Units in Thermodynamics
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Hello, this presentation is designed to take
away some of the mystery from units of measurement in the world of engineering technology. How we measure things is just as important
as what we measure because, if you don’t understand the method of measurement, then how can possibly
measure things accurately, or understand measurements made by other people? Now, first of all there are countless systems
of measurement in the world used by different people for different purposes; however, in
the world of engineering, there are two main systems. There is the S.I., which stands for “Systme
Internationale” – that’s a newer system originating in France that’s now becoming more and more
popular across the world. It’s also sometimes called the “mks system”,
and that is an abbreviation for metres, kilograms and seconds. Now, this is an important concept because
every system of measurement is based on, primarily, its chosen units for distance mass and time. The S.I. uses the metre for distance, the
kilogram for mass and second for time, and every other unit in the system is actually
a mathematical combination of those three units. The other system you need to know about is
the “British Imperial” system, also sometimes called the “American System”, and its abbreviation
is “fps”, for foot, pound and second, which are its chosen measurements for distance,
mass and time respectively. This system tends to be most popular in any
country that used to be part of the British Empire. That inclues the United States, Canada, the
United Kingdom, and any other English-speaking nation, although most, aside from the United
States, tend to be shifting more and more towards the S.I. So let’s take a closer look at some of the
units used by these two systems. We’ll start with mass, which I give the very
vague definition of “the amount of stuff in something”. Stuff, in this case, is matter, and this isn’t
a very good scientific… or scientifically correct definition, but this presentation
isn’t designed for theoretical physics, so this is what I’m going to go with for now. The key thing is that, since mass is the amount
of matter in an object, it won’t change depending on the location of that object. So where I move the object, it will still
have the same amount of matter contained within it. The S.I. unit for mass is the kilogram, which
is also the mass of 1000 cubic centimetres of water at 4 degrees Celcius. The imperial unit is the pound, or pound-mass. Another unit that you might see in imperial
system for mass is the slug, which isn’t used very often, but you might see it at some point,
and 1 slug is equal to 32.174 pounds-mass. And in case you want to convert between the
two systems, it’s a good thing to note that 1 kilogram is equal to pretty close to 2.2
pounds-mass. The next quantity we’ll talk about is force,
which is closely related to mass in many ways. The S.I. unit for force is called the Newton,
and 1 Newton is the force required to bring an object with a mass of 1 kilogram up to
a rate of acceleration of 1 metre per second squared. If you remember Newton’s second law, force
equals mass times acceleration, so a unit of force should be made out of a unit of mass
times a unit of acceleration. Therefore, a Newton is kilogram times a metre
per second squared. Remember S.I. is the mks system, so every
unit in it is made of metres, kilograms and seconds, and the Newton is one very good example. You can see kilograms, metres and seconds
as part of it. For the imperial system, the unit of force
is unfortunately the pound or pound-force. This is unfortunate because it causes a lot
of confusion between force and mass, both of which are measured in pounds, which forces
us to pounds-force and pounds-mass to specify which one we’re using at a given time. The pound-force is actually defined using
the pound-mass. 1 pound-force is should be the force of gravity
that is exerted on an object with a mass of 1 pound-mass on Earth at sea level. Another unit of force you may never see, but
I’m putting it in because of its similarity to the Newton, is the poundal. This is an imperial unit, and 1 poundal is
the force required to bring a mass of 1 slug to a rate of acceleration of 1 foot per second
squared. So I mention this because it is similar to
the Newton in that it is also a mass times a unit of acceleration. So it works well with Newton’s second law,
unlike the pound-force. Now, another very important measurement is
weight, which we sometimes think of as being the same as mass. However, weight is actually defined using
force. The weight of an object is defined as the
amount of gravitational force acting on it, so the units we use for weight should be the
same as for force. For example, if I stand on a scale in my bathroom
and it says I weight 190 pounds, is it pounds-mass or pounds-force? The answer is it should be pounds-force, not
pounds-mass. So how would I measure my mass, if I wanted
to. Well, to measure mass directly, you shouldn’t
use a spring scale. Instead, you should use an equal arm balance
scale. Then if I put an object with a mass that I
know is equal to, say, 100 kilograms on one side, and then I sit on the other side, then
