PHYSICAL CHEMISTRY IN BRIEF

CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 114

If a system behaves as an ideal gas, we may write (4.26) in the form

Wvol=−pex

(

nRT 2

pex

−

nRT 1

p 1

)

. (4.28)

Note:Equations (4.26)−(4.28) do not serve only for the calculation of work. If we know

the initial state of a system, i.e. T 1 , p 1 (V 1 =nRT 1 /p 1 ), andpex, we can ascertain the

final state, i.e.T 2 , V 2 by solving the equations.

Example

An ideal gas expanded adiabatically from temperatureT 1 = 300 K and pressurep 1 = 1 MPa to

pressurep 2 = 100 kPa. Provided that the external pressure was constant for the whole time of

expansion and equal to pressurep 2 , and thatCpm=^52 R, find the temperature after expansion,

T 2. Is it possible to calculate volumesV 1 andV 2 at the beginning and end of the expansion?

Solution

We rewrite equation (4.27) to the form

Wvol=n(Cpm−R)(T 2 −T 1 ),

compare it with (4.28)

n(Cpm−R)(T 2 −T 1 ) =−p 2

(

nRT 2

p 2

−

nRT 1

p 1

)

and after rearrangement we obtain

T 2 =T 1

(

1 +

R

Cpm

p 2 −p 1

p 1

)

= 192K.

The volumes cannot be determined from the specification because we do not know the amount

of substance of the expanding gas.