Physical Chemistry
Lecture 13
Carnot Cycles and Engines
Engines and cycles
Want to transform heat into mechanical
work
Engine – a device that turns heat into
work
Carry out continuously
Cycle – a sequence of events that
carries a system away from a state and
returns it to that state

Cycles allow repetitive transfer of energy
Types of cycles
Otto cycle – commonly used in
automobiles
Diesel cycle – also used in automobiles
Wankel cycle – used at one time in
automobiles
Carnot cycle – theoretical analysis
Carnot cycle
Theoretical analysis of the
thermodynamics of transforming heat
into work
Sadi Carnot – French engineer who first
proposed the concept
Rudolf Clausius – German
thermodynamicist who described the
concept mathematically
Carnot cycle with an ideal gas
Remove heat from
high-T reservoir
Do work
Dump heat in a lowT reservoir
Involves four steps
Carnot cycle
Step 1: isothermal
expansion
Step 2: adiabatic
expansion
Step 3: isothermal
compression
Step 4: adiabatic
compression
Mathematics of the Carnot
cycle with an ideal gas
The points at intersections of the steps
are related
These relations determine the amount
of heat absorbed and work done
Work done
V 
Heat
Internal energy
w = − R(Th − Tc ) ln A 
 VB 
q = q h + qc
∆U = 0
Efficiency of a Carnot cycle
Efficiency – determines how effectively
heat is used as work
−w
ε =
qh
Using the determined values of these
quantities for a reversible cycle
ε reversible
Th − Tc
=
Th
The Otto cycle
Used in automobile
engines
Four stroke cycle




Adiabatic compression
Isochoric heating
Adiabatic expansion
Isochoric cooling
Efficiency less than for
the ideal Carnot cycle
Summary
Carnot cycle – fundamental to
understanding transformation of heat to
mechanical work
Other cycles are in use
Ideal efficiency depends only on the
temperature difference

Can never be 1 (except in unusual
circumstances)