Solution
a.First, the change in volume is needed. We find it as follows:
VVfVi5.50 L 2.00 L 3.50 L
To calculate the work against the constant external pressure, we use equa-
tion 2.4:
wpextV(1.75 atm)(3.50 L) 6.13 Latm
If we want to convert units to the SI units of joules, we use the appropriate
conversion factor:6.13 Latm
1
L
0
1
a.3
tm2J
621 J
That is, 621 joules have been lost by the system during the expansion.
b.Because of the assumption of an ideal gas, we can use Boyle’s law to cal-
culate the final gas pressure. We get
(2.00 L)(8.00 atm) (5.50 L)(pf)
pf2.91 atmFigure 2.3 illustrates a condition that occasionally occurs with gases: the ex-
pansion of a gas into a larger volume which is initially a vacuum. In such a
case, since the gas is expanding against a pextof 0, by the definition of work in
equation 2.4 the work done by the gas equals zero. Such a process is called a
free expansion:
work 0 for free expansion (2.5)Example 2.2
From the conditions and the given definitions of the system, determine
whether there is work done by the system, work done on the system, or no
work done.
a.A balloon expands as a small piece of dry ice (solid CO 2 ) inside the bal-
loon sublimes (balloon system).
b.The space shuttle’s cargo bay doors are opened to space, releasing a little
bit of residual atmosphere (cargo bay system).
c.Gaseous CHF 2 Cl, a refrigerant, is compressed in the compressor of an air
conditioner, to try to liquefy it (CHF 2 Cl system).
d.A can of spray paint is discharged (can system).
e.Same as part d, but consider the spray to be the system.Solution
a.Since the balloon is increasing in volume, it is undoubtedly doing work:
work is done by the system.
b.When the shuttle’s cargo bay doors are opened in space, the bay is being
opened to vacuum (although not a perfect one), so we are considering rela-
tively free expansion. Therefore no work is done.
c.When CHF 2 Cl is compressed, its volume is decreased, so work is being
done on the system.2.2 Work and Heat 27p 0 p 0p 0 p 0
Figure 2.3 No work is performed if a sample
of gas expands into a vacuum.