PHYSICAL CHEMISTRY IN BRIEF

CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 116

d

d

d

d

T 1

T 2

1

2

3

4

a

b

c

d

p

Vm

Obr.4.1:The Carnot cycle in variablesp−Vm. The curvesaandcare the isotherms [T 2 ] and [T 1 ],
curvesbanddare adiabats.

Figure4.1shows a diagram of the Carnot cycle in the pressure—molar volume coordinates,
Figure4.2shows it in the temperature—molar entropy coordinates. TheCarnot engine
efficiencyηis defined by the relation

η=

work done

heat supplied from the warmer container

=

−W

Q 2

. (4.29)

It also holds that

η=

T 2 −T 1

T 2

. (4.30)

This equation is called the Carnot formulation of the Second Law of thermodynamics.

Note: A reversibly operating heat engine cannot exist in practice because, among other

reasons, the processes in such an engine would progress at an infinitesimal rate.

The following inequality holds for the efficiency of two engines operating reversibly and
irreversibly between the same reservoirs:

ηreversible engine > ηirreversible engine. (4.31)

This inequality is called the Clausius formulation of the Second Law of thermodynamics.