Chapter 17: Temperature and Heat

Welcome to Last Minute Lecture.

This free chapter overview is designed to help students review and understand key concepts.

These summaries supplement not replaced the original textbook and may not be redistributed or resold.

For complete coverage, always consult the official text.

Ever feel like you just want to like cut to the chase and really understand something without wading through a ton of extra stuff?

Yeah, totally.

That's what we're doing here on the Deep Dive.

Absolutely.

You're with us because you are interested in temperature and heat and we're taking a deep dive into a chapter literally called temperature and heat.

We're going to pull out all the good stuff, all the really interesting stuff to give you a real grasp on these concepts without like, you know, bogging you down.

Yeah, that's the goal.

So let's just jump right into it.

Thermal equilibrium.

Oh yeah.

It's this idea that the chapter talks about where two systems, they're in thermal equilibrium if they're not exchanging heat.

And that kind of naturally happens when they get to the same temperature.

Right.

It sounds kind of straightforward.

It does.

But then you start thinking about how the world is constantly trying to find this balance, you know?

Yeah, it is.

It's like, it makes you think about how like different materials reach that equilibrium at different rates.

Okay.

So, you know, you can have a metal spoon and a wooden bowl in the same room.

Right.

And they'll eventually reach the same temperature, but the spoon will feel colder to the touch.

Right.

And it's not that it is actually colder.

Right.

It's just that it's conducting heat away from your hand faster.

It's just moving that heat.

Exactly.

Yeah.

That's really interesting.

Yeah.

So this whole idea of reaching the same temperature, it actually leads us to something called the zeroth law of thermodynamics.

Oh yeah.

And you might be thinking,

zero.

Yeah.

Why is it zero?

Well, it turns out that this law, it's like so basic that it had to be established before they even came up with the first and second laws.

Right.

It's like the foundation.

Yeah.

It underpins the whole thing.

Yeah.

So this idea is basically, if you have a system A and it's in equilibrium with C.

Right.

And then you have system B, which is also in equilibrium with C,

A and B must also be in equilibrium with each other.

It seems pretty obvious.

It seems really obvious.

And what's crazy is that it was actually formalized after the first and second laws.

I know.

Wild, right?

Yeah.

Just shows how fundamental it is, you know?

It's really the foundation for how we think about temperature.

And it really like, it lets us use thermometers to compare temperatures.

Yeah.

Because the thermometer is the C.

Yeah.

And then we're comparing A and B to that C.

It's like our reference point.

Exactly.

Okay.

So now that we know what thermal equilibrium means, like how do we actually measure temperature?

Oh, that's where these handy little devices called thermometers come in.

Yes.

And the chapter talks about how they use some measurable property that changes predictably with temperature.

Okay.

There are a bunch of different kinds.

Yeah, there's a lot.

Like there's the classic liquid in tube thermometer that probably a lot of people are familiar with.

Yes, definitely.

They're filled with mercury or alcohol.

Often.

And they just rely on the principle of thermal expansion.

You know, as the temperature goes up, the liquid expands and it moves up that calibrated scale.

It's a really simple concept, but it works.

It works.

Yeah.

So then the chapter goes into the constant volume gas thermometer.

Oh, yes.

So this one uses the behavior of gases to define temperature scales.

Yeah.

It's kind of a mind bender.

Yeah.

It's a little more complex.

So basically you've got this container of gas with a fixed volume.

Okay.

And the pressure of that gas changes directly in proportion to the absolute temperature.

Oh, wow.

So by measuring the pressure, you can figure out the temperature.

Okay.

So we're using the pressure to actually like read the temperature.

Exactly.

And this is actually how we define the Kelvin scale.

Okay.

Which is really important in physics.

So this type of thermometer, it's really about like the fundamental properties of matter.

It is.

Yeah.

It's like getting down to the nitty gritty.

And then there's also the bimetallic strip thermometer.

Oh, yeah.

I've seen those in thermostats.

Yeah, me too.

It's so clever.

Like how does that even work?

Well, it leverages this neat little fact that different metals expand and contract at different rates when the temperature changes.

Okay.

So a bimetallic strip is literally just two different metals bonded together.

Oh.

And as it heats up, one side will expand more than the other, and it causes the whole strip to bend.

That's so cool.

And that bending can be used to like open or close an electrical circuit.

