Charles' Law Experiment | Gas Laws | Class 9 | CBSE | NCERT | ICSE

Summary

The 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

• 🏃‍♂️ A person running at double speed hits the boundaries double the number of times within the same time frame.
• 📏 To limit the number of boundary hits while running at double speed, the person must cover a greater distance, specifically double the original distance.
• 💡 Charles' Law experiment demonstrates how the volume of gas increases with temperature when pressure is kept constant.
• 🔥 The capillary tube in Charles' experiment shows that as temperature rises, the volume of gas increases, and as temperature decreases, the volume decreases.
• 🔬 Charles' Law states that at constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).
• 📊 A graph of volume vs. temperature at constant pressure (isobar) shows a linear relationship, where volume increases as temperature increases.
• ❄️ Absolute zero (0 Kelvin or -273°C) is the temperature at which molecular motion ceases and the volume of gas becomes zero.
• 🔍 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.
• 🌡️ In an example, cooling a gas at 300K to reduce its volume to one-third results in a final temperature of 100K.
• 🎈 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

00:00

🏃 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.

05:01

🧑‍🔬 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.

10:03

📈 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 × 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.

15:06

❄️ The Concept of Absolute Zero and Charles' Law Graph

Charles’ 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.

20:10

💡 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.

Keywords

💡Charles' Law

Charles' Law states that the volume of a gas is directly proportional to its temperature, provided the pressure remains constant. In the video, this law is explained using an experiment where a gas in a capillary expands when heated and contracts when cooled. The key takeaway is that, as temperature increases, so does the volume of a gas, which reflects how the law links temperature and volume under constant pressure.

💡Proportionality

Proportionality refers to the direct relationship between two variables. In Charles' Law, volume is directly proportional to temperature, meaning as one increases, so does the other, as long as pressure remains unchanged. The video highlights this concept by comparing the running speed and distance covered, showing that increasing one variable (speed or temperature) results in a corresponding increase in the other (distance or volume).

💡Constant Pressure

Constant pressure is a condition in which the pressure exerted by or on a gas does not change. In the video, the experiment with the capillary ensures constant pressure by keeping the capillary at the same height throughout the experiment. This constant pressure allows for the direct observation of how temperature affects gas volume without other variables influencing the outcome.

💡Volume

Volume refers to the amount of space a gas occupies. In the experiment, as the gas inside the capillary tube is heated, its volume increases, and as it cools, its volume decreases. The video emphasizes that under constant pressure, volume changes in direct proportion to temperature, illustrating the foundational concept of Charles' Law.

💡Temperature

Temperature is the measure of thermal energy within a system. The video shows how an increase in temperature causes gas molecules to move faster, increasing their kinetic energy and causing the gas to expand. Charles' Law relies on temperature as a crucial variable, with volume responding to changes in temperature when pressure is held constant.

💡Kelvin Scale

The Kelvin scale is an absolute temperature scale where 0 K is the point at which molecular motion theoretically stops, known as absolute zero. In the video, temperatures are converted to Kelvin to properly apply Charles' Law, as it is the standard unit of temperature for gas laws, ensuring consistency in scientific calculations.

💡Water-bath

A water-bath is used to maintain a uniform temperature in scientific experiments. In the video, the scientist heats the water in a water-bath to evenly raise the temperature of the gas trapped in the capillary tube. The water-bath ensures consistent thermal conditions, allowing for an accurate observation of how temperature changes affect gas volume.

💡Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. In the context of Charles' Law, as temperature increases, the kinetic energy of gas particles increases, causing them to move faster and expand the volume of the gas. The video explains how this relationship underpins the gas's behavior as temperature changes.

💡Isobar

An isobar is a graph representing a constant-pressure process, showing the relationship between volume and temperature. In the video, the graph of Charles' Law is described as an isobar because it depicts how volume increases with temperature while pressure remains the same. The straight line on the graph highlights the direct proportionality between volume and temperature.

💡Absolute Zero

Absolute zero is the lowest possible temperature, at 0 K, where all molecular motion stops, and theoretically, the volume of a gas would become zero. The video references absolute zero to explain the point at which the volume of any gas would cease under the conditions of Charles' Law, offering a theoretical limit to gas behavior.

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 Charles’ Law.

Charles’ 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 Charles’ Law, as it represents the absolute temperature scale.

In Charles’ 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 Charles’ Law shows a direct proportional relationship, resulting in a straight line that intercepts at absolute zero.

Charles’ 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

Charles’ experiment in 1787. Let's see what he performed.

He took this apparatus. This has a beaker,

which has water inside this, there’s a thermometer,

there’s 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 you’ll 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 Charles’ 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

Charles’ 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 Charles’ experiment or for Charles’ 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 Charles’ law as the pressure

remains constant the volume of the gas is directly proportional to its

temperature.

So let's revisit the Charles’ 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 Charles’ 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 Charles’ 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 Charles’ law, we always use the

Kelvin value.

Now let's perform an experiment to prove the Charles’ law.

So a gas is enclosed in a container.

The pressure is kept constant which you'll observe here.

Now we’ll 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 Charles’ 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 Charles’ 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 Charles’ 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 Charles’ law,

which is also known as an isobar.

Iso means same and bar is used for pressure,

so in this graph since in Charles’ 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 Charles’ 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 Charles’ 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 we’re talking of Charles’ 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 Charles’ law or a particular gas.

So let's revisit the Charles’ law- it states that V by T

is constant, let’s 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 Charles’ 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 Charles’ 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 Charles’ 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 Charles’ law.

So let's use Charles’ 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 we’re given-

So we’re given that the initial temperature of the gas

is 300K.

Keep in mind whenever we’re doing Charles’ law,

we have to use the absolute or the Kelvin values.

So in this we’re 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 Charles’ 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 Charles’ 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 Charles’ law which states that the volume of a gas

is directly proportional to its temperature at a constant pressure.