B.1 Thermal Energy Transfers

Size of atoms

10^-10m in diameter

Atoms as a "concept"

We can think of them as very small perfectly elastic balls. This means that when they collide, both momentum and kinetic energy are conserved.

How many types of atoms are there?

118

Element

a material made of just one type of atom is called an element.

Compounds

Materials made from molecules that contain more than one type of atom.

Solid

Fixed shape and volume so the molecules must have a fixed position. Molecules of a solid are not free to move about but they can vibrate.

Intermolecular force

1. If we try to pull the molecules apart, there will be a force pulling them back together.

2. This force is due to a property of the molecules called charge.

3. Hold the particles together and stops the particles getting too close.

4. Responsible for the tension in a string (as the molecules are pulled apart they pull back) and the normal reaction when the surfaces are pushed together the molecules push back).

Water molecules

The molecules of a liquid are often drawn further apart than molecules of a solid but this is not always the case; water is a common but atypical example of the opposite. When ice turns to water, it contracts, which is why water is more dense than ice and ice floats on water.

Liquid

does not have a fixed shape but does have a fixed volume so the molecules are able to move about but still have an intermolecular force between then.

Forces in a liquid

1. The force is quite large when you try to push the molecules together (a liquid is very difficult to compress) but not so strong when pulling molecules apart (if you throw a bucket of water in the air it does not stay together).

2. When a liquid is put into a container, it presses against the sides of the container. This is because of the intermolecular forces between the liquid and the container. At the bottom of the container, the molecules are forced together by the weight of liquid above. This results in a bigger force per unit area on the sides of the container. The pressure under a solid block also depends on the height of the block but this pressure only acts downward on the ground not outward or upward as it does in a fluid.

Pressure

force per unit area

Effect of depth on pressure

Pressure increases with depth. The increase in pressure with depth is also the reason why submerged objects experience a buoyant force.

Example: If you consider the submerged cube, the bottom surface is deeper than the top so experiences a greater force, resulting in a resultant upward force. This is only the case if the water is in a gravitational field, e.g. on the Earth, as it relies on the weight of the water pushing down on the water below.

Gas

A gas does not have fixed shape or volume; it simply fills whatever container it is put into.

Gas forces

The molecules of a gas are completely free to move about without any forces between the molecules except when they are colliding.

Gas pressure

Since the molecules of a gas are moving, they collide with the wall of the container. The change in momentum experienced by the gas molecules means that they must be subjected to an unbalanced force, resulting in an equal and opposite force on the container. This results in gas pressure.

If the gas is on the Earth, then the effect of gravity will cause the gas nearest the ground to be compressed by the gas above. This increases the density of the gas so there are more collisions between the gas molecules and the container, resulting in a higher pressure. The difference between the pressure at the top of an object and the pressure at the bottom results in a buoyant force

Air resistance

A car moving through air will collide with the air molecules. As the car hits the air molecules, it increases their momentum so they must experience a force. The car experiences an equal and opposite force which we call air resistance or drag.

Brownian motion

Chaotic movement of colloidal particles. The reason we do not see this random motion in larger

objects is because they are being bombarded from all sides so the effect cancels out.

Density

ratio of the mass of a body to its volume

Density formula

p=m/V

p is density in kg m^-3

m is mass in kg

V is volume in m^3.

Density of gas vs solid vs liquid

The density of a gas is lower than the density of a solid. But not all liquids are less dense than solid bodies.

Macroscopic level density

On a macroscopic level, densities cause bodies to float or sink.

Microscopic level density

On a microscopic level, density is related to the spacing of particles.

Why is density a material property

Because density is unrelated to the dimensions of a body, it is a material property. A given material will always have the same density, irrespective of whether it is a gigantic sphere or stretched out into a sheet.

Informally, some refer to density as 'the amount of stuff in a thing'.

Internal energy

All the energy contained in an object, including both kinetic energy and potential energy. Internal energy is the sum of the energies of the molecules of a body.