Right.

Which is how a thermostat works.

Oh, so it's a very simple mechanical switch.

Exactly.

Oh, that's so cool.

Yeah, it's a really clever application of thermal expansion.

And then there's also the resistance thermometer.

Oh, yeah.

Those are pretty cool.

So these use the fact that the electrical resistance of a material changes with temperature.

Yeah, for a lot of materials, especially metals,

as the temperature goes up,

the resistance also goes up.

Okay.

So you can actually measure the resistance and then calculate the temperature very precisely.

Oh, okay.

These are really useful in like in gust real settings and scientific labs where you need a really accurate reading.

And then there's also the temporal artery thermometer.

Oh, yeah.

Those are super common now.

Yeah, they seem pretty high tech.

They are.

They use infrared radiation.

Oh, wow.

So everything emits infrared radiation, including our bodies.

Oh, okay.

And the amount and the type of radiation that something emits depends on its temperature.

Oh, wow.

So temporal artery thermometers, they measure the infrared radiation coming from your forehead.

Okay.

And it's actually a really good way to measure core body temperature.

Okay.

So we've looked at how to measure temperature, but what about the scales that we use?

So the chapter talks about the Celsius scale, which is based on the freezing and boiling points of water.

Yeah.

Zero degrees Celsius is the freezing point and 100 degrees Celsius is the boiling point.

Right.

And that's under standard atmospheric pressure.

Of course.

That's the scale that most of the world uses for everyday stuff.

Yeah.

It's pretty easy to understand.

It is.

Yeah.

Then there's the Fahrenheit scale.

Oh, yes.

Which the chapter reminds us sets the freezing point of water at 32 degrees Fahrenheit and the boiling point at 212.

Yeah.

And then it gives us that lovely conversion formula.

Yeah.

TF equals 9 fifths TC plus 32.

Oh, yeah.

That one.

So it's a little less intuitive than Celsius.

It is.

Yeah.

It's kind of arbitrary.

Yeah.

But, you know, it's what a lot of people are used to in certain parts of the world.

Yeah.

But from a scientific standpoint,

the Kelvin scale is where it's at.

Yes.

The Kelvin scale.

It's the absolute temperature scale.

The chapter points out that zero Kelvin corresponds to negative 273 .15 degrees Celsius.

Exactly.

And that's absolute zero.

Right.

Like the coldest possible temperature.

Yeah.

Theoretically, all molecular motion stops at that point.

That's wild.

It is.

Yeah.

So how do you actually convert between Celsius and Kelvin?

It's super easy.

You just add 273 .15 to the Celsius temperature.

OK.

So the freezing point of water is 273 .15 Kelvin.

Exactly.

And the boiling point is 373 .15 Kelvin.

So a change of one degree Celsius is the same as a change of one Kelvin.

Exactly.

So it's really easy to work with.

It is.

Yeah.

Especially for scientific calculations.

The chapter points out that we should say Kelvins not degrees Kelvin.

Right.

It's a small thing, but it matters to scientists.

Yeah.

Oh, I get it.

It's like using the right terminology, you know, shows that you understand the concept.

So the Kelvin scale, it can be defined using the constant volume gas thermometer.

Yes, exactly.

It's all tied together.

OK.

Remember how the pressure of the gas is directly proportional to the absolute temperature?

Yeah.

Well, that relationship is the basis for defining the Kelvin scale in a really fundamental way.

Oh, OK.

So it's like we're using the properties of matter to define our measurement system.

Exactly.

It's pretty neat.

The chapter also mentions the triple point of water.

Oh, yeah.

Which is 0 .01 degrees Celsius or 273 .16 Kelvin.

Right.

Why is that specific point so important?

Well, it's the temperature and pressure where water can exist as ice liquid water and water vapor all at the same time.

Wow.

All three states at once.

Exactly.

It's a really precise and reproducible point.

OK.

So it's used to calibrate thermometers, especially for the Kelvin scale.

OK.

So it's like our anchor point.

Exactly.

OK.

So we've talked about temperature now.

Let's talk about how things change when their temperature changes.

Oh, yeah.

Thermal expansion.

Right.

The chapter says that usually stuff expands when it's heated and contracts when it's cooled.

Right.

Because at a molecular level, heat is really just the kinetic energy of those molecules.

