Charles' Law Experiment | Gas Laws | Class 9 | CBSE | NCERT | ICSE
Summary
TLDRThe video explains the relationship between speed, distance, and frequency of boundary hits, using a running person as an analogy. It then transitions into Charles' Law, where a scientist named Charles conducted an experiment in 1787 to demonstrate that the volume of gas is directly proportional to its temperature at constant pressure. The law is illustrated using examples and experiments, showing how volume increases with temperature and decreases when cooled, as demonstrated through a plastic bag deflating in a freezer and inflating when heated. The video concludes with a mathematical example of applying Charles' Law.
Takeaways
- đââïž A person running at double speed hits the boundaries double the number of times within the same time frame.
- đ To limit the number of boundary hits while running at double speed, the person must cover a greater distance, specifically double the original distance.
- đĄ Charles' Law experiment demonstrates how the volume of gas increases with temperature when pressure is kept constant.
- đ„ The capillary tube in Charles' experiment shows that as temperature rises, the volume of gas increases, and as temperature decreases, the volume decreases.
- đŹ Charles' Law states that at constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).
- đ A graph of volume vs. temperature at constant pressure (isobar) shows a linear relationship, where volume increases as temperature increases.
- âïž Absolute zero (0 Kelvin or -273°C) is the temperature at which molecular motion ceases and the volume of gas becomes zero.
- đ The formula V1/T1 = V2/T2 is used to calculate changes in volume and temperature for a gas at constant pressure, based on Charles' Law.
- đĄïž In an example, cooling a gas at 300K to reduce its volume to one-third results in a final temperature of 100K.
- đ A practical example of Charles' Law: a plastic bag filled with air deflates when cooled and reinflates when heated, demonstrating the direct relationship between gas volume and temperature.
Q & A
What happens to the number of times the person touches the boundaries when their speed is doubled?
-When the person's speed is doubled, they touch the boundaries double the number of times in the same time period.
How can the person touch the boundaries only eight times when running at double speed?
-The person can touch the boundaries only eight times at double speed by covering double the original distance.
What is the main observation from Charles' experiment with the gas in the capillary tube?
-Charles observed that as the temperature of the water bath increased, the volume of gas trapped in the capillary tube increased, and when the temperature decreased, the volume of gas decreased, while pressure remained constant.
What does Charles' Law state?
-Charles' Law states that for a particular gas, if the pressure is kept constant, the volume of the gas is directly proportional to its temperature.
What is the relationship between speed and distance in the context of the running person analogy?
-In the analogy, the speed of the person is compared to temperature, and the distance they cover is compared to the volume of gas. Greater speed (temperature) leads to covering a greater distance (increased volume), with the number of boundary hits (pressure) remaining constant.
Why do we use the Kelvin scale in Charles' Law calculations?
-We use the Kelvin scale in Charles' Law because it is the absolute temperature scale, where 0 K represents the point where all molecular motion ceases, and it's essential for accurate temperature-volume proportionality calculations.
What happens to the volume of a gas at absolute zero temperature according to Charles' Law?
-At absolute zero (0 K), the volume of the gas becomes zero because the particles no longer move, and molecular motion ceases entirely.
What kind of graph is obtained when plotting volume against temperature for Charles' Law?
-A straight-line graph is obtained when plotting volume against temperature at constant pressure, showing that volume increases as temperature increases.
What is the significance of the -273°C value in the context of Charles' Law?
--273°C corresponds to 0 K, which is absolute zero, the temperature at which the volume of any gas would theoretically become zero.
How does kinetic energy affect the volume of gas in Charles' Law?
-As temperature increases, the kinetic energy of the gas particles increases, causing them to move faster and hit the container walls more often. This increases the volume of the gas, assuming constant pressure.
Outlines
đ Person Running at Different Speeds and Boundary Hits
This paragraph discusses a scenario where a person runs at a certain speed and touches the boundaries eight times in one minute. When the speed doubles, the number of hits also doubles to sixteen. A condition is then imposed where the person, despite doubling the speed, is limited to eight boundary hits. This is achieved by increasing the distance to be covered, which demonstrates that distance is directly proportional to speed, given constant time. The paragraph introduces the concept of proportionality between distance and speed, setting the foundation for a later connection to scientific laws.