if the scale is balance, I know my mass is the same as the 100 kilograms. This measurement doesn’t change depending
on the force of gravity, so I can do this measurement on Earth or on the moon or anywhere
else, and I should get the same result. However, you can also calculate mass mathematically
using your weight, but you know one more piece of information to do that, which is the gravitational
acceleration at the place where you happen to be standing. This slide shows the calculation you would
make using Imperial units, which is probably harder than with S.I. units. Start with Newton’s second law – force equals
mass times acceleration. So weight, or force of gravity, equals mass
times gravitational acceleration, which abbreviated as ‘g’. So mass would equal force of gravity divided
by g. In this case, I use the weight I measured
as 190 pounds-force, so divided by g, g equals 32.174 feet per second squared, which is standard
acceleration due to gravity at sea level on Earth. But you can’t do this calculation yet because
the units aren’t right. If you divide by pounds-force by feet per
second squared, the result won’t be in units anyone will understand. It will be in pounds-force per foot per second
squared, but we want the result to be in pounds-mass because that’s something that’s easier to
understand. So first, we have to convert pounds-force
to pounds-mass times feet per second squared. And pounds-mass times feet per second squared
is actually another measure of force that is more useful because it comes from a mass
times an acceleration as per Newton’s second law, so it’s more like Newtons or poundals. So, we need to use this unit conversion here
to change pounds-force to pounds-mass times feet per second squared, and to do that, multiply
190 by 32.174. That gives 6113 pounds-mass feet per second
squared. So just to be extra clear, this is what happened
when I converted 190 pounds-force, so instead of 190 pounds-force, we’ve got this number
here in pounds-mass feet per second squared. So then that number is divided by 32.174 feet
per second squared because that was the value of g. And the result is 190 pounds-mass. So, what just happened here? It may seem a little strange that we started
out with a weight of 190 pounds-force, did all this weird calculation, and came up with
an answer that was the same, only in pounds-mass instead of pounds-force. Well the problem is that they won’t always
be the same. The only reason this was the same this is
because I assumed I measured my weight in a place where g equals exactly 32.174 feet
per second squared. So let’s try measuring it somewhere where
g equals exactly 32 feet per second squared instead, like at the top of a mountain, where
gravity is just a little bit less than at sea level. So this time, we’ll assume I still measured
my weight as 190 pounds-force, so I put then in for force of gravity equals my mass times
32 feet per second squared, which is g. Weight comes out to be 6113 pounds-mass feet
per second squared divided by 32 feet per second squared, which leaves an answer of
191 pounds mass. So this time my mass came out a little higher
than it did before. Why is it higher? Well if you think about it, pounds-mass and
pounds-force are defined to be the same when g=32.174 because that’s the standard gravitational
acceleration. And if g is less than 32.174, my mass will
be a bit more than my weight. But if g is more than 32.174 like on Jupiter
or somewhere else with a lot of gravity (if I could stand on Jupiter anyway), then my
weight would be more than my mass in that case. In the S.I., everything is a bit simpler,
partly because it uses kilograms for mass and Newtons for weight, which makes it easier
to keep them separate, rather than using the same word for both things. So if I happen to measure my mass as 86 kilograms,
all I need to do is multiply this by the gravitational acceleration measured in metres per second
squared. In this case 86 kilograms times 9.8 metres
per second squred is 842.8 Newtons. And that’s the answer. There’s no need for an extra of converting
the units of force because a Newton is defined to be a kilogram times a metre per second
squared. So, that takes care of one of the more confusing
things in measurement, which is the difference between mass and weight, and combine that
with the difference between pounds-force and pounds-mass. But let’s move on to some other types of measurements
using both the S.I. and the British Imperial systems. So, here are a few other compound units. A compound unit is simply unit that is a combination
of other units being multiplied and divided together. And all are actually a combination of units
for length, mass and time. You’ve already seen one such unit, which is
the Newton, which is kilograms times metres divided by seconds squared. So other ones include the units for work and
energy, which are actually the same – they’re measured the same way. And there’s power, which is the rate of work
being done, and pressure and density. Those are all important units in engineering. So, starting with energy, the S.I. unit for
energy is the Joule, and 1 Joule is equal to the amount of work you would do on an object