Oh, OK.

So as the temperature increases,

the molecules are jiggling around more and more.

And they're bumping into each other.

Exactly.

And that makes them spread out a bit.

OK.

And that's what causes the material to expand.

So the chapter first talks about linear expansion, which is like how much the length of an object changes.

Right.

When the temperature changes.

And they use the formula delta L equals alpha L not delta T.

OK.

So delta L is the change in length.

Yes.

And alpha is the coefficient of linear expansion.

Exactly.

What is that exactly?

So it's basically a number that tells you how much a material will expand for every degree Celsius or Kelvin that the temperature changes.

Different materials have different coefficients of linear expansion.

Oh, OK.

So like metals, they generally expand more than something like glass.

OK.

So that's why bridges need expansion joints.

Exactly.

So they don't buckle when it gets hot.

Exactly.

You got it.

OK.

Then the chapter talks about volume expansion.

Right.

So that's how much the volume of something changes when the temperature changes.

OK.

And the formula is delta V equals beta V not delta T.

That's it.

So delta V is the change in volume.

Yep.

And beta is the coefficient of volume expansion.

Right.

And for isotropic materials.

What are isotropic materials?

Oh, it just means that the material has the same properties in all directions.

OK.

Like most metals.

Got it.

So for those materials, beta is approximately three times alpha.

OK.

That makes sense because volume is three dimensional.

So each dimension is expanding linearly.

Yeah.

Like think of a cube expanding.

Yeah.

OK.

Its length, width, and height all increase.

So the chapter mentions the molecular basis of thermal expansion.

Oh, yeah.

And it talks about these asymmetrical interatomic forces.

Yeah.

It's getting into like the nitty gritty of why things expand.

OK.

So what's going on at the atomic level?

So you know how we often picture atoms as being connected by springs?

Yeah.

Like a simple model.

Right.

Well, in reality, the forces between atoms are not perfectly symmetrical.

OK.

So when the temperature increases and those atoms are vibrating more, the average distance between them actually increases.

OK.

Because the repulsive forces at short distances are stronger than the attractive forces at larger distances.

Oh, so it's like they're being pushed apart more than they're being pulled together.

Exactly.

And that's what causes the overall expansion.

That's it.

What happens if you heat something up but prevent it from expanding?

Oh, that's when you get thermal stress.

OK.

So the chapter talks about that.

Yeah.

It's a big deal in engineering.

Yeah.

Because if a material can't expand or contract freely when the temperature changes, it's going to experience internal stresses.

Right.

And those stresses can be huge.

Wow.

It can cause all sorts of problems like bending, cracking, or even failure.

Yeah, like railway tracks buckling in the heat.

Exactly.

So it's really important to design structures that can handle those temperature changes.

Absolutely.

OK.

So we've explored temperature now.

Let's talk about heat itself.

Right.

The chapter defines heat as energy transfer.

Yeah.

And it's important to distinguish that from internal energy.

OK.

So what's the difference?

So internal energy is the total energy of all the molecules in a system.

OK.

But heat is specifically the energy that flows between objects or systems because of a temperature difference.

OK.

So it's energy in motion.

Exactly.

It's energy in transit.

So an object doesn't contain heat.

It contains internal energy.

Right.

And heat is how some of that internal energy is transferred from a hotter object to a colder object.

Exactly.

OK.

That makes sense.

Good.

So the chapter lists some units for measuring heat.

Oh, yeah.

There are a few.

Like the calorie, the kilocalorie,

the British thermal unit or BTU, and then the joule, which is the SI unit.

That's the one that scientists usually use.

OK.

But it's good to be familiar with all of them because you'll see them used in different contexts.

So one calorie is equal to 4 .186 joules.

That's the conversion factor.

Right.

Good to remember.

How do we quantify the amount of heat needed to change the temperature of a substance?

Well, that's where specific heat capacity comes in.

OK.

It's represented by the letter C.

OK.

And it tells you how much heat energy you need to raise the temperature of one kilogram of a substance by one degree Celsius.

OK.

So different substances have different specific heat capacities.

Exactly.

So what does that mean practically?

Well, it means that some substances are easier to heat up or cool down than others.

OK.

So for example, water has a really high specific heat capacity.

Which means it takes a lot of energy to change its temperature.

