The document discusses the Carnot engine, a theoretical thermodynamic cycle that provides an estimate of the maximum possible efficiency for heat engines operating between two temperature reservoirs. It describes the principles of the Carnot engine, including that the efficiency of any irreversible engine is less than a reversible one operating between the same reservoirs, and that the efficiencies of all reversible engines between the same reservoirs are the same. The document then provides further details on the Carnot cycle and theorem, explaining that no engine can be more efficient than a reversible Carnot engine between the same temperatures, and that the efficiency depends only on the temperatures and not the working substance.

1. DR. MUHAMMAD GHAFFAR DOGGAR
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CARNOT ENGINE
HEAT TRANSFER AND
THERMODYNAMICS

2. What is a Carnot Engine?
Carnot engine is a theoretical thermodynamic cycle proposed by Leonard
Carnot. It gives the estimate of the maximum possible efficiency that a heat
engine during the conversion process of heat into work and conversely,
working between two reservoirs, can possess.
Carnot Engine Principles: are only for the cyclical devices like heat engines,
which state that:-
 The efficiency of an irreversible heat engine is always less than the
efficiency of a reversible one operating between the same two reservoirs.
 The efficiencies of all reversible heat engines operating between the same
two reservoirs are the same.
ACCORDING TO CARNOT THEOREM
 Any system working between two given temperatures T1 (hot reservoir)
and T2 (cold reservoir), can never have an efficiency more than the Carnot
engine working between the same reservoirs respectively.
 The efficiency of this type of engine is independent of the nature of the
working substance and is only dependent on the temperature of the hot
and cold reservoirs.

3. Carnot Engine
 The Carnot theorem states that no engine working between two
given temperatures (T1 hot and T2 low) can be more efficient than a
reversible engine working between the same two temperatures and
that “all the reversible engines working between the same two
temperatures have the same efficiency, whatever the working
substance may be”.
 According to the Carnot theorem, the reversible engine will always
have a greater efficiency than the irreversible one. The reversible
heat engine operates on a reverse cycle and functions as a heat
pump (or refrigerator).
 The Carnot cycle is reversible representing the upper limit on the
efficiency of an engine cycle. Practical engine cycles are irreversible
and thus have inherently lower efficiency than the Carnot efficiency
when operating at the same temperature. One of the factors
determining efficiency is the addition of to the working fluid in the
cycle and its removal.
 The Carnot cycle achieves maximum efficiency because all the heat
is added to the working fluid at the maximum temperature.

5. Explanation
For an ideal gas operating inside a Carnot cycle, the following
are the steps involved:
Step 1: Isothermal expansion:
The gas is taken from P1, V1, T1 to P2, V2, T2. Heat Q1 is
absorbed from the reservoir at temperature T1. Since the
expansion is isothermal, the total change in internal energy is
zero and the heat absorbed by the gas is equal to the work
done by the gas on the environment.
Step 2: Adiabatic expansion:
The gas expands adiabatically from P2, V2, T1 to P3, V3, T2.
Step 3: Isothermal compression:
The gas is compressed isothermally from the state (P3, V3, T2)
to (P4, V4, T2). Here, the work is done on the gas by the
environment.
Step 4: Adiabatic compression:
The gas is compressed adiabatically from the state (P4, V4, T2)
to (P1, V1, T1). Here, the work is done on the gas by the
environment

6. Efficiency of Carnot’s Cycle:
The Carnot cycle is reversible representing the upper limit on the efficiency
of an engine cycle. Practical engine cycles are irreversible and thus have
inherently lower efficiency than the Carnot efficiency when operating at the
same temperatures.
One of the factors determining efficiency is the addition of heat to the
working fluid in the cycle and its removal. The Carnot cycle achieves
maximum efficiency because all the heat is added to the working fluid at
the maximum temperature.

7. Video
QUESTIONS AND SOLUTIONS