Boyle and charles

P R E S S U R E A N D V O L U M E R E L A T I O N S H I P
A T C O N S T A N T T E M P E R A T U R E
Boyle’s Law
1
Gas laws: Prepared By, JV Temporal

 Gas particles have a very weak
intermolecular force of attraction,
hence they move as far as possible from
each other. They have the tendency to
occupy all the spaces they are contained
in. If the pressure is increased, the
volume will be decreased forcing the
gas particles to move closer to one
another.
2

V α 1/PThe volume of a gas is inversely
proportional to its pressure, if
temperature and amount of gas are
held constant.
3

4
 This proportionality was first stated by
Robert Boyle during the 6th century. He
performed an experiment wherein he
trapped fixed amount of air in the J-
tube, he changed the pressure and
controlled the temperature and then,
he observed its effect to the volume of
the air inside the J-tube.

V α 1/P
V= volume; P= pressure
This means that as pressure
decreases the volume increases.
As pressure increases the
volume decreases.
5

V α 1/P
 To remove the
proportionality symbol
(α) we have to
introduce a constant,
thus, leading us to the
equation to the right.
V = k/P
k=VP
The product of
volume and
pressure is
constant.
6

According to Boyle’s law VP=k
If we subject the gas to a change in pressure we’ll have:
V₁P₁ =k
V2P2 =k
Therefore,
V₁P₁ =V₂P₂
7

V₁P₁ =V₂P₂
1. V₁ = V₂P₂ / P₁
2. P₁ = V₂P₂ / V₁
3. V₂ = V₁P₁ / P₂
4. P₂ = V₁P₁ / V₂
8

9
 Practical example of this is the Lungs as we
exhale and inhale.
 Will you please cite another practical
example of Boyle’s Law.

Try this!!! 
 The inflated balloon that slipped from the
hand of Roshan has a volume of 0.50 L at
sea level (1.0 atm) and it reached a height of
approximately 8km where the atmospheric
pressure is approximately 0.33 atm.
Assuming that the temperature is constant,
compute for the final volume of the balloon.
10

Let us analyze the problem!
The inflated balloon that
slipped from the hand
of Roshan has a volume
of 0.50 L at sea level
(1.0 atm) and it
reached a height of
approximately 8km
where the atmospheric
pressure is
approximately 0.33
atm. Assuming that the
temperature is constant,
compute for the final
volume of the balloon.
 Given:
V₁ = 0.50 L
P₁ = 1 atm
V2 = ?
P2 = 0.33 atm
 What equation should you use?
Equation #3.
 Let us try this on the board.
11

Analyze your solution
 Notice that the pressure as it goes up
decreases, and we know that as gas receives
lower pressure it will have an increase in
volume.
 Did you obtain a higher V2 than V₁ ?
 Now, try to multiply V₁ and P₁ then,
Multiply V2 and P2.
What have you observed with the product of the two?
12

Try this on your own!  
1. Oxygen gas inside a 1.5 L gas tank
has a pressure of 0.95 atm.
Provided that the temperature
remains constant, how much
pressure is needed to reduce its
volume to o.75 L.?
13

2. Compute for the initial volume
of a gas in a tank with initial
pressure of 1.5 atm if its final
volume is 5L and its pressure is
decreased to 1.0 atm.
14

Assignment: Answer this on your notebook
1. A scuba diver needs a diving tank
in order to provide breathing gas
while he is underwater. How much
pressure is needed for 6.oo L of gas
at 1.01 atm to be compressed in a
3.00 L cylinder.
15

T E M P E R A T U R E A N D V O L U M E R E L A T I O N S H I P
16
Charles’ Law

17
From the properties of gases we
have mentioned that the gas
particles will expand with the
temperature. Meaning, as
temperature increases the
volume of gas will also increase.

18
Vα T
The volume of the gas is directly
proportional to the temperature at
constant pressure.

19
This relationship was determined by and
named after Jacques Charles. In his
experiment, Charles trapped a sample of gas
in a cylinder with a movable piston in water
bath at different temperatures.
It is important to note that the
temperature should always be in
Kelvin (k).

Vα T
20
V=volume; T=temperature (k)
As the temperature increases the
volume of the gas also increases.
As the temperature decreases the
volume of the gas also decreases.

21
Vα T
To remove the
proportionality
symbol (α) we
have to introduce a
constant, refer to
the equation to the
right.
V=kT
K=V/T
The quotient of
volume and
temperature is
constant

22
According to the Charles’ law;
V/T = k
Then, if we subject a gas to a temperature difference,
we’ll get:
V₁/T₁ = k
V₂/T₂ = k
Thus,
V₁/T₁ = V₂/T₂
k here means
constant and
not kelvin.

V₁/T₁ = V₂/T₂ or V₁T₂= V₂T₁
23
1. V₁ = V₂T₁/T₂
2.T₁ = V₁T₂/ V₂
3.V₂ = V₁T₂/ T₁
4.T₂ = V₂T₁/ V₁

24
 Practical example of this is the Hot Air
Balloon (HAB) and Sky Lanterns (SL).
The flame at the bottom part of the
HAB and SL increases the volume thus
decreasing the density, and we know
that objects with lower density tends to
float.

25
 Why should you not pump large
amount of gas inside the tire during
summer?
 Explain why should aerosol cans must
not be placed near a fire?

Try this! 
26
 An inflated balloon with a volume of
0.75 L at 30 ⁰C was placed inside the
freezer where the temperature is -10
⁰C. find out what will happen to the
volume of the balloon if the pressure
remains constant. Support your answer
with computation.

Analysis of the problem.
27
An inflated balloon with a
volume of 0.75 L at 30
⁰C was placed inside
the freezer where the
temperature is -10 ⁰C.
find out what will
happen to the volume of
the balloon if the
pressure remains
constant. Support your
answer with
computation.
Given:
 T₁ = 30 ⁰C
 V₁ = 0.75 L
 T₂ = -10 ⁰C
 V₂ = ?
What equation should we
use?
Equation #3
Let us try this on the board.

Let’s analyze it more
28
 Notice that the problem stated that the balloon was
placed in a freezer meaning there is a lower
temperature in there. And we have mentioned
earlier that if the temperature decreases the
volume of the gas will also decrease.
 Did you obtain Lower V2 than V1?
 Now, try to divide V1 by T1 then divide V2 by T2.
 What can you infer with the quotient?

Try this!! 
29
1. A cylinder with a movable piston
contains 250 cm³ air at 10⁰C. if the
pressure is kept constant, at what
temperature would you expect the
volume to be 150 cm³?

30
2. A tank (not rigid) contains 2.3
L of helium gas at 25 ⁰C. What
will be the volume of the tank
after heating it and its
content to 40 ⁰C temperature
at constant pressure.

Assignment: answer this in your notebook
31
1. At 20 ⁰C, the volume of chlorine
gas is 0.015L. Compute for the
resulting volume if the
temperature is adjusted to 318 k
provided that the pressure
remains the same.

Reminders!
32
 On your notebook do your EAR!
 EAR #2 for the Boyle’s Law.
 EAR #3 for Charles’ Law.
I will check and sign your notebook during your quiz
#1 on Friday. Coverage, Properties of gases, Boyle’s
Law and Charles’ Law.
-Sir JV.

Boyle and charles

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