Oh.

That's why it's so good at regulating climates.

OK.

On the other hand, metals have a low specific heat capacity.

So they heat up and cool down quickly.

Exactly.

OK.

That makes sense.

And there's a formula that relates heat transfer, mass specific heat capacity, and temperature change.

Right.

Q equals MC delta T.

That's the one.

So Q is the amount of heat energy transferred.

M is the mass.

C is the specific heat capacity.

Exactly.

And delta T is the change in temperature.

You got it.

That's a really important equation.

It is.

Yeah.

It lets you calculate how much heat is involved in all sorts of processes.

OK.

And then there's also molar heat capacity.

OK.

Which is basically the same thing.

But instead of using mass, you use the number of moles.

OK.

So it's the heat capacity per mole.

Right.

And the formula is Q equals MC delta T.

Yep.

Where N is the number of moles.

Exactly.

So the chapter also talks about specific heat at constant pressure and specific heat at constant volume.

Oh, yeah.

That's an important distinction for gases.

OK.

So why is it different for gases?

Well, it's because when you heat up a gas at constant pressure,

it can expand.

Right.

And that expansion takes energy.

So some of the heat energy you put in goes into doing work to push against the surroundings.

OK.

So it's not all going into raising the temperature.

Exactly.

But if you heat up a gas at constant volume,

then all the heat energy goes into raising the temperature.

OK.

So that's why there are two different specific heat capacities for gases.

Exactly.

But for solids and liquids, the difference is pretty small.

Yeah, because they don't expand as much.

OK.

And then there's this interesting rule called the Rule of DeLong and Petit.

Oh, yeah.

The chapter mentions that.

It's an empirical observation from like the 1800s.

OK.

And it says that the molar heat capacity for most elemental solids at high temperatures is roughly the same.

Oh, wow.

Yeah.

About 25 joules per mole per Kelvin.

So it's like a universal constant for solids.

Well, kind of.

It's not perfectly accurate, but it's a good approximation.

So what does it tell us?

Well, it was one of the first clues that the energy of atoms in a solid is quantized.

What does that mean?

It means that the energy can only exist in discrete values.

OK.

Like it can't be any value.

It has to be one of these specific values.

OK.

And that was a really big deal because it led to all sorts of breakthroughs in quantum physics.

Oh.

Yeah.

It's amazing how this simple observation about heat capacity led to such profound discoveries.

OK.

So moving on, the chapter talks about calorimetry and phase changes.

All right.

So calorimetry is basically the science of measuring heat flow.

Exactly.

And a phase is a distinct state of matter.

Right.

Like solid liquid or gas.

Exactly.

And phase changes are the transitions between those states.

Right.

Like melting, freezing, boiling, condensation, sublimation.

Yep.

So these transitions happen at specific temperatures.

For a given pressure.

Right.

And what's interesting is that during a phase change, the temperature stays constant.

OK.

So even though heat is being added or removed, the temperature doesn't change.

Exactly.

So where's that energy going?

It's going into breaking or forming the bonds between the molecules.

OK.

So during melting, for example,

the heat energy is used to break the bonds that hold the molecules in a rigid structure.

OK.

So that's why the temperature doesn't go up until all the solid has melted.

Exactly.

The chapter talks about the heat of fusion.

Oh, yeah.

So that's the amount of heat energy needed to melt one kilogram of a substance at its melting point.

OK.

And the formula is Q equals MLF.

So LF is the heat of fusion, and there's also the heat of vaporization.

Yeah.

That's the amount of heat energy needed to vaporize one kilogram of a substance at its boiling point.

OK.

And the formula is Q equals MLV.

Where LV is the heat of vaporization.

Exactly.

And the chapter also mentions sublimation.

Right.

That's when a solid goes directly to a gas.

Like dry ice just disappears into the air.

OK.

So that's sublimation.

Yep.

It also has its own heat of sublimation.

Yeah.

OK.

So all these phase changes involve heat transfer, but no temperature change.

Exactly.

And then the chapter talks about calorimetry.

Yeah.

Which is basically the measurement of heat transfer.

Right.

And it mentions this important principle for isolated systems.

Oh, yeah.

The conservation of energy.

So the total heat exchanged is zero.

Right.

And if one part of the system loses heat, another part has to gain that same amount of heat.

OK.

