# Boyle Law

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Have you ever traveled by road to a hilly area- that is to a higher altitude place?

Did you carry chips packets with you? Have you observed that if you go to higher altitudes, the chips packets start to expand and

at times they even burst? Well, why does that happen? Think about it. So we have a person. He’s running.

So let’s count the number of times the person hits the boundaries in one minute. One, two, three, four, five, six, seven, eight. So in one minute the postman touches the

boundaries eight times. Now if the person runs at the

same speed- that is the speed of the person remains

constant, and he has to cover double the distance in

the same time- that is in one minute only the person

now has to cover double the distance and he’s running at the same speed.

How many times will he touch the boundaries? Let’s count. One, two, three four. So now if he has to cover double the

distance, he touches the boundaries half number of times.

So let’s compare this. The person in both the cases is running

at the same speed. In one minute he touches the boundaries eight number of times and if he has to cover

double the distance, the number of times he touches the boundaries

is reduced to half. So by the time he covers one distance

he has already covered double the distance. So you see that the distance covered is related to

the number of hits per unit time. If the distance covered is less-

that is if he had to cover lesser distance the number of hits per unit time

increases and if the distance covered, that he had

to cover is more the number of hits per unit time decreases

if the speed of the person remains constant. Similarly we have distance covered is

inversely proportional to the number of hits per unit time. This means greater is the number of hits per unit time,

lesser is the distance covered. So this also is the case when the speed remains constant. In physics you must have studied that

pressure at the same height remains the same. So if an experiment is

performed- in this we have different shaped tubes. Now if a liquid is poured in these

tubes, all the tubes are different in shape, so it is observed that they take the same

heights irrespective of their shapes. The height in all the tubes is the same,

so by this we know that the pressure at the same height remains the same.

This concept was used by a scientist named Robert Boyle. He performed an experiment which was known as Boyle’s experiment.

He performed the experiment in 1662. Let’s see what he performed.

He took a J-shaped tube. A gas is enclosed in this tube and this is the scale that he used to measure the

volume of the gas enclosed. Now he added mercury in the tube. So let’s see what happens. As he added mercury, the volume of the gas enclosed reduces. So now, the volume enclosed is 60cm³. This is the pressure exerted by gas and this is the atmospheric pressure.

We know that pressure at same heights remains the same, so at this point this

is the pressure of gas, at this point the pressure exerted is

the atmospheric pressure, which is 760mm of mercury. This remaining same, he added more mercury so as to make the volume of the

gas enclosed half. So when he added more mercury he saw that the

volume reduced to half. Now it occupies 30cm³. This is the pressure exerted by gas

and when he calculated the pressure on the other side, he observed that the pressure was the

atmospheric pressure, plus 760mm of mercury. So now the

pressure was two times 760mm of mercury.

Now this set-up remaining the same, he added more mercury so as to make the

volume of the gas enclosed one by third. So when he added more mercury, the volume

becomes one-third, that is 20cm³. This is the

exerted by gas. Pressure at same height remains the same,

so on the other side when he calculated- the pressure was the pressure of

atmosphere plus 1520mm of mercury. So the

overall pressure is 3 times 760mm of mercury.

So he observed as the pressure becomes three times,

the volume becomes one-third. So he concluded that if the pressure was

doubled at constant temperature- all the

calculations the entire experiment which Boyle had performed was at a constant temperature, and he was able to observe that when the pressure was doubled the volume

of the gas became half- half the original volume, and as the pressure was tripled the volume became one-third the original

volume. So as the pressure was doubled volume became half, as the pressure was tripled volume became one-third. So based on this, as we’ve seen already from this

experiment- that is a gas enclosed in a container. In nine seconds there are nine hits.

So there’s one hit per second. If the volume is reduced to half, so in the same time that is in nine seconds

only there are 18 hits. As the volume is halved the pressure doubles. So based on this experiment, Boyle gave the law. His law states that the volume is inversely proportional to pressure,

temperature remaining constant. This is something that we have seen

through the person running. So there we had the

distance covered is inversely proportional to the number

of hits per unit time, the speed remaining constant.

So, in Boyle’s law the distance covered is the volume

occupied by the gas, the number of hits per unit time is

the pressure of the gas and speed is the temperature.

So according to Boyle’s law, the volume of the gas is inversely proportional to pressure

at temperature remaining constant. So the Boyle’s law states that the volume of a

given mass of gas, so the law holds for a particular gas,

so for a given mass of gas the volume is inversely proportional,

so you have to keep in mind that the volume is inversely proportional to pressure at

constant temperature. So the law holds only at a constant

temperature for a particular gas. So from the law we have that the volume is

inversely proportional to pressure temperature remaining constant for a

particular gas. So to remove the proportionality sign we

introduce a constant, so we get volume is equal to

constant divided by pressure. Now if we take pressure on the other side,

we get pressure into volume is equal to constant. So the product of pressure and volume is

a constant value and this is the Boyle’s law.

So for a particular gas the product of pressure and volume at a constant temperature is constant. So let’s see a small experiment. So a gas is enclosed in a container. Now, we will increase the pressure which

can also be seen through this pressure gauge. We increase the pressure from top. So as the pressure is increased the volume decreases. So you see the values- as the pressure is increasing the volume which is enclosed in the container is reducing. And you see that the product of pressure

and volume is constant. So as the pressure increases volume decreases but the product of pressure and volume is always constant. So from this we can also plot the values. So if you draw a graph between the pressure and

volume of a gas we get a curve which shows that as volume increases the pressure decreases.

