. . 2
ma ma
1
TH = C
WT
ADIABATIC ADIABATIC TURBINE
COMPRESSOR S=C S=C OR EXPANDER
TL = C
. .
ma ma
Cold Souce 3
4
QR
P-v diagram T-s diagram
P T
1
PV = C
1 T=C 2
PVk = C TH = T1 = T2
2
WNET WNET
PVk = C S=C or S=C
QNET
4
PV = C 3
TL = T4 = T3 3
4 T=C
Pm WNET
v s
Definitions
Vmax
a.) Expansion Ratio, re =
Vmin
Vmax
b.) Compression Ratio, rk =
Vmin
Vmax
c.) Cut-off Ratio, rc =
Vmin
Pmax
d.) Pressure Ratio, rp =
Pmin
“Practice random acts of kindness and senseless acts of beauty.”

3. Equations:
1. PVT Relationships
Process 1-2 (T = C)
P1 V2
= = re(T=C) isothermal expansion ratio
P2 V1
Process 2-3 (S = C)
1
k-1 k-1 k-1
k
T3 P3 V2
= =
T2 P2 V3
1 1
k-1 k
T2 P2 V3
= = = re(S=C) isentropic expansion ratio
T3 P3 V2
Process 3-4 (T = C)
V3 P4
= = rk(T=C) isothermal compression ratio
V4 P3
Process 4-1 (S = C)
1 1
k-1 k
T1 P1 V4
= = = rk(S=C) isentropic compression ratio
T4 P4 V1
Since T2 = T1 and T4 = T3, Hence;
V3 V4
=
V2 V1
Isentropic expansion ratio = Isentropic compression ratio
re(S=C) = rk(S=C)
And; V3 V2
=
V4 V1
re(T=C) = rk(T=C)
Isothermal expansion ratio = Isothermal compression ratio
2. Heat Added, QA
Process 1-2 (T = C)
QA = +Q
P1 P1
QA = mRT1 ln = mRT2 ln
P2 P2
3. Heat Rejected, QR
Process 3-4 (T = C)
QR = -Q
P3 P3
QR = mRT3 ln = mRT4 ln
P4 P4
4. Net Work, WNET
WNET = QA - -QR
P1
WNET = mR (T1 - T4) ln
P2
“Everything is created twice - first mentally, then physically.”

4. 5. Carnot cycle thermal efficiency, e cc
WNET
e cc = Q * 100%
A
T1 - T4
e cc = * 100%
T1
TH - TL
e cc = * 100%
TH
6. Mean effective pressure, Pm
WNET
Pm =
VD
e cc QA
Pm =
(V3 - V1)
PROBLEM SET:
1. Consider a three-process air standard power cycle in which process 1-2 is an isothermal compression, 2-3 is a constant-
pressure heat addition, and 3-1 is an isentropic expansion. Given that P1 = 100 kPa, t1 = 20oC, and P2 = 600 kPa,
determine:
(a) The work and heat transfer for each process and the thermal efficiency of the cycle. [
]
(b) Show the cycle on Ts and Pv coordinates.
2. Consider a three-process air-standard power cycle in which process 1-2 is an isentropic compression, 2-3 is a constant
pressure heat addition, and 3-1 is a constant-volume heat rejection. Given that P1 = 100 kPa, T1 = 330 K, and P2 =
800 kPa, determine:
(a) The work and heat transfer for each process and the thermal efficiency of the cycle. [
]
(b) Show the cycle on Ts and Pv coordinates.
3. A three-process cycle operating with nitrogen as the working substance has: constant temperature 1-2 (t1 = 40oC, P1 = 110
kPa); constant volume heating 2-3; and polytropic expansion 3-1 (n=1.35). The isothermal compression requires -
67 kJ/kg of work. Determine:
(a) P, T, and v around the cycle
(b) The heat in and out [ ]
(c) The net work [ ]
4. Two and half kg of an ideal gas with R = 296.9 J/kg.K and cv = 0.7442 kJ/kg.K at a pressure of 827.4 kPa and a
temperature of 677oC reject 132.2 kJ of heat at constant pressure. The gas is then expanded according to PV1.25 =
C to a point where a constant volume process will bring the gas back to its original state. Determine P3, QA, and the
power in kJ. [ ]
5. An air-standard Carnot cycle is executed in a closed system between the temperature limits of 350 and 1200 K. The
pressures before and after the isothermal compression are 150 kPa and 300 kPa, respectively. If the net work
output per cycle is 400 kJ, determine.
(a) The maximum pressure in the cycle [ ]
(b) The heat transferred to air [ ]
(c) The mass of air [ ]
6. Consider a three-process thermodynamic cycle which operates on 0.5 kg/s of air is composed of the following reversible
processes:
(1) constant volume heating process 1-2;
(2) isentropic expansion process 2-3;
(3) constant pressure heat rejection 3-1
Given that P1 = 345 kPa, t1 = 38oC and P2 = 4P1, determine:
(a) the heat transfer for each process [ ]
(b) the network [ ]
(c) and the thermal efficiency [ ]
7. A thermodynamic cycle is composed of the following processes: isothermal expansion 1-2; isometric 2-3; isentropic 3-1. The
cycle runs on 0.125 kg of air and has an expansion ratio of 5.4. For P3 = 100 kPaa and t3 = 27oC, find
(a) P,V and t for each point of the cycle.
(b) Qin and Qout
(c) WNET [ ]
(d) ecyc [ ]
(e) mean effective pressure [ ]
8. The following thermodynamic cycle operating at 30 Hz is composed of the following reversible process; isothermal
expansion 1-2; polytropic 2-3; isometric 3-1. The cycle uses 0.725 kg of air, for which P2 = 105 kPaa, t2 = 735oC,
and t3 = 37oC, n = 0.75 for the polytropic process. Determine (a) the volume at each corner of the cycle (b) Qin and Qout (c)
the power [ ] (d) the Pm.
9. A Carnot engine rejects 1000 Btu/min at 50oF and produces 40 hp. Determine the temperature of heat addition and the
amount of heat flow into the engine. [ ]
10. A Carnot cycle uses air as the working substance. The heat supplied is 50 Btu. The temperature of the heat rejected is 70oF,
and the isentropic compression ratio V4/V1 = 10. Determine (a) the cycle efficiency [ ] (b) the temperature of
heat added [ ] (c) the work [ ]
“Either you run the day or the day runs you.”