1. This document discusses various thermodynamic concepts related to internal combustion engines including: thermal efficiency, mechanical efficiency, brake thermal efficiency, volumetric efficiency, specific fuel consumption, and air-fuel ratios. Key equations are provided for calculating these values. 2. Useful thermodynamic relations for analyzing engine cycles are presented, including the ideal gas law, specific heats at constant pressure and volume, adiabatic and isothermal processes, enthalpy, and the first law of thermodynamics. 3. The Carnot cycle is described as the most efficient theoretical thermodynamic cycle. The thermal efficiency of the Carnot cycle depends only on the highest and lowest temperatures of the cycle.

1. Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE
TERMODYNAMIC AND CYCLING
1. First Law Analysis of Engine Cycle-Energy Balance
a). Indicated thermal efficiency ( tη ).
Indicated thermal efficiency is the ratio of energy in the indicated horse power to fuel
energy.
hpfuel
ihp
ηt =
valuecalorificfuel/min xofmass
4500xihp
=
b). Mechanical efficiency ( mη )
Mechanical efficiency is the ratio of brake horse power (delivered power) to the indicated
horse power (power provided to the piston)
ihp
bhp
m =η
and bhpihpfhp −=
7
Fuel in
System boundary
Air in
Engine
Qt
Work out
Exhaust
Energyinfuel
ihp
bhp
Energy lost in exhaust, coolant, radiation etc
Energy loss in fiction, pumping etc
Engine
bhpihp
friction

2. Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE
c). Brake thermal efficiency ( tbη ).
Brake thermal efficiency is ratio of energy in brake horse power to the fuel energy.
hpfuel
bhp
ηtb =
valuecalorificfuel/min xofmass
4500xbhp
=
The brake thermal equals the product of the indicated thermal efficiency tη and the
mechanical efficiency mη .
mttb ηxηη =
d). Volumetric efficiency ( Vη )
conditionpressureandretemperatuintakeatvolumecylinderbydrepresentechargeofmass
indicatedactuallychargeofmass
ηV =
e). Specific fuel consumption.
The fuel consumption characteristics of an engine are generally expressed in terms of
specific fuel consumption in grams per horsepower-hour. Brake specific fuel
consumption and indicated specific fuel consumption, abbreviated as bsfc and isfc, are
the specific fuel consumptions on the basis of bhp and ihp, respectively.
f). Fuel-air (F/A) or air-fuel (A/F) ratio.
The relative proportions of the fuel and air in the engine are very important from the
standpoint of combustion and efficiency of engine. This expressed either as the ratio of the
mass of the fuel to that of the air.
ratioairfueltricstoichiome
ratioairfuelactual
Fr
−
−
=
Stoichiometric = a chemically correct is mixture that contains just enough air for complete
combustion of all fuel.
2. Useful Thermodynamic Relations
The following are the useful thermodynamic relations used in the analysis of air standard
cycles.
a). For ideal gas cycle the working fluid is a perfect gas which follows the law
mRTpV = , or RTpv =
where p is the pressure, V volume, v specific volume, m mass, R gas constant and T
absolute temperature (0
Kelvin).
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3. Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE
b). For perfect gas
J
R
cc VP =−
where cP (= 0,24) is the specific heat at constant pressure and cV (= 0.17) is the specific
heat at constant volume. The ratio 4.1
c
c
V
p
==γ will be designated by the symbol γ .
c). From the perfect gas law, it can be seen that an isothermal process will follow the
relationship
ttanconspv =
d). It is readily shown that for perfect gas the reversible adiabatic or isentropic process will
follow the relationship
ttanconspv =γ
e). The definition of enthalpy h is given by the expression
pvuh +=
which for a perfect gas, becomes
RTuh +=
f). For a perfect gas internal energy u and enthalpy h are functions of temperature only
∫=∆
2
1
T
T
vdTcu ∫=∆
2
1
T
T
pdTch
g). In a compression process, if p1, V1, and T1 represent the initial conditions p2, V2, and T2 the
final conditions are given by
( ) n/1n
1
2
1n
2
1
1
2
p
p
V
V
T
T
−−






=





=
where n is the index of compression.
For reversible adiabatic or isentropic compression n = γ.
h). For isothermal process of a perfect gas, the change in u and h is zero. Therefore, for both
flow and non-flow process
1
2
isothermal
v
v
logmRTWQ ==
where Q is the heat interchange and W the work done
i). The work done in a non-flow polytrophic process is given by
( )
1n
TTmR
1n
VpVp
W 212211
−
−
=
−
−
=
9
u
u + pv

4. Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE
where m = mass of gas
The work transfer during flow process is given by
( )
1n
TTmR
n xW 21
−
−
=
j). The heat transfer to any fluid can be evaluated from
∫ ∫== dTcTdsQ nrev
where cn = specific heat of the fluid in which subscript n refers to the property which
remains constant during the process.
k). For any general process, according to the first law of thermodynamics,
for non-flow process UWQ ∆=−
and for flow process HWQ ∆=−
l). For any cycling process
addedtrejectedadded QxηQQΣQΣW =−==
Where the symbol Σ refers to over the cycle and tη is the thermal efficiency.
added
t
Q
ΣW
=∴η
THE CARNOT CYCLE
(Carnot is a French Engineer)
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5. Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE
During the isentropic process bc and da the heat transfer form or to the working
substance is zero. Therefore, heat transfer takes place during isothermal process ab and cd
only.
Let r = ratio of expansion Vb/Va during process ab
= ratio of compression Vc/Vd during process cd
If the ratio of expansion and compression are not equal it would be a closed cycle.
Now, consider 1 kg of working substance:
Heat supplied during process ab, rlogRTrlogvpq e1eaac =−
Heat rejected during process cd, rlogRTrlogvpq e2eccd =−
Work done = heat supplied – heat rejected
= rlogRTrlogRT e2e1 −
∴Thermal efficiency of the Carnot cycle,
pliedsupheat
workdone
carnot =η
rlogRT
rlogRTrlogRT
e1
e2e1 −
=
1
2
1
21
T
T
1
T
TT
−=
−
=
peraturHigher tem
ΔT
=
Carnot cycle on T-s diagram.
On T-s diagram the two isothermal processes ab and cd are represented by horizontal lines
and two isentropic processes bc and ad by vertical lines.
The heat supplied during the isothermal process ab is given by
)s(sTssbaareaq 121211 −==
Similarly, the heat rejected during the isothermal process cd is given by
)s(sTssdcareaq 122212 −==
Hence we have thermal efficiency of Carnot cycle
( ) ( )
( )121
122121
carnot
ssT
ssTssT
−
−−−
=η
1
2
1
21
T
T
1
T
TT
−=
−
=
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6. Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE
Net work output = (T1 – T2)(s2 – s1)
Gross work of expansion = work done during process ab + work done during process bc.
For isothermal process Q = W
i.e., Wab = Qab = area under line ab on T-s diagram
= T1(s2-s1)
For isentropic process from b and c
Wbc = ub - uc
Therefore, for a perfect gas
( )21vbc TTcW −=
( )( )
( ) ( )21v121
1221
TTcssT
ssTT
ratioWork
−+−
−−
=∴
Relative work outputs of various piston engine cycles is given by mean effective
pressure (mep or pm), which is defined as the constant pressure producing the same net work
output whilst causing the piston to move through the same swept volume as in the actual cycle
Let pm = mean effective pressure
Vs = swept volume
W = net work output per cycle
Then,
volumestroke
cycleperdonework
pm =
ss V
pdV
V
W ∫==
Also,
diagramtheoflength
diagramindicatortheofarea
pm =
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