Everything Science Grade 11

5.2 CHAPTER 5. THERMAL PROPERTIES AND IDEAL GASES

This equation means that, assuming the temperature is constant, multiplying any pressure and volume

values for a fixed amount of gas will always givethe same value. So, for example, p 1 V 1 = k and p 2 V 2

= k, where the subscripts 1 and 2 refer to two pairs of pressure and volume readings for the same mass

of gas at the same temperature.

Tip

In the gas equations,k
is a ”variable constant”.
This means that k is con-
stant in a particular set of
situations, but in two dif-
ferent sets of situations
it has different constant
values.

From this, we can then say that:

p 1 V 1 = p 2 V 2

Remember that Boyle’sLaw requires two conditions. First, the amount of gas must stay constant.

Clearly, if you let a littleof the air escape from the container in which it is enclosed, the pressureof the

gas will decrease alongwith the volume, and the inverse proportion relationship is broken. Second,

the temperature must stay constant. Cooling or heating matter generally causes it to contract or expand,

or the pressure to decrease or increase. In our original syringe demonstration, if you were to heat up

the gas in the syringe, itwould expand and require you to apply a greater force to keep the plunger at

a given position. Again,the proportionality would be broken.

Activity: Boyle’s Law

Shown below are someof Boyle’s original data.Note that pressure would originally have

been measured using a mercury manometer and the units for pressure would have been mil-

limetres mercury or mm Hg. However, to make things a bit easier for you, the pressuredata

have been converted toa unit that is more familiar. Note that the volume is given in terms of

arbitrary marks (evenly made).

Volume Pressure Volume Pressure

(graduation (kPa) (graduation (kPa)

mark) mark)

12 398 28 170

14 340 30 159

16 298 32 150

18 264 34 141

20 239 36 133

22 217 38 125

24 199 40 120

26 184

1. Plot a graph of pressure (p) against volume (V). Volume will be on thex-axis and pressure
   on the y-axis. Describethe relationship that yousee.


2. Plot a graph of p against 1 /V. Describe the relationship that you see.


3. Do your results support Boyle’s Law? Explainyour answer.

FACT

Did you know that the
mechanisms involved in
breathing also relate to
Boyle’s Law? Just below
the lungs is a muscle
called the diaphragm.
When a person breathes
in, the diaphragm moves
down and becomes
more ’flattened’ so that
the volume of the lungs
can increase. When the
lung volume increases,
the pressure in the
lungs decreases (Boyle’s
law). Since air always
moves from areas of
high pressure to areas
of lower pressure, air
will now be drawn into
the lungs because the
air pressure outside the
body is higher than
the pressure in the
lungs. The opposite
process happens when
a person breathes out.
Now, the diaphragm
moves upwards and
causes the volume of the
lungs to decrease. The
pressure in the lungs
will increase, and the air
that was in the lungs will
be forced out towards
the lower air pressure
outside the body.

See simulation: VPiiu atwww.everythingscience.co.za)

Example 1: Boyle’s Law 1

QUESTION

A sample of helium occupies a volume of 160 cm^3 at 100 kPa and 25◦C. What volume will