Internal energy in solids and liquids

In solids and liquids, there are forces between the molecules so to move them around requires work to be done (like stretching a spring). The internal energy of solids and liquids is therefore made up of the total kinetic + potential energy.

Internal energy in gases

There is no force between molecules of a gas so changing their position does not require work to be done. The internal energy of a gas is therefore only the total kinetic energy.

What happens when there's an increase in internal energy?

increase in temperature

Example: If we rub our hands together, we are doing work since there is movement in the direction of the applied force. If work is done, then energy must be transferred but we are not increasing the kinetic energy or potential energy of our hands; we are increasing their internal energy. As we do this, we notice that our hands get hot.

What do you need to define a scale?

two fixed points

Celcius scale

T= LT-Lo/L100-L0 x 100

Lowest temperature

The lowest theoretical temperature is

273.15°C, but for conversion purposes, we usually find it more convenient to use

-273 °C.

SI unit of temperature

Kelvin (K)

Why does liquid expand when it gets hotter?

The reason that a liquid expands when it gets hot is because its molecules vibrate more and move apart. Higher temperature implies faster molecules so the temperature is directly related to the average kinetic energy of the molecules.

Kinetic energy of the particles when ice freezes

since the kinetic energy of the particles is not zero when ice freezes, the average kinetic energy cannot be directly proportional to the temperature in °C.

What is temperature at which the kinetic energy of molecules becomes zero?

-273°C

What is an alternative way to define a temperature scale

to use the pressure of a constant volume of gas.

What happens when temperature increases?

As temperature increases, the kinetic energy of the molecules increases so they move faster. The faster moving molecules hit the walls of the container harder and more often, resulting in an increased pressure.

Absolute zero

As the temperature gets lower and lower, the molecules slow down until at some point they stop moving completely. This is the lowest temperature possible or absolute zero.

What happens when you use the absolute zero in the temperature scale?

If we use this as the zero in our temperature scale, then the average kinetic energy is directly proportional to temperature. In defining this scale, we then only need one fixed point in addition to absolute zero. This point could be the freezing point of water but the triple point is more precisely defined. This is the temperature at which water can be solid, liquid, and gas in equilibrium, which in degrees Celsius is 0.01°C. If we make this 273.16 in our new scale, then a change of 1 unit will be the same as 1°C. This is called the Kelvin scale.

temperature and molecular speed

We have a temperature scale that begins at absolute zero, we can say that, for an ideal gas, the average kinetic energy of the molecules is directly proportional to its temperature in kelvin.

Equation: Ēk=3/2kbT

Where kb=Boltzmann constant, 1.38 × 10^-23 m^2 kg s^-2 K^-1.

Graphing

The average kinetic energy of the molecules. The different molecules of a gas travel at different random velocities, some faster and some slower. The range of velocities can be represented by the velocity distribution curve. Because the curve is not symmetrical, the mean value is to the right of

center.

Thermal energy

The internal energy of a body can also be increased by putting it in contact with a hotter body. Energy transferred in this way is called thermal energy (or sometimes heat).

the energy contained within a system that is responsible for its temperature

Thermal equilibrium

When bodies are in thermal contact, heat will always flow from a high temperature to a low temperature until the bodies are at the same temperature. Then we say they are in thermal equilibrium.

How can the kinetic energy of the molecules be increased?

the kinetic energy of the molecules can be increased by doing work, for example, against friction.

Temperature

average kinetic energy of molecules

How can thermal energy be transferred?

Three ways that thermal energy can be transferred from one body to another are conduction, convection, and radiation.

Conduction

Conduction takes place when bodies are in contact with each other.

The vibrating molecules of one body collide with the molecules of the other. The fast-moving hot molecules lose energy and the slow-moving cold ones gain it.

Good conductors of thermal energy

Metals - not only are their atoms well connected but metals contain some free particles (electrons) that are able to move freely about, helping to pass on the energy.

