IGCSE Physics [Syllabus 1.8] Pressure

Summary

This educational video delves into the concept of pressure, defined as force per unit area, and its measurement using a mercury barometer. It explains how atmospheric pressure pushes mercury upwards in a vacuum-sealed tube, creating a measurable column height. The video further explores calculating air pressure using the formula ρgh, where ρ is the density of mercury, g is gravity, and h is the column height. It also covers manometers for gas pressure measurement, demonstrating how to calculate gas pressure based on liquid column height differences, emphasizing the importance of considering the correct sign for accurate results.

Takeaways

• 📘 Pressure is the force exerted per unit area, with units of newtons per meter squared.
• 📊 A mercury barometer measures air pressure by the height of mercury in a column, where air pressure pushes mercury upwards.
• 🌡️ In a mercury barometer, the equilibrium height of mercury indicates that atmospheric pressure equals the pressure exerted by the mercury column.
• 📏 Pressure beneath a liquid surface can be calculated using the formula rho gh, where rho is the density, g is gravity, and h is the height of the liquid column.
• 💧 Pressure at a point under water is due to the water's density and the gravitational force acting on it.
• 🔄 In a U-shaped manometer, the difference in liquid height between the two arms indicates the pressure difference between the gas and the atmospheric pressure.
• ➕ Positive height difference in a manometer indicates the gas pressure is higher than atmospheric pressure, while a negative height difference indicates it is lower.
• 🧮 To calculate gas pressure using a manometer, use the formula pressure of gas equals atmospheric pressure plus rho gh, considering the sign of h.
• 📉 When gas pressure is lower than atmospheric pressure, the liquid level in the gas side of the manometer will be higher than the air side, and vice versa.
• 📚 For educational resources and past papers on physics, chemistry, and biology, check out free resources and the patreon channel mentioned in the video.

Q & A

What is the definition of pressure?

Pressure is defined as the force exerted per unit area, mathematically expressed as pressure = force / area.

What are the units for force, area, and pressure?

The units for force are newtons (N), for area are square meters (m^2), and for pressure are newtons per square meter (N/m^2), also known as pascals (Pa).

How does a mercury barometer measure atmospheric pressure?

A mercury barometer measures atmospheric pressure by observing the height to which the mercury column rises due to the air pressure pushing down on the mercury in the barometer.

Why is the space above the mercury column in a barometer a vacuum?

The space above the mercury column is a vacuum to ensure that the only force acting on the mercury is the atmospheric pressure, allowing for an accurate measurement of air pressure.

How can the height of the mercury column be used to calculate air pressure?

The height of the mercury column can be used to calculate air pressure using the formula P = ρgh, where P is the pressure, ρ is the density of the mercury, g is the acceleration due to gravity, and h is the height of the mercury column.

Outlines

00:00

🔬 Introduction to Pressure and the Mercury Barometer

This paragraph introduces the concept of pressure as force per unit area, using the formula P = F/A, where P is pressure in newtons per square meter, F is force in newtons, and A is area in square meters. The video then explains how a mercury barometer measures atmospheric pressure. It describes the setup of the barometer, with mercury exposed to air, and how air molecules collide with the mercury, creating a downward force. This force causes the mercury inside the tube to rise, creating a vacuum at the top. The height of the mercury column stabilizes, indicating the atmospheric pressure, which can be calculated using the pressure formula for a liquid surface, P = ρgh, where ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid column.

05:00

📡 Calculating Atmospheric Pressure with the Mercury Barometer

The speaker elaborates on the mercury barometer's function, emphasizing the equilibrium state where atmospheric pressure is equal to the pressure exerted by the mercury column. The formula for calculating this pressure is P = ρgh, with ρ being the density of mercury, g the acceleration due to gravity, and h the height of the mercury column. An example calculation is provided using the density of mercury, gravity, and the measured height of the mercury column to determine atmospheric pressure. The video also explains that this formula can be applied to other liquids and situations where pressure beneath a liquid surface needs to be calculated.

