CHEMISTRY TEXTBOOK

-Q : Heat is released by the system to the
surroundings.

+W : Work is done on the system by the
surroundings.

-W : Work is done by the system on the
surroundings.

Note W and Q are path functions.

4.4 Expression for pressure-volume (PV)
work : Consider a certain amount of gas at
constant pressure P is enclosed in a cylinder
fitted with frictionless, rigid movable piston of
area A. This is shown in Fig. 4.7.

W = f × d (4.2)

Substitution from Eq. (4.1) gives

W = - Pext × A × d (4.3)

The product of area of the piston and

distance it moves is the volume change (∆V)

in the system.

∆V = A × d (4.4)

Combining equations (4.3) and (4.4) we write

W = - Pex ∆V (4.5)

W = - Pex (V 2 - V 1 )

where V 2 is final volume of the gas.

When the gas expands, work is done by the

system on the surroundings. Since V 2 > V 1 , W

is negative. When the gas is compressed, work

is done on the system by surroundings. In this

case V 1 < V 2 , and -Pext ∆V or W is positive.

Eq. (4.5) shows the external pressure

determines the work during expansion (or

compression) of the gas. A volume change

does no work unless the system is linked to the

surroundings by external pressure.

Fig. 4.6 : Sign conventions

Fig. 4.7 : Pressure-volume work

Let volume of the gas be V 1 at temperature T.

On expansion the force exerted by a
gas is equal to area of the piston multiplied
by pressure with which the gas pushes against
piston. This pressure is equal in magnitude and
opposite in sign to the external atmospheric
pressure that opposes the movement and has
its value -Pext. Thus,

f = -Pext × A (4.1)

where Pext is the external atmospheric pressure.

If the piston moves out a distance d,
then the amount of work done is equal to the
force multiplied by distance.

Remember...

Remember during expansion

of a gas, work is done by the

system on the surroundings and during

compression work is done on the system by

the surroundings.

4.4.1 Free expansion : A free expansion

means expansion against zero opposing force.

Such expansion occurs in vacuum. The work

done by a system during such expansion is

given by Eq. (4.5), W = - Pext ∆V. When the

gas expands in vacuum, there is no opposing

force that is Pext and hence, W = 0. In other

words no work is done when the gas expands

freely in vacuum.