TITLE.PM5

IDEAL AND REAL GASES 407

dharm

\M-therm\Th8-2.pm5

3

vcp

F

H

G

I

K

J × (ii) + (iii) gives

−

−

(^30)
2
RT
vv bcp()cp

• (^20)
  3
  RT
  ()vbcp−
  = 0
  or
  3
  vcp =
  2
  ()vbcp−
  or vcp = 3b
  Substituting for b in (ii), we get
  −
  −
  RT
  vv
  cp
  cp cp
  0
  [(/)] 13 2 +
  2
  3
  a
  ()vcp
  = 0
  ∴ a =
  9
  8 R^0 Tcp
  vcp
  Substituting for a and b in (i), we get
  pcp =
  RT
  vv
  cp
  cp cp
  0
  −(/ ) 13

(/)98 0

2

RT v

v

cp cp

cp

∴

pv

RT

cp cp

0 cp

=

1

(/) 23

• (/)98
  1

But

pv

RT

cp cp

(^0) cp
= Zcp
∴ Zcp =
3
2
9
8
− =^3
8

. (Ans.)

Highlights

1. An ‘ideal gas’ is defined as a gas having no forces of intermolecular attraction. It obeys the law pv = RT. The
   specific heat capacities are not constant but are functions of temperature.
   A ‘perfect gas’ obeys the law pv = RT and has constant specific heat capacities.


2. The relation between the independent properties, such as pressure, specific volume and temperature for a
   pure substance is known as ‘equation of state’.


3. Each point on a p-v-T surface represents an equilibrium state and a line on the surface represents a
   process.


4. Joule’s law states that the specific internal energy of a gas depends only on the temperature of the gas and
   is independent of both pressure and volume.


5. Van der Waals’ equation may be written as

p a

v

F +

HG

I

(^2) KJ (v – b) = RT
where a and b are constants for the particular fluid and R is the gas constant.