10:01

📊 Understanding Manometers for Gas Pressure Measurement

This section introduces the manometer, a device used to measure the pressure of a gas. It explains how a U-shaped tube containing a liquid, such as water, can be used to compare the pressure of a gas to atmospheric pressure. When a gas is introduced into the system, the pressure exerted by the gas causes a difference in the liquid levels on either side of the tube. The height difference is used to calculate the pressure of the gas using the formula P_gas = P_atm + ρgh, where h is the height difference between the two sides. The importance of correctly interpreting the height difference as either positive or negative depending on the relative pressures is highlighted.

15:04

📐 Calculating the Pressure of a Gas Supply Using a Manometer

The final paragraph provides a practical example of using a manometer to calculate the pressure of a gas supply. It describes a scenario where the left side of a U-tube is connected to a gas supply, causing the water level to drop by 0.2 meters, resulting in a height difference of 0.4 meters. The pressure of the gas is then calculated using the formula P_gas = P_atm + ρgh, taking into account the atmospheric pressure, the density of water, gravity, and the height difference. The importance of using the correct sign for the height difference is emphasized to ensure an accurate calculation of the gas pressure, which must be less than atmospheric pressure if the gas pressure is weaker than the air pressure.

Keywords

💡Pressure

Pressure is defined as the force exerted per unit area and is a fundamental concept in the video. It is measured in newtons per square meter (N/m²). In the context of the video, pressure is used to explain the working principle of a mercury barometer, where atmospheric pressure pushes down on the mercury, causing it to rise in a column, and the height of the mercury column is directly related to the air pressure.

💡Mercury Barometer

A mercury barometer is an instrument used to measure atmospheric pressure. It consists of a glass tube filled with mercury inverted in a reservoir of mercury. In the video, the barometer is explained as a device where air pressure exerts a downward force on the mercury's surface, causing the mercury in the tube to rise to an equilibrium height, which can be used to calculate the atmospheric pressure.

💡Atmospheric Pressure

Atmospheric pressure, also known as air pressure, is the weight of the air molecules pressing down on Earth's surface. The video discusses how atmospheric pressure can be measured using a mercury barometer, where the pressure exerted by the air above the mercury is equal to the pressure at the base of the mercury column once equilibrium is reached.

💡Density

Density is the mass per unit volume of a substance. In the script, the density of mercury is used in the formula for calculating pressure exerted beneath a liquid surface (rho gh), where 'rho' represents the density of the liquid mercury, a key factor in determining the height the mercury will rise in the barometer.

💡Gravity

Gravity is the force that attracts a body towards the center of the Earth, or towards any other physical body having mass. In the context of the video, gravity (represented as 'g' in the formula) is essential for understanding how it presses down on the mercury in the barometer, contributing to the pressure that can be measured.

💡Manometer

A manometer is a tool used to measure the pressure of a gas by comparing it to atmospheric pressure. The video describes a U-tube manometer filled with a liquid, where the difference in liquid levels on either side of the tube indicates the pressure difference between the gas being measured and the atmospheric pressure.

💡Equilibrium

Equilibrium in this context refers to the state where the atmospheric pressure is balanced with the pressure exerted by the column of mercury in the barometer. The video explains that when the mercury level stabilizes, it indicates that the downward atmospheric pressure is equal to the upward pressure exerted by the mercury's weight.

💡Pascals

Pascals (Pa) is the SI unit for pressure, defined as one newton per square meter. The video uses pascals to express the calculated atmospheric pressure, such as when it states the result of the atmospheric pressure calculation as 1.1 times 10 to the power of 5 pascals.

💡U-Tube Manometer

A U-tube manometer is a specific type of manometer with a U-shaped tube that contains a liquid. The video explains how the difference in liquid height in the U-tube can be used to determine the pressure of a gas, with the atmospheric pressure on one side and the gas pressure on the other, resulting in a height difference due to the pressure differential.

💡Significant Figures

Significant figures refer to the digits in a number that carry meaning contributing to its precision. The video mentions the need to give answers in three significant figures when calculating the pressure of a gas supply using the manometer, indicating the importance of precision in scientific measurements.

Highlights

Pressure is defined as the force exerted per unit area.

The formula for pressure is force divided by area, with units of newtons per meter squared.

