PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 45

Note:The critical volume is themolar volumeat the critical point, with the subscriptm

usually left out for the sake of greater simplicity.

At the critical point we have

(

∂p

∂Vm

)

T

= 0,

(

∂^2 p

∂Vm^2

)

T

= 0, [critical point]. (2.5)

S Symbols: Equations (2.5) are to be understood as follows: p=f(T, Vm) is differentiated with

respect toVmat a fixedT. The text in square brackets specifies the conditions under which

the equations apply. In the above case, the equations apply at the critical point.

2.1.5 Reduced quantities

Definition

reduced temperature Tr =

T

Tc

, (2.6)

reduced pressure pr =

p

pc

, (2.7)

reduced volume Vr =

Vmpc

RTc

. (2.8)

U Main unit:dimensionless quantities.

Note:Note the different definition of the reduced volume (the definition (2.8) is used in a

generalized diagram of compressibility factors).

2.1.6 Coefficient of thermal expansionαp

Definition

αp=

1

Vm

(

∂Vm

∂T

)

p

=

(

∂lnVm

∂T

)

p

. (2.9)

U Main unit: K−^1.