That makes sense.

Good.

So finally, the chapter ends by talking about the three ways that heat can move.

Conduction, convection, and radiation.

Right.

So let's start with conduction.

Right.

So conduction is the transfer of heat through a material by direct contact.

OK.

So like when you touch a hot stove,

the heat flows from the stove to your hand by conduction.

OK.

And it happens because the molecules in the hotter object are vibrating faster than the molecules in the colder object.

Right.

And when those molecules collide, they transfer some of that kinetic energy.

So it's like a chain reaction.

Exactly.

The heat energy just keeps getting passed along from molecule to molecule.

OK.

So the chapter introduces thermal conductivity.

Right.

Which is a measure of how well a material conducts heat.

Yeah.

Some materials are better conductors than others.

Right.

Like metals are really good conductors.

Right.

While things like wood or plastics are good insulators.

OK.

So insulators don't conduct heat very well.

Exactly.

OK.

And there's an equation that describes the rate of heat transfer by conduction.

Right.

H equals Ka delta T over L.

That's it.

So H is the rate of heat transfer, K is the thermal conductivity, A is the cross -sectional

area, delta T is the temperature difference, and L is the thickness of the material.

Exactly.

OK.

So the rate of heat transfer depends on all those factors.

It does, yeah.

OK.

So that's conduction.

Right.

Now let's talk about convection.

Right.

So convection is the transfer of heat through the movement of fluids.

So liquids and gases.

Exactly.

OK.

So when a fluid is heated, it becomes less dense and it rises.

Right.

And then cooler, denser fluid sinks to take its place.

OK.

So it creates a circular flow.

Exactly.

And that flow carries heat energy with it.

OK.

So there are two types of convection, forced convection and natural convection.

OK.

What's the difference?

So forced convection is when you use something like a fan or a pump to move the fluid.

Oh.

In a convection oven.

Right.

And natural convection is when the fluid moves on its own because of density differences.

OK.

Like when hot air rises from a radiator.

OK.

That makes sense.

Good.

And then the last way that heat can move is radiation.

Right.

Which is through electromagnetic waves.

Yeah.

So that's how we get heat from the sun.

Exactly.

And the chapter says that all objects emit radiation.

Yeah, they do.

OK.

And the amount and type of radiation depends on the object's temperature.

OK.

So there's this law called the Stefan -Boltzmann law.

Right.

Which describes the power radiated by a perfect black body.

OK.

So what's a perfect black body?

It's an idealized object that absorbs all radiation that hits it.

And it emits radiation perfectly according to its temperature.

OK.

So real objects aren't perfect black bodies.

Right.

So how do we account for that?

Well, we use something called emissivity.

OK.

Which is a number between zero and one.

OK.

And it tells you how well an object emits radiation compared to a perfect black body.

OK.

So a perfect black body has an emissivity of one.

Exactly.

And a perfect reflector has an emissivity of zero.

Right.

So the power radiated by a real object is equal to its emissivity times the power radiated by a perfect black body at the same temperature.

OK.

So that's how we account for the fact that real objects aren't perfect emitters.

Right.

And then the chapter says that the net radiative heat transfer between an object and its surroundings depends on the difference in their temperatures.

Yeah.

So a hotter object will radiate more energy than it absorbs.

Right.

And a cooler object will absorb more energy than it radiates.

Exactly.

OK.

So that's how heat moves by radiation.

Yep.

Well, I think we've covered pretty much everything in this chapter.

Yeah.

We've gone through all the main points.

So for listeners out there.

Yes.

Hopefully this deep dive has given you a really solid understanding of temperature and heat.

Yeah.

We talked about the difference between the two.

Right.

How we measure temperature, the different temperature scales.

Yes.

How materials respond to temperature changes.

Right.

The concept of specific heat phase changes.

Yep.

Calorimetry.

Yes.

And the three ways that heat can move.

Conduction, convection, and radiation.

It's really amazing how all these concepts are connected.

Yeah.

It's a beautiful subject.

So as you go about your day.

Yes.

Think about how these principles are at work all around you.

Exactly.

From your coffee cup to the weather outside.

All thermodynamics.

Yeah.

And I hope this deep dive has given you a new appreciation for the world around us.

You too.

So thanks for joining us and we'll see you next time for another deep dive.

Bye.