Mercury barometers measure atmospheric pressure by the height of a mercury column.

The vacuum space in a barometer is crucial for accurate pressure measurement.

The height of the mercury column in a barometer is directly related to the atmospheric pressure.

Pressure beneath a liquid surface can be calculated using the formula ρgh.

The density of mercury is 1.4 times 10 to the power of 4, which is used in atmospheric pressure calculations.

An example calculation shows atmospheric pressure as 1.1 times 10 to the power of 5 pascals.

Manometers are used to measure the pressure of a gas by comparing it to atmospheric pressure.

The height difference in a manometer indicates the pressure difference between the gas and the air.

Positive and negative heights in a manometer correspond to different pressure relationships.

The formula for gas pressure in a manometer includes atmospheric pressure plus ρgh.

An example problem demonstrates calculating the pressure of a gas supply using a manometer.

The importance of using the correct sign for height differences in pressure calculations is emphasized.

Conceptual understanding is crucial for verifying the accuracy of pressure calculations.

The video concludes with a transition to future topics like waves in physics.

Free resources for IGCSE subjects and Patreon channel information are provided for further learning.

Transcripts

hey guys welcome to another video today

we're going to be going through

the topic of pressure so here we've got

a few things that we want to cover today

so have a read through that before we

begin

so quite simply pressure is the force

exerted per unit

area you've got um here in this diagram

an exemplification of the force a block

of force

acting on a certain area and the

pressure is force divided by the area

force is a newton's and area is a meter

squared and naturally

pressure the units for it is newtons per

meter squared

so very important formula

um now

one way that we can measure air pressure

or atmospheric pressure is using

the mercury barometer and there's a few

important concepts that we have to go

through

uh with this but let's just

let's just think about how the mercury

barometer actually works you've got the

mercury inside the setup

some of the mercury is exposed to the

air

and it's going to cause air

molecules to collide against the surface

of the mercury here right and

what that will do is cause a downwards

force or um

you know the air pressure is going to

push the mercury downwards

and when that happens the mercury that's

inside this column

tube here will go upwards

naturally as you might expect and the

space here in the tube it's completely

vacuum you might have a few little

vaporized mercury molecules sitting

inside this uh

chamber but for the most part it's

vacuum okay and so

obviously the stronger the air pressure

the more higher up the mercury mercury

will go

in this column and we can actually

calculate the air pressure

after the height has stabilized

inside the column by utilizing

the concept of pressure that's exerted

beneath

a liquid surface okay

so let me just take you to you know this

uh white board here i want you to

imagine

a big block

a big container right

now in this container you have

water like this okay

all of that stuff is water

and so if you think about it

if you were standing up here

well you wouldn't feel any pressure from

the water right because you know there's

no water above you or anything like that

but

imagine if you were right down here

what you'll feel is the pressure

of the water above you this entire block

is pressing down against you okay

and the reason that happens is because

water molecules have a density

and you've got the gravity that's

pressing down against you um and

obviously

water has a mass and everything which is

you know part of density but

ultimately speaking the concept that i

want you to get aware of

is that when you are beneath a certain

extent of the surface of the liquid then

that

bulk of the liquid that is above you is

gonna is gonna exert

pressure against you right and that's

exactly what we're talking about when we

talk about the mercury barometer here um

so if you ex you know if you place the

mercury barometer outside

it's going to um the air pressure is

going to press against

this uh surface here and it's going to

push the mercury upwards and eventually

it'll come to an equilibrium where the

height

has stabilized inside this column

okay and so

what we can do then is what we know at

this point in equilibrium

is that this downwards force

pressure so atmospheric pressure

is actually at this point the same as

the downwards pressure exerted by

the column of mercury here so you've got

the height of the mercury

right here and just like we talked about

with you standing at the very bottom of

this column of order

if you calculate the pressure right down

at the bottom here at the base of the

column

that's the pressure of the mercury

column

okay and for this height to be stable

and for this to be in equilibrium what

it means

is that the atmospheric pressure

is equal

to the pressure

caused by the mercury column

and that makes sense because otherwise

the height would change for example if i

suddenly amplified the pressure and you

know times that by five

you know suddenly increasing the

atmospheric pressure then what you'll

find is that

it'll break the equilibrium and you'll

start to find that the mercury

will start to rise inside the column

and obviously that would decrease down

like that

because um

you're increasing the pressure more

downwards force will cause that to

happen

but given that everything is in

equilibrium um then

what you know is that the atmospheric

pressure must be equal

to the pressure inside uh the mercury

column so

given that to be the case in order for

us to calculate

the atmospheric pressure all we need to

do is calculate

what the pressure is at the base of this

mercury column

which we use the formula rogue gh

and what rogue is is the density

of the material in this case the density

of the mercury

gravity is g and the

height is the height of the mercury

column

and in fact this doesn't apply only to

this this certain experiment

this formula rho gh calculates the

pressure

that exer that is exerted beneath any

liquid surface so you can still use this

formula for example if you were

underneath the c and you're like

right here and you know you've got

a height of let's say you know 10 meters

uh

you've got the density of water being a

certain amount then yes you can

calculate the

amount of pressure exerted like that as

well

um but for this particular example

we're going to be looking at strictly

the mercury barometer because that's the

focus of

our thing today um so here

the pressure beneath the liquid surface

is equivalent to rogue

gh and you've got the density you've got

the gravity and you've got the

height um so let's actually go through

an example here you've got the density

of miraculous 1.4 times 10 to the power

4.