Bad conductors of thermal energy

Gases - because their molecules are far apart. However, heat is often transferred to a gas by conduction. This is how heat would pass from a room heater into the air of a room, for example. For a conducting material, the rate of flow of thermal energy is proportional to the temperature gradient.

Formula: ΔQ/Δt=kA x ΔT/Δx

where k is material conductivity (WK^-1 m^-1) and A is cross-sectional area (m^2).

Convection

Convection is the way that heat is transferred through fluids by collections of fast-moving molecules moving from one place to another.

What happens when heat is given to air?

1. the molecules move around faster.

2. causes an increase in pressure in the hot air, which enables it to expand, pushing aside the colder surrounding air.

3. The hot air has now displaced more than its own weight of surrounding air so experiences an unbalanced upward force, resulting in motion in that direction.

Convection current

As the hot air rises, it will cool and then come back down (this is also the way that a hot air balloon works). The circular motion of air is called a convection current and is the way that heat is transferred around a room.

Radiation

Radiation is the mechanism by which thermal energy can pass directly between two bodies without increasing the temperature of the material in-between.

Infrared radiation

there does not even have to be a material between since radiation can pass through a vacuum. The name of this radiation is infrared and it is a part of the electromagnetic spectrum.

What does the amount of radiation emitted and absorbed by a body depend on?

The amount of radiation emitted and absorbed by a body depends on its color. Dark, dull bodies both emit and absorb radiation better than light shiny ones. When you stand in front of a fire and feel the heat, you are feeling radiated heat.

Black-body radiation

A black body is a perfect radiator of thermal energy. The power radiated per unit area of the body is related to the temperature of the body.

Emissivity

a measure of how effectively a body radiates heat.

It is measured from 0 to 1, with 1 being a perfect radiator and 0 being the opposite; a perfect

reflector.

Viewing the visible spectrum of a filament lamp

If we view the visible spectrum of a filament lamp, we see that it is made up of a continuous spread of visible wavelengths

Measuring the intensity of different colors

By using sensors, we can measure the intensity of the different colors and also electromagnetic radiation outside the visible range to produce the complete black-body spectrum. The peak in the spectrum is actually in the infrared region, which is why a light bulb gives out more heat than light.

Bodies with the same temperature but lower emissivity...

Bodies with the same temperature but lower emissivity will emit radiation with the same peak wavelength but less power.

Wien's displacement law

states that peak wavelength and absolute temperature are inversely proportional. The relationship between the peak wavelength in meters and the temperature in kelvin is given by Wien's displacement law.

What type of radiation does a body at room temperature emit?

A body at room temperature emits infrared radiation but not visible light.

(However, the spectrum of infrared radiation will be a similar shape to that of the tungsten bulb, except that the peak will be moved to the right and, as the total power emitted is less, the area under the graph will be smaller).

Wien's Displacement Law equation

λpeak = 0.0029/T

where 0.0029 is a constant with the unit m K (not millikelvin)

Inverse square law

The intensity of the radiation is inversely proportional to the square of the distance

Radiation from a spherical body

The radiation from a spherical body spreads out radially in all directions so the power per unit area decreases as distance from the source increases. At distance r, the radiation from a source emitting a total power P has spread out to cover a sphere of area 4πr^2 so the power per unit area, I, is given by the formula:

I=P/4πr^2

In the case of stars, we refer to brightness, b, in place of intensity.

Preventing heat loss

Insulating materials are often made out of fibrous matter that traps pockets of air. The air is a poor conductor and when it is trapped it cannot convect. Covering something with silver-colored paper will reduce radiation.

Thermal capacity (C)

The thermal capacity, C, of a body is the amount of heat needed to raise its temperature by one unit.

Typical units: J°C^-1 or J K^-1.

What happens when thermal capacity is added to a body?

If thermal energy is added to a body, its temperature rises, but the actual increase in temperature depends on the body.

Thermal capacity (C) equation

If the temperature of a body increases by an amount ΔT when quantity of heat Q is added, then the thermal capacity is given by the equation:

C=Q/ΔT

What does thermal capacity depends on?