đ§âđŹ Introduction to Charles' Experiment
The focus shifts to Charles' experiment, conducted in 1787. He used a water-bath apparatus containing a capillary tube filled with gas, a thermometer, and a scale. The water-bath ensures uniform temperature distribution. Charles kept the pressure constant by maintaining the capillary's height throughout the experiment. As the temperature of the water increased, the volume of gas trapped in the capillary expanded, causing the water level to fall. When the temperature was lowered, the gas volume decreased, and the water level rose. This established a relationship between gas volume and temperature, which Charles further explored.
đ Charles' Law and Proportionality Between Volume and Temperature
This section explains Charles' observations and the formation of Charles' Law. The law states that at constant pressure, the volume of a gas is directly proportional to its temperature. As temperature increases, the gas volume also increases, and vice versa. To remove the proportionality, a constant is introduced, leading to the equation: volume of gas = constant Ă temperature. The paragraph also highlights that Charles' law is based on absolute temperature (Kelvin), not Celsius. It provides a detailed explanation of how Charles' experiment demonstrated this law using gas volumes and temperature changes.
âïž The Concept of Absolute Zero and Charles' Law Graph
Charlesâ law implies that if the temperature of a gas is reduced to absolute zero (0 K or -273°C), the gas volume becomes zero, and all molecular motion ceases. A graph plotting volume versus temperature shows a direct proportional relationship, with the line intersecting at -273°C, which represents absolute zero. This graph is known as an isobar since it is plotted under constant pressure. The paragraph explains how this graph supports Charles' law and how the volume of a gas consistently increases with temperature.
đĄ Kinetic Theory and Practical Application of Charles' Law
This part delves into the kinetic theory explanation of Charles' law. As temperature increases, the kinetic energy and speed of gas particles rise, leading to more collisions with the container walls, which increases the volume. Conversely, when the temperature decreases, the kinetic energy drops, resulting in fewer collisions and reduced volume. A question is posed to illustrate how temperature reduction affects gas volume, using Charles' law to calculate that cooling a gas from 300K to 100K reduces its volume to one-third. The plastic bag experiment further demonstrates the law: as temperature decreases, volume decreases, and vice versa.
Mindmap
Keywords
đĄCharles' Law
đĄProportionality
đĄConstant Pressure
đĄVolume
đĄTemperature
đĄKelvin Scale
đĄWater-bath
đĄKinetic Energy
đĄIsobar
đĄAbsolute Zero
Highlights
A person runs at a specific speed and hits boundaries a certain number of times. Doubling the speed doubles the number of boundary hits.
To maintain the same number of boundary hits at double speed, the person must cover double the distance.
The experiment illustrates that distance covered is directly proportional to speed when the number of hits per unit time remains constant.
Charles' experiment in 1787 used a water-bath to heat gas in a capillary tube, observing changes in volume at constant pressure.
When the water is heated, the volume of gas trapped in the capillary increases; when the heat is removed, the volume decreases.
Charles observed that as the temperature increased, the volume of gas increased at constant pressure, leading to Charlesâ Law.
Charlesâ Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature.
The temperature must always be measured in Kelvin when applying Charlesâ Law, as it represents the absolute temperature scale.
In Charlesâ Law, the relationship between volume and temperature (V/T) is always a constant value at constant pressure.
At absolute zero (0 Kelvin or -273°C), all molecular motion ceases, and the volume of gas becomes zero.
A graph of volume vs. temperature for Charlesâ Law shows a direct proportional relationship, resulting in a straight line that intercepts at absolute zero.
Charlesâ Law is based on the kinetic theory: as temperature increases, particle kinetic energy and speed increase, leading to greater volume.
When temperature decreases, particle speed and kinetic energy decrease, causing a reduction in gas volume to maintain constant pressure.
To reduce a gas's volume to 1/3 of its original volume while keeping the pressure constant, the temperature must be reduced from 300K to 100K.
A real-life example of Charles' Law: a plastic bag filled with air shrinks when placed in a freezer (temperature decreases, volume decreases) and re-inflates when exposed to heat (temperature increases, volume increases).
Transcripts
A person is running at some speed. Let's count the number of times
the person hits the boundaries in one minute.
