IGCSE Physics [Syllabus 1.8] Pressure
Summary
TLDRThis 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
🔬 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.
📡 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.
📊 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.
📐 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.
Mindmap
Keywords
💡Pressure
💡Mercury Barometer
💡Atmospheric Pressure
💡Density
💡Gravity
💡Manometer
💡Equilibrium
💡Pascals
💡U-Tube Manometer
💡Significant Figures
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]
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