Everything Science Grade 11

CHAPTER 5. THERMAL PROPERTIES AND IDEAL GASES 5.2

Time (mins) Distance (km)

10 20

20 40

30 60

40 80

What you will notice isthat the two quantitiesshown are constant multiples of each other. If

you divide each distance value by the time thecar has been driving, you will always get 2. This

shows that the values are proportional to eachother. They are directly proportional because

both values are increasing. In other words, as the driving time increases, so does the distance

covered. The same is true if the values decrease. The shorter the driving time, the smaller the

distance covered. This relationship can be described mathematically as:

y = kx

where y is distance, x istime and k is the proportionality constant, which in this case is 2.Note

that this is the equationfor a straight line graph!The symbol∝ is also used to show adirectly

proportional relationship.

2. Inversely proportional
   Two variables are inversely proportional if oneof the variables is directly proportional to the
   multiplicative inverse ofthe other. In other words,

y∝

1

x

or

y =

k

x

This means that as one value gets bigger, the other value will get smaller. For example, the time

taken for a journey is inversely proportional tothe speed of travel. Look at the table below to

check this for yourself. For this example, assumethat the distance of the journey is 100 km.

Speed (km/h) Time (mins)

100 60

80 75

60 100

40 150

According to our definition, the two variables areinversely proportional ifone variable is directly

proportional to the inverse of the other. In other words, if we divide one of the variables by the

inverse of the other, weshould always get the same number. For example,

100

1

60

= 6000

If you repeat this usingthe other values, you will find that the answeris always 6 000. The

variables are inversely proportional to each other.

We know now that thepressure of a gas is inversely proportional to the volume of the gas, provided
the temperature stays the same. We can write this relationship symbolically as

p∝

1

V

This equation can also be written as follows:

p =

k

V

where k is a proportionality constant. If we rearrange this equation, we can saythat:

pV = k