One, two,
three, four,
five, six, seven,
eight. Now what happens
if he's running at a speed double of this speed? Now let's count the number of
times he hits the boundaries
in the same time- that is in one minute only.
One, two, three, four, five,
six, seven, eight, nine, ten,
eleven, twelve, thirteen, fourteen, fifteen, sixteen.
So when he was running at a speed which was double the initial speed,
he touched the boundaries double number of times.
Now we give him a condition. We say that he can touch the boundaries eight times only
when he is running at double the speed.
How is that possible?
Since now he's running at double the initial speed
so if he has to touch the boundaries eight times only
that will only be possible if he covers a greater distance.
And how great the distance or how big the distance should it be?
Since now he's running at double the speed,
so now he should cover double the original distance.
So now he has double the distance to cover in the same time-
that is one minute only. Let's count the number of times he hits the
boundaries.
One, two,
three, four,
five, six, seven,
eight. So if he's running at double the speed,
in order to touch the boundaries the same number of times-
that is the initial number of times he has to cover double the original distance.
So let's compare.
So now the person is running at double the speed. So in order to cover the
distance- that is in order to
touch the boundaries the same number of times if he's running at double the speed
he has to cover a greater distance. So here you see- they touch the boundaries at the
same time.
So when the person was running at double the speed
in order to touch the boundaries the same number of times
he had to cover double the distance. So we see
that the distance covered is directly proportional to speed.
So greater the speed- greater the distance covered,
lesser the speed- lesser is the distance covered given that the number of
hits per unit time remains constant.
Something like this was used by a scientist.
Scientist named Charles. He performed an experiment known as
Charlesâ experiment in 1787. Let's see what he performed.
He took this apparatus. This has a beaker,
which has water inside this, thereâs a thermometer,
thereâs a scale and a capillary- a small
capillary is a very small fine tube.
So a capillary is attached to this scale
using rubber bands.
Such an apparatus in which water is present
to provide heat to the other
devices present inside it is known as water-bath.
What is the purpose of water-bath?
Well, when we have a system like this the purpose of water-bath is that it provides
a uniform temperature throughout. Since it gains a temperature
so the temperature throughout this water- that is the temperature of
the thermometer, the temperature of the capillary and the scale- so the
temperature
throughout remains the same. So he used this device.
The pressure for this experiment
was maintained constant. How was this done? We know pressure at the same height
remains the same,
so this capillary tube which he had used
during the experiment is at the same height throughout the experiment.
Since it is tied by rubber bands it is maintained
at the same height throughout the experiment.
The height of the capillary is not changed so throughout it
experiences a constant pressure.
Now if youâll observe there is gas enclosed
in the capillary.
This area shows that there is a gas which is trapped in the capillary.
The remaining volume is the water which is filled in the capillary.
So there is gas enclosed in this part of the capillary.
Now he started heating this water.
As he heated the temperature started to increase
and the volume of the gas in this capillary started to increase.
So you observe when he closed the burner- he switched it off, the temperature decreases
and the
volume of the gas also decreases.
So what did you observe here? As he was increasing the temperature-
as he was heating the water-bath, the volume of the gas
trapped in the capillary- that also started to increase.
As the volume of the gas started to increase, the water in the capillary
started to fall.
That is how the volume of gas in the capillary started to increase.
When he switched off the Bunsen burner- he switched off the flame
so the temperature started to decrease. As the temperature decreased
the level of water increased. This was because
the volume of gas enclosed started to decrease.
As the volume in the capillary started to decrease the water level in the
capillary started to increase.
So from this experiment,
Charles observed as the temperature of the water-bath was increased
at constant pressure
since he was observing the gas which was trapped in the capillary tube,
the capillary tube was maintained at the same height throughout the experiment.
So he maintained constant pressure throughout the experiment.
He observed as the temperature of the water-bath was increased
the volume of the gas enclosed in the capillary tube increased,
and if the temperature was decreased the volume of the gas enclosed decreased.
So he observed that when he increased the temperature the volume of gas enclosed increased.
When he
decreased the temperature the volume of the gas
enclosed decreased.
So based on this experiment, he gave his law
which is known as Charlesâ law, according to which- for a particular gas
if the pressure is kept constant the volume
is directly proportional to temperature. This means
greater the temperature- greater is the volume of the gas,
lesser the temperature- lesser is the volume of the gas. So, this law
is known as
Charlesâ law.