and so figure 3.1 shows that an

experiment is used to determine the

atmospheric pressure

and remember you've got the atmospheric

pressure pressing against here

but you've also got the pressure of the

mercury

going against going down here and you've

got the

pressure point right at the base here

which is the pressure of mercury um

and so we know that an equilibrium

pressure of atmosphere

is equal to the pressure of mercury

at the base of the column which is of

course equal to

rho g h and we'll be using that in a

second so

the name of the experi uh the instrument

is obviously the

mercury barometer

and the space a has a vacuum in it as i

said before

which is the space here now calculate

atmospheric pressure well

p atm equals rogue

gh we know that rogue

or the density is 1.4 times 10 to the

power four

we know that gravity is ten and we know

that the height

is seven hundred and sixty millimeters

uh but we wanna convert that into meters

so if you divide that by one thousand

you got 0.76

and so therefore when you calculate that

you get

1.1 times 10 to the power of

5 pascals

okay so i hope that makes sense for you

um now when we want to measure the

pressure of a gas

we can use the setup called the

manometer which is actually sort of very

similar to the barometer but

essentially what you do is you

have a guess whose pressure you want to

measure and it

enters through this tube here now as it

enters through that tube it's going to

exert some sort of

pressure against the liquid

surface that you see over here

and on the other end in this u-shaped

setup you have

just open tube which is exposed to the

ear

and the air will exert some sort of

pressure on the liquid

and what we're trying to do is sort of

see what the difference is

in height between left and right

okay so just have a little think about

this

um let's take you back to this um

whiteboard

if you've got this u-shaped set up here

right

and let's just imagine that you don't

have any extra gas coming in like you've

just got

air and air

then what do you think would be the

levels of each of these

two different um uh

two different tubes well given that the

air pressure is the same on both sides

sides you're gonna have

an exactly level height between the two

tubes right

so the height difference is going to be

zero

but let's just imagine that you've got

this time you're going to have gas

and again of course this one's going to

be air

and we're just going to imagine that the

pressure of the gas

is higher than the pressure of the ear

then

what do you think will happen in terms

of the

height differences between these two

tubes

well as you might expect the stronger

pressured gas is going to force

the liquid down more than the less

less pressure gas so in this case if

we're assuming that this gas on the left

hand side

has a higher pressure than air pressure

what you'll find

is the height levels might look

something like this

right because there's more force being

exerted here

than here and oppositely

one more scenario

that you might get is of course when the

gas that you put in

on the left-hand side is less stronger

than ear

pressure

in which case you'll find the opposite

to be the case

because air is exerting more pressure

than the gas itself

then you'll have a setup like this

where the height of the gas side is

going to be higher than the height of

the airside

and this height difference is

extremely important

and i want you to listen very carefully

here but what we're going to say

is that when you have the

pressure of the gas being higher than

the pressure of the air in other words

when you have

the mercury or whatever liquid it is

lower on the gas side than the air side

we're going to say that it's

positive height so when we calculate the

height we're going to use a positive

number but when the gas

is when the gas pressure is lower than

the air pressure or in other words when

you have

the liquid being higher on the gas side

than the air side

we're going to use negative height

okay so even if the heights were both 10

millimeters

in this example it'd be 10 millimeters

as normal but here would be minus 10

millimeters and you'll see why this is

relevant in a second but

in fact you know just just be aware of

that and we'll we'll go through some