We know that according to Boyle’s law pressure is inversely related to volume, or we can also say that volume is inversely related to pressure. So as the volume increases the pressure decreases. Now let’s say if this 1/V is x so we get that pressure is directly proportional to 1/V

which is x. So we get pressure directly proportional to x and over here x is 1/V. So pressure is inversely proportional to volume and pressure is directly proportional to 1/V. So if we plot a graph between 1/V and pressure we get a straight line. So you see

that as one by volume increases, the pressure increases. So pressure is directly proportional

to one by volume. Since these graphs are plotted at constant temperature, so these are also known as isotherms. ‘Iso’ means same, ‘therm’ means for temperature. Since Boyle’s laws is valid for a gas at constant temperature so

these graphs are known as isotherms. That means the temperature remains constant. The pressure of a gas increases with the

increase in volume. Is it true or false? So from Boyle’s law we know that pressure is inversely related

to volume. So as volume increases, pressure decreases. So with the increase in volume, pressure decreases. So the pressure of a gas decreases with the increase in volume.

So the statement that we have is false. It does not increase, it decreases with the increase in volume. From Boyle’s law we saw that PV- that is the pressure into volume

of a gas is constant. Let us denote this constant by k

and we know this is valid for a particular gas at a constant temperature. So if we have the initial conditions- say at

some initial pressure and at initial volume, the product comes out to be k.

The final pressure of the gas is P? and the final volume is V?.

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00:12:20,560 –>00:12:23,560

Again the product is constant which is k. So we get that P? into V? is

equal to P? into V?. So initial pressure into initial volume is equal to

final pressure into final volume which is k and which is a constant.

So from this we get that these two quantities are same. So P?V? is equal to P?V?.

That is the initial pressure of a gas, for a

particular gas and the initial volume of a particular

gas is equal to the final pressure of a particular gas into the final volume of that gas and temperature remains constant. Now let’s explain the Boyle’s law in terms of kinetic theory. So we know, we’ve seen that pressure

and volume are inversely related. So what is happening here is,

as external pressure increases the internal pressure has to increase.

This means the number of hits per unit time has to

increase and this is possible only when the volume is decreased. As the volume is decreased the number of

hits per unit time increases and the pressure increases.

Let’s recall- as outside pressure increases to

balance it the inside pressure has to increase. This means the number of hits per unit time has to increase. For the

same number of particles, this is possible only when the volume

decreases. When the volume decreases the number of

hits per unit increases, so we get as the pressure increases the volume decreases. Similarly the vice-versa case- if we decrease the external pressure, to

balance it the internal pressure has to decrease.

This means number of hits per unit time has to decrease. Now again we have the same number of molecules so to reduce the number of hits per unit time

they should travel a great distance. This is possible only when the

volume increases as the number of particles remain the same

so to get number of hits per unit time lesser, they should travel a great distance. This means the volume increases. So as pressure decreases the volume

increases. So now, did you find an answer to why the chips

packets burst when they are taken to higher altitudes? Well okay, so this follows the Boyle’s law.

When we go to a higher altitude, the outside pressure is less so to balance it the pressure inside the chips packet

should also be reduced. So now the inside pressure has to be less. How is that possible? By Boyle’s law- if the inside pressure is less

the volume increases, and if the volume increases- the

chips packet expand in size and at times they expand to such an

extent that they burst. So why do the chips packets burst

when taken to higher altitudes? At higher altitudes, the outer- that is the outside pressure is less so to balance it the

inside pressure- that is the pressure inside the chips packets that has to decrease. So by Boyle’s law

if the inside pressure that is the pressure inside the

chips packets is less the volume has to increase. As the volume increases the chips

packets expand in size and at times they expand to such an extent

that they burst. So this is the reason why the chips packets

burst when they are taken to higher altitudes. You use Boyle’s law even when you are breathing.

So while breathing there is a relationship between the volume and the pressure. While breathing in we lower the diaphragm. When we lower the diaphragm the volume

inside increases. So by Boyle’s law as the volume inside increases the pressure decreases. So the inside pressure is less and so outside air flows in. So this is how we breathe in. So we lower the diaphragm, the volume

increase, pressure decreases so to balance it the outside air from outside it moves in. This is how we breathe in. So, while breathing out what happens? We push the diaphragm up. As push the diaphragm up, the volume inside decreases, so

by Boyle’s law as the volume decreases the pressure increases, so to balance it the air inside flows outside. Since the inside pressure is more so air from inside flows outside and

this is how we breathe out. So we even use Boyle’s law during breathing. Now let’s try to solve a question.

At a constant temperature, the volume of a gas was found to be 400 cm³ at a pressure of 760 mm of mercury. If the pressure of the gas is

increased by 25 percent what should be the new volume? Okay, now let’s write down the data that we’re provided. So we have the initial pressure which is 760mm of mercury and the final pressure we know that the pressure is

increased by 25 percent this means that if this is the initial pressure then we increase the pressure by 25 percent. So what do we get? We get 125 P? by 100. So if we divide this by 25 we get 5 P? 25 fives are 125 and 25 fours are 100. So this is the final pressure. We need not write this for 760 mm of mercury because this will make the calculations

lengthier. Now we are given that the initial

volume is 400 cm³ and we have to find out the final volume. So now we know that the Boyle’s law says that the initial pressure of the gas into initial volume is equal to final pressure into final volume. So if we solve this- so let’s try to solve this. Initial pressure is P?, initial volume is 400. Final pressure- let’s write it in terms of P?. We have 5P? by 4 and we have to find out the final volume,

which is V?. So if we calculate V? from this, we can cancel out P? from both the sides. So we get V? is equal to 400 into four divided by five. This we can cancel out again. So we get 320. 8 fours are 32, so we get 320 cm³. Had we substituted the 760 instead of P? we would have just increased the calculations so we let the values remain in terms of P?. So what do you observe here?

As the pressure increases so the final pressure has increased-

so the final volume decreases.

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