So this is as we had seen before for the person running-
so we had observed greater is the speed of the person
greater is the distance covered by the person,
provided the number of hits per unit time remains constant.
So for Charlesâ experiment or for Charlesâ law, what did we observe?
The distance covered is the volume of the gas,
the speed is the temperature,
and number of hits per unit time remaining constant
which is the pressure. So for Charlesâ law as the pressure
remains constant the volume of the gas is directly proportional to its
temperature.
So let's revisit the Charlesâ law-
it states that for a particular gas at a constant pressure,
the volume of a gas is directly proportional to temperature.
This means to remove the proportionality sign we introduce a constant.
So we get that the volume of a gas is equal to constant into temperature.
Now we bring the temperature on this side. We get that the volume of a gas
divided by the temperature of the gas is a constant.
So according to Charlesâ law, for a particular gas
volume by temperature for a particular gas is constant,
provided the pressure is constant.
So the value on the Celsius scale, we already know can be converted
into the Kelvin scale by adding 273 to it.
So in Charlesâ law, whenever we talk of temperature
we always use the Kelvin value.
This Kelvin value was given by
Lord Kelvin and this scale is known as the absolute scale.
The Kelvin scale is also known as the absolute scale of temperature,
so whenever we talk of temperature in the Charlesâ law, we always use the
Kelvin value.
Now let's perform an experiment to prove the Charlesâ law.
So a gas is enclosed in a container.
The pressure is kept constant which you'll observe here.
Now weâll increase the temperature of the gas.
So observe what happens- you can see through the thermometer
that it is heated so the temperature rises. As the temperature increases,
the volume which is enclosed increases or vice versa-
as the volume increases the temperature increases.
So you observe these values and you see
that V by T, so according to Charlesâ law volume by temperature is a
constant.
So these values that is we know that the temperature
is always taken in Kelvin. So all these readings
are converted to Kelvin, and volume by temperature in Kelvin
that value- that is V by T,
temperature in Kelvin is always a constant value
as you can see. So from this experiment we see
that V by T is always a constant value,
provided the pressure is kept constant.
So according to Charlesâ law as the temperature decreases
volume decreases. How far can this volume decrease?
We know a temperature 0 K was given by Lord Kelvin,
which he called absolute zero. At this temperature
all molecular motions cease- that is
the speed of the particles becomes zero
and at this temperature the volume of the gas
is reduced to zero.
So this is the temperature at which the speed of the particles becomes zero
and the volume of gas is also reduced to zero. 177 00:10:55,570 --> 00:10:59,080 So if a graph is plotted for the Charlesâ law,
we see that volume is directly proportional to temperature.
So we get a straight line- that is as temperature increases- volume increases.
Now if this value we extend backwards
we see that it meets the graph at -273°C,
this is zero Kelvin.
That is the absolute zero temperature at which
the volume of all gases becomes zero.
So at this temperature, we see from the graph that as the temperature is reduced
to 0 K, the volume of the gas becomes zero.
So this is the graph for Charlesâ law,
which is also known as an isobar.
Iso means same and bar is used for pressure,
so in this graph since in Charlesâ law the pressure remains constant,
so this shows that for the same pressure, this is the graph that is obtained
for the values of volume of a gas for a particular gas
versus its temperature.
The volume of a gas increases with the increase in temperature.
Is it true or false?
So from Charlesâ law, we know that the volume
is directly proportional to temperature. As temperature increases- volume increases,
as temperature decreases- volume decreases,
provided the pressure is constant.
So we have the volume of a gas
increases with the increase of temperature. So this is true.
We see that as the temperature increases the volume increases.
So based on the experiment that Charlesâ had performed
and the data collected he gave his law. His law states-
that the volume of a given mass of air,
so notice that the law is valid for a particular gas,
the volume is directly proportional to its absolute temperature.
We know whenever weâre talking of Charlesâ law the temperature which is referred to is always
the Kelvin or the absolute temperature.
So the volume is directly proportional to temperature
provided its pressure remains constant.
So we know that the volume is directly proportional to temperature,
provided the pressure remains constant. So this is the law-
this is the Charlesâ law or a particular gas.
