University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Carnot engine
The characteristics of such ideal engine were first described by N. Carnot in 1824,
the four steps that make up a Carnot cycle
Step 1: A system at the temperature of a cold reservoir TC undergoes a reversible
adiabatic process that causes its temperature to rise to that of a hot reservoir at TH.
Step 2: The system maintains contact with the hot reservoir at TH, and undergoes a
reversible isothermal process during which heat ½ QH½
½ is absorbed from the hot
reservoir.
Step 3: The system undergoes a reversible adiabatic process in the opposite
direction of step 1 that brings its temperature back to that of the cold reservoir at
TC.
Step 4: The system maintains contact with the reservoir at TC, and undergoes a
reversible isothermal process in the opposite direction of step 2 that returns it to its
initial state with rejection of heat ½ QC½
½ to the cold reservoir.
Since a Carnot engine is reversible, it may be operated in reverse; the Carnot cycle
is then traversed in the opposite direction, and it becomes a reversible refrigeration
½, ½QC½
½, and ½ W½
½ are the same as for the
cycle for which the quantities ½ QH½
engine cycle but are reversed in direction.
Ideal-Gas Temperature Scale; Carnot's Equations
The cycle traversed by an ideal gas serving as the working fluid in a Carnot engine
is shown by a below PV diagram. It consists of four reversible steps:
· a → b Isothermal expansion to arbitrary point b with absorption of heat ½ QH½
½.
· b → c Adiabatic expansion until the temperature decreases to T2 .
· c → d Isothermal compression to the initial state with rejection of heat ½ QC½
½.
· d → a Adiabatic compression until the temperature rises from T2 to T1.
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Step 1 : DU = 0 and Q = W = RT 1 ln
PA
PB
Step 2: Q = 0 and W = C V (T 2 - T 1 )
T 2 PC
=
]
Reversible adiabatic process
T1 PB
Step 3: DU = 0 and Q = W = RT 2 ln
Step 4: Q = 0 and W = C V (T 1 - T 2 )
( g -1)
g
PC
PD
æT
Þ çç 1
èT2
g
ö ( g -1) P B
÷÷
=
PC
ø
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Reversible adiabatic process
Eff . =
Q1 - Q 2
=
Q1
RT 1 ln
T 2 PD
=
]
T1 PA
( g -1)
g
æT
Þ çç 1
èT2
ö
÷÷
ø
g
( g -1)
=
PA
PD
PA
P
- RT 2 ln D
PB
PC
P
RT 1 ln A
PB
PA
P
= D
PB
PC
\h =
T1 - T 2
T
=1- 2
T1
T1
Where T1 and T2 in Kelvin scale
This equation are known as Carnot`s equation .The thermal efficiency of a Carnot
engine approaches unity only when TH (T1) approaches infinity , or TC
(T2)approaches zero.
Conclusions:
· no engine operating between two heat reservoir each having a fixed
temperature can be more efficient than a reversible one operate between the
same temperature.
· All reversible engine operation between two heat reservoirs at the same
temperature , each having the same efficiency.
· The efficiency of any reversible engine operate between two reservoirs is
independent of the nature of the working but depend on the temperature of
reservoirs.