# Charles Law

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.