So let's revisit the Charlesâ law- it states that V by T
is constant, letâs denote this constant by k, at a constant pressure.
Now say this is the initial volume of a gas,
this is the initial temperature of a gas so V? by T?
is some constant k.
If this is the final volume of a gas- volume 2,
and this is the final temperature of the gas- T?.
So V? by T? is also constant.
So if we combine these two, we get that V? by T?
is equal to V? by T? which is the same constant k.
So we get that V? by T?
is equal to V? by T?. This means for a particular gas
at a constant pressure, the volume-
the initial volume of a gas divided by its initial temperature
is equal to the final volume of a gas divided by its
final temperature.
Let's try to study the Charlesâ law,
based on the kinetic theory.
So we see that there is a direct relationship between the volume and
temperature of a gas. So as the temperature increases- volume increases,
as the temperature decreases- volume decreases.
What is happening here?
So as you see the pressure remains constant,
which you can observe from this pressure gauge. So the pressure remains constant.
As the temperature increases, the kinetic energy of the particles
increases,
as the kinetic energy of the particles increase- the speed of the
particles increases. As the speed increases
they strike the walls of the container more.
Since the pressure has to be maintained constant,
so if they strike the walls of the container they increase the volume of the container.
So with the increase in temperature the volume increases.
Similarly we get the vice-versa case, if we decrease the temperature
the kinetic energy decreases, the speed of the particles decreases.
This means the number of strikes or the number of hits per unit time
has to decrease. Since pressure is constant
this is possible only for a lower volume or a lesser volume.
So let's revisit-
as temperature increases,
the kinetic energy of the particles increases, as the kinetic energy
of the particles increases-
the speed of the particles increase. As the speed increases
the number of hits per unit time also increases,
but in Charlesâ law the pressure has to be kept constant.
This means that pressure is constant so this is possible
only if the volume is increased. So the increase in number of hits
increases the volume for a constant pressure. Similarly we get
the vice-versa case.
If the temperature is decreased the kinetic energy decreases-
the speed decreases, as the speed decreases the number of hits per unit time
decrease.
Since pressure has to be kept constant, so the volume decreases.
Only when the volume decreases the number of hits will decrease
for a constant pressure. So for Charlesâ law-
as the temperature decreases the volume decreases.
Now let's try to solve a question. To what temperature must a gas
at 300K be cooled in order to reduce
its volume to 1/3 its original volume, the pressure remaining constant?
Since we see that the pressure remains
constant, this means this law
or this condition is valid for Charlesâ law.
So let's use Charlesâ law here. It states
that volume is directly proportional to temperature
or V? by T?
is equal to V? by T?.
Let's write the data that weâre given-
So weâre given that the initial temperature of the gas
is 300K.
Keep in mind whenever weâre doing Charlesâ law,
we have to use the absolute or the Kelvin values.
So in this weâre already given the temperature in Kelvin so we do not have to
convert it.
If the temperature was given in °C, we always have to convert
it to the Kelvin value.
Now we have to find the final temperature.
Let's take the initial
volume to be V, since we're not given any volume
and it says that the volume is reduced to 1/3rd.
This means the final volume
is 1/3rd the original volume.
Now let's apply Charlesâ law to this.
So we have
V? by T?
is equal to
V? by T?.
So we can cancel- this V? is V,
so we can
substitute this by V
as we have taken V? is equal to V so we cancel this V
on both the sides.
What do we get?
And we get T?
is equal to 300
divided by 3
which is equal to 100K.
So to what temperature should it be cooled? It should be cooled to 100K.
What do you observe here?
We know by Charlesâ law that the volume is directly proportional to temperature,
so as the final volume is reduced,
this was the initial volume, the final volume is reduced
so we see that the final temperature is also reduced.
Since the initial temperature was 300K the final temperature is 100K.
Here there is a plastic bag filled with air. So now
if this plastic bag is kept in a freezer.
It's taken out after twenty minutes.
It's observed that the plastic bag has deflated.
So as the temperature decreases the volume of the gas decrease,
and if it is heated on top of a flame- so as the temperature increases
the volume of gas increases, so you observe that the plastic bag
re-inflates.
So this is the Charlesâ law which states that the volume of a gas
is directly proportional to its temperature at a constant pressure.
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