by exerting a force of 1 Newton to it across a distance of 1 metre. Work is just the net change in energy over
an interval of time, so we actually use the same unit to measure both: Joules. The imperial system uses the foot-pound, or
foot-pound-force to be more specific, which you can see is similar to the Joule. If a Joule is a Newton times a metre, then
both are actually a unit of force times a unit of distance. There just isn’t a special name for the foot-pound
the way a Newton-metre is called a Joule. And other units for energy that you may run
into are BTU’s as Calories. Both of these are defined in different ways
based on the energy required to raise the temperature of water by a certain amount,
and even though these definitions are very different from the definitions for the Joule
and foot-pound, you can still convert between all of these things easily because they all
measure the same thing: energy. Now power is just the rate of work being done,
so all we need to do is take the unit used for work and divide it by the unit for time. So, in S.I., the unit is called the Watt,
and a watt is a Joule per second, so 1 Watt is equal to 1 Joule divided by 1 second. In the imperial system, the usually unit is
horsepower. Now, you could measure this thing in foot-pounds
per second, and that would actually make a lot of sense because it would be the same
as I just said with the Watt. You take the unit we were just using for energy
or work and divide that by seconds, and you would get foot-pounds per second and that
is one way you can measure power in the imperial system. And the horsepower is actually defined using
that. 1 horsepower is equal to exactly – it’s defined
to be equal to exactly 550 foot-pounds per second. So other units you may run into – the foot-pound
per second like I said or also BTU’s per second, since BTU is a unit for energy, BTU’s per
second would be a unit for power. Another important quantity is pressure, and
its important in thermodynamics, particularly in studying engines, fluid power systems,
a lot of different kinds of power generation. Pressure is actually defined as being a force
exerted spread out across and area. In S.I. the main unit for pressure is the
pascal, which is 1 Newton per square metre. So for example, if you had a weight of 100
Newtons and placed it on the floor and measured the area of the floor that the weight was
sitting on as being exactly 1 metre then the pressure would be 100 Pa. 100 Newtons divided 1 metre would give 100
pascals. Another unit we see very often for measuring
pressure is bars, which comes from the pascal. The reason for using bars to measure pressure
is that it is a nice round number that is very close to the atmospheric pressure on
the surface of Earth (or barometric pressure – same thing). So engineers like using the bar to measure
pressure because it gives a good idea of how much more or how much less the pressure is
in, say a cylinder, or another type of thermodynamic system versus its surroundings. The surroundings, you would assume to have
a pressure very close to 1 bar because that would be atmospheric pressure. So if you want a number even close, though,
to the normal atmospheric pressure, you could use the unit called atmospheres, which is
exactly 101325 pascals, which is very close to the 100000 pascals that make up a bar. In the imperial system the unit for pressure
is pounds per square inch or psi. And just remember that its pounds-force divided
by square inches, which again is like the pascal – it’s a force divided by an area. And I’ll mention one or two more measurements
here with compound units. Density is an important one and its defined
as the mass per unit volume, so its measured in kilograms per metre cubed in S.I., there’s
no special word for it, or it could be measured in pounds-mass per foot cubed in imperial. The symbol for density is the greek letter
rho, which is important to know because it looks like a ‘p’, you can see it here. So don’t get it confused with the symbols
for pressure or power, because that’s not a ‘p’, it’s a rho. And that comes from the Greek alphabet. Now another very similar unit or measurement
is specific volume, which is volume of a material per unit mass. Now, in the language of thermodynamics, anything
specific – anything with the word specific in front of it is almost always measured per
unit mass. So specific volume is volume divided by mass,
specific energy is actually energy divided by mass as well. I’m not going to get into that but it’s a
good thing to remember that anything specific is divided by mass. Now, you might also notice that means specific
volume is the same thing as density, but it’s turned upside down, so specific volume is
volume over mass while density was mass over volume. The symbol for specific volume is a lower
case ‘v’, which is another thing to keep in mind, and usually you’ll see it written in
italics, like it is here, or in cursive, just to separate it from net volume, which is the
upper case ‘V’. That would be the total volume that an object
has, whereas the smaller one is specific volume. And we measure that in metres cubed per kilogram
or feet cubed per pound mass because that’s the same as the units up here but flipped
upside down.

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