The document describes the Carnot engine, which operates using a reversible Carnot cycle consisting of four processes: 1) Isothermal expansion where gas absorbs heat Q1 from a hot source at temperature T1. 2) Adiabatic expansion where gas expands and cools to temperature T2. 3) Isothermal compression where gas rejects heat Q2 to a cold sink at temperature T2. 4) Adiabatic compression where gas compresses back to the initial state. The efficiency of the Carnot engine is the highest possible and is calculated as η = (1 - T2/T1) × 100%, depending only on the temperature of the hot and cold

1. B.Sc. Physics PaperII
MuhammadAzhar
M.S. Physics, NEDUET azharphysicist@gmail.com
CARNOT ENGINE
In 1824 Sadi Carnot describedanideal heatengine whichoperatesonreversible process. This hypothetical heat engine
is known as Carnot engine. The reversible process is called Carnot cycle which is the principle of this engine.
CONSTRUCTION
Carnot engine is supposed to be consist of gas filled cylinder having non-conducting walls and piston and conducting
base. Gas used as working substance while hot body (source) and cold body (sink) is also required.
WORKING
The operating cycle of Carnot engine consist of following four processes;
i. Isothermal Expansion ii. Adiabatic Expansion
iii. Isothermal Compression iv. Adiabatic Compression
i. ISOTHERMAL EXPANSION
The gas is allowedtoexpandisothermally at temperature T1. During this process system absorb amount of heat Q1
from the source. The process represented by curve AB.
Initial State Final State
(P1, V1, T1) (P2, V2, T1)
ii. ADIABATIC EXPANSION
The gas is allowed to expand adiabatically until its temperature down to T2. The process represented by curve BC.
Initial State Final State
(P2, V2, T1) (P3, V3, T2)
iii. ISOTHERMAL COMPRESSION
At thisstepthe gas isallowedtocompressisothermallyattemperatureT2.Duringthisprocesssystemrejectamount
of heat Q2 to the sink. The process represented by curve CD.
Initial State Final State
(P3, V3, T2) (P4, V4, T2)
iv. ADIABATIC COMPRESSION
At the laststepthe gas isallowedtocompressadiabaticallyuntilthe system restored to its initial state from where
the system started. The process represented by curve DA.
Initial State Final State
(P3, V3, T2) (P1, V1, T1)
EFFICIENCY OF CARNOTENGINE
The efficiency of anymachine canfindbyusingfollowingformula;
η =
𝑂𝑢𝑡𝑝𝑢𝑡
𝐼𝑛𝑝𝑢𝑡
---------- (1)

2. B.Sc. Physics PaperII
MuhammadAzhar
M.S. Physics, NEDUET azharphysicist@gmail.com
In Carnot engine the heat absorbed “Q1” by the system is actually the input and the output can be written as;
Output = Q1 – Q2
Equation (1) can be written as
η =
𝑄1− 𝑄2
𝑄1
η =
𝑄1
𝑄1
−
𝑄2
𝑄1
η = 1 −
𝑄2
𝑄1
The percent efficiency can be written as
η = ( 1 −
𝑄2
𝑄1
) ×100%
Since the hot body and cold body characterized by temperature then
𝑄2
𝑄1
=
𝑇2
𝑇1
So
η = ( 1 −
𝑇2
𝑇1
) × 100%