questions in a second but

here the pressure due to the gas

the formula we're going to use is

atmosphere

plus rho gh and h

being the difference in the height

between the two

tubes okay

so let's have a look at that

uh here they say that a u-u-shaped tube

of constant cross-sectional area

contains water of density 1000

okay both sides of the youtube are open

to the atmosphere

so the atmospheric pressure is uh 1

times 10 to the power 5 pascals

the left hand side of the tube is now

connected to a gas supply

using a length of rubber tubing this

causes the level of the water and the

left hand side

to of the tube to drop by 0.2 meters

as shown in figure 3.2 calculate the

pressure of the gas supply

give your answer in three significant

figures okay

well the first thing we're going to do

is analyze the situation well you've got

the gas coming in

from the top here now is the gas

stronger weaker than air pressure that's

gas

that's air well you know that this

is lower than this so this gas must be

stronger than air

now what we want to do is calculate the

difference in height now

remember if this is 0.2 meters

then this must be 0.2 meters and the

total difference

between the heights is 0.4

meters okay and

so what we're going to do is put that

into the formula so

pressure of gas equals atmosphere

plus rho gh

so atmosphere is 1.000

times 10 to the power 5. you add that

to rogue which is 1000.

get rid of that gravity

oops

sorry i'm just gonna see if i can get

rid of that

so density again is 1000

multiplied by gravity and then multiply

that by the height which is what

0.4 and so when you do the calculations

you get 1.04 times 10 to the power of

5

as the pressure and you can see why

the the sign that you put in front of

the height

matters right because i want you to

consider

another example where you might have had

the opposite

situation where you have something like

this and let's just say the height

difference here was

uh 0.4 meters as well

but if you were to think about it right

if you just pluck that into the formula

without doing anything

right without changing the sign to a

minus 0.4

meters then you'll get the same result

1.04 times 10 to the power of 5

as the pressure of gas but that can't be

true because we know for a fact that

air pressure is higher than the gas

pressure here remember gas is coming

this way

and air is coming this way but given

that

the level of the fluid is lower here

than here the air pressure must be

stronger than the gas pressure

but we know that the atmospheric

pressure is actually

1.00 times 10 to the power of 5.

so whatever pressure we get for the gas

must be less than this amount in this

situation

but if we calculate the 0.4

meters without putting the minus sign in

front of it then you'll get 1.04 which

is clearly wrong

so that's why it's important that for

you to do the calculations

of pressure of gas equals atmosphere

plus rogue gh this h

in this case if you did it properly and

put minus

0.4 meters then

you'll get the right answer because then

that will become the same as atmosphere

minus rho gh um

so then what you'll get is an answer

that is less than the atmospheric

pressure which is correct okay so the

the thing i want to demonstrate is just

make sure that you appropriately put the

correct sign

in front of the height when you do this

calculation

using this formula otherwise you might

get the wrong answer but also just use

your conceptual awareness as well and

when you arrive at an answer just make

sure okay well

do i know that um you know the gas gases

lower or higher than the air pressure

just by looking at

the liquid levels and then just uh

sort of go from there so i

hope that video helped guys and we're

finally at the end of

general physics and we'll be moving on

to some other stuff like waves in the

next segment

um free resources on free exam academy

just

notes and things like that for igcs

biology chemistry and physics and

please check out my patreon channel as

well not a lot of physics

content at the moment but i will be

going through a lot of past paper stuff

there eventually on physics but i've got

a lot of it already on chemistry and

biology so make sure you check that out

and i will see you in the next video

[Music]