The thermal capacity depends on the size of the object and what it is made of.

What does specific heat capacity depend on?

The specific heat capacity depends only on the material.

Raising the temperature of 1 kg of water requires more heat than raising the temperature of 1 kg of steel by the same amount, so the specific heat capacity of water is higher than that of steel.

Power

energy per unit time

Typical units: J°C^-1 or J K^-1.

The specific heat capacity of a material is the amount of heat required to raise the temperature of a unit mass of the material by one unit.

Typical units: J°C^-1 or J K^-1.

Specific heat capacity equation

If a quantity of heat Q is required to raise the temperature of a mass m of material by

AT, then the specific heat capacity c of that material is given by the following equation:

Q=mc∆T

Water boiling

When water boils, this is called a change of state (or change of phase). As this happens, the temperature of the water does not change - it stays at 100°C. In fact, we find that while the state of a material is changing, the temperature stays the same provided that no particles are added or lost. This can be explained in terms of the particle model.

Solid to liquid

Solid molecules have kinetic energy since they are vibrating and when energy is added liquid molecules are then free to move about but have the same kinetic energy as before.

When matter changes state, the energy is needed...

When matter changes state, the energy is needed to enable the molecules to move more freely.

Boiling

Boiling takes place throughout the liquid and always at the same temperature (for a given pressure).

Evaporation

Evaporation takes place only at the free surface of the liquid and can happen at all temperatures.

When a liquid evaporates, the fastest-moving particles leave the free surface. This means that the average kinetic energy of the remaining particles is lower, resulting in a drop in temperature for the liquid that remains.

How can the rate of evaporation be increased?

1. INCREASING THE SURFACE AREA. This increases the number of molecules near the free surface, giving more of them a chance to escape

2. BLOWING ACROSS THE FREE SURFACE. After molecules have left the free surface, they form a small 'vapor cloud' above the liquid. If this is blown away, it allows further molecules to leave the free surface more easily

3. RAISING THE TEMPERATURE. This increases the kinetic energy of the liquid molecules, enabling more to escape.

People sweating?

People sweat to increase the rate at which they lose thermal energy. When you get hot, sweat comes out of your skin onto the surface of your body. When the sweat evaporates, it cools you down. In a sauna, there is so much water vapor in the air that the sweat does not evaporate.

Specific latent heat (L)

The specific latent heat of a material is the amount of heat required to change the state of a unit mass of the material without change of temperature.

Typical unit: Jkg^-1

When is specific latent heat used?

Latent means hidden. This name is used because when matter changes state, the heat added does not cause the temperature to rise, but seems to dissapear.

Specific latent heat equation

If it takes an amount of energy Q to change the state of a mass m of a substance, then the specific latent heat of that substance is given by the equation:

L=Q/m

Key Points

Solid → liquid (or vice versa)

Specific latent heat of fusion

Liquid → gas (or vice versa)

Specific latent heat of vaporization

This equation (L= Q/m) can also be used to calculate the heat lost when a substance changes from gas to liquid, or liquid to solid.

What type of graph represents an increase of temperature?

The increase of the temperature of a body can be represented by a temperature-time graph.

Key point 2

The amount of thermal energy loss is proportional to the difference between the temperature of the kettle and its surroundings. For this reason, a graph of temperature against time is actually a curve. The fact that the gradient decreases tells us that the amount of heat given to the water gets less with time. This is because as it gets hotter, more and more of the heat is lost to the room.

How can thermal quantities be measured?

The method of mixtures can be used to measure the specific heat capacity and specific latent heat of substances.

Why does sugar take a long time to cool down?

This is because as it changes from liquid to solid it is giving out heat but does not change temperature.

Thermal energy loss

In both of these experiments, some of the heat coming from the hot source can be lost to the surroundings. To reduce heat loss, the temperatures can be adjusted, so you could start the experiment below room temperature and end the same amount above (e.g. if room temperature is 20°C, then you can start at 10°C and end at 30°C).