BioPHYSICAL chemistry

expansion, and exhaust. This cycle occurs several thousand
times each minute and is used to perform work in the form
of moving the car. This traditional type of engine is termed
a heat engine since the work is a result of heat released in
the combustion process. The ideal gas is trapped inside a
piston that expands due to changes in temperature. The
expansion drives the piston and the motion of the piston
is used to perform work. Theefficiency of any heat engine
(Figure 3.8) is defined as the ratio of work performed to
the total amount of energy available in the form of heat:

(3.34)

According to this definition, increased efficiencies result from
a greater work output for a given amount of heat from a reservoir. The
thermodynamic parameters that determine the heat output can be under-
stood by considering the Carnot cycle, named after the French engineer
Sadi Carnot. The Carnot cycle has four stages (Figure 3.9), as follows.

1 Reversible isothermal expansion from ato
bat temperature Thot. The heat supplied to
the system is q 1 and the entropy change is
q 1 /Thot.
2 Reversible adiabatic expansion from bto c.
No heat leaves the system so the entropy
change is zero. The temperature decreases
from Thotto Tcold.
3 Reversible isothermal compression from c
to d. The heat released to the cold resevoir
is q 3 , and the entropy change is q 3 /Tcold.
4 Reversible isothermal compression from d
to a. No heat leaves the system and so the entropy change is zero. The
temperature changes from Tcoldto Thot.

The work per cycle is the sum of the two heat terms, yielding:

(3.35)

For an ideal gas, it can be shown that the ratio of the heat terms is the
same as the ratio of the temperatures (see Justification below) yielding:

Ef ciency 1 =− 1 (3.36)

T

T

cold

hot

Ef ciency 1 ==

+

=+

w

q

qq

hot q

hot cold

hot

1

qq

q

cold q

hot

where cold< 0

Ef ciency 1 =
w
q

CHAPTER 3 SECOND LAW OF THERMODYNAMICS 61

Hot reservoir

THOT

TCOLD

Cold reservoir

Heat flow W

Figure 3.8A model

of heat flow in an

engine operating in

a reversible Carnot

cycle.

Isothermal

expansion

Isothermal

compression

Adiabatic

compression

Adiabatic

expansion

a

b

c

Pressure ( d

P)

Volume (V)

Figure 3.9

An example of a

reversible Carnot

cycle.