Thermal Energy Transfers (DP IB Physics)

The particles in a solid have a fixed structure in a lattice formation. This is the first diagram.

In a gas, the particles are spaced far apart and in a random arrangement. This is the third diagram.

The object on the right is more dense because it has more mass per unit volume.

Density is the mass per unit volume of an object.

False.

A bucket filled with feathers will have a lower mass than the same bucket filled with sand because feathers have a lower density than sand.

The equation for density is

Where:

• = density, measured in kilograms per metre cubed (kg m^-3)

• = mass, measured in kilograms (kg)

• = volume, measured in metres cubed (m³)

The units used for density if the mass is measured in grams and volume in cubic centimetres are grams per cubic centimetre (g cm^–³).

The units used for density if the mass is measured in kilograms and volume in cubic meters are kilograms per cubic metre (kg m^–³).

Gases are less dense than liquids because they tend to have more particles (and therefore more mass) per unit volume.

125 m converted to cm is 12,500 cm

Cubic centimetres are converted to cubic metres by:

• dividing by 100³

• multiplying by 1 × 10⁻⁶ m³

Absolute zero is the lowest possible temperature, equal to 0 K or −273 °C.

Absolute zero is the temperature at which the molecules in a substance have zero kinetic energy.

False.

It is not possible to have a temperature lower than 0 K.

To convert degrees Celsius to kelvin, use the formula

Where:

• = temperature, measured in kelvin (K)

• = temperature, measured in degrees Celsius (°C)

To convert kelvin to degrees Celsius, use the formula

Where:

• = temperature, measured in degrees Celsius (°C)

• = temperature, measured in kelvin (K)

A temperature of 300 K corresponds to 27 °C.

True.

A change in temperature of 1 K is equal to a change in temperature of 1 °C.

The equation for the average kinetic energy of the particles in a gas is

Where:

• = kinetic energy, measured in joules (J)

• = Boltzmann constant, measured in joules per kelvin (J K^-1)

• = absolute temperature, measured in kelvin (K)

True.

Absolute temperature is directly proportional to the average kinetic energy of the molecules.

Boltzmann constant, , is 1.38×10⁻²³JK⁻¹

Absolute temperature is measured on the Kelvin scale, starting from absolute zero, where molecules have zero kinetic energy.

The absolute temperature of a body is directly proportional to the average kinetic energy of the molecules within the body.

The formula that connects the average speed of particles and temperature of a gas is

Where:

• = average speed of gas particles, measured in metres per second (m s^-1)

• = Boltzmann constant, measured in joules per kelvin (J K^-1)

• = mass of particle, measured in kilograms (kg)

• = absolute temperature, measured in kelvin (K)

Internal energy is defined as the sum of the total kinetic energy and the total intermolecular potential energy of the particles within a substance.

The internal energy of a substance increases when it gains thermal energy.

False.

Temperature is a measure of the average kinetic energy of the molecules.

The relationship between the thermal and kinetic energy of molecules is:

• an increase in thermal energy leads to an increase in the average kinetic energy of molecules

• this causes them to move at higher speeds

Potential energy increases during the thermal expansion of a substance as the particles get further away from each other.

There is no effect of a change in the potential energy of the molecules on the temperature.

The temperature of a substance does not change during a change of state.

The two energy types that make up internal energy are:

• kinetic energy

• potential energy

The type of energy that changes in a substance due to a change in temperature is kinetic energy.

The gas on the right is being heated because it has higher kinetic energy.

The resultant temperature of both regions of the substance in the diagram is 50 C.

Thermal equilibrium is when two substances in contact with each other no longer exchange heat energy as they both reach an equal temperature.

False.

Thermal energy is always transferred from a hotter region to a cooler region.

The temperatures of two regions in thermal contact will change as follows:

• the hotter region will cool down

• the cooler region will heat up

• until they reach the same temperature

Thermal equilibrium means there is no longer thermal energy transfer between the two regions.

For two regions to reach thermal equilibrium they need to be in thermal contact.

The direction of thermal energy flow when ice is placed in room temperature water is from the water to the ice.

The final temperature in the thermal equilibrium between water and ice depends on the initial temperature difference between the water and the ice.

When two regions are at different temperatures, energy flows from the hotter to the cooler region.

From the bottom of the diagram to the top the internal energy increases because the particles in the gas have more kinetic energy than in a solid.

A change of state is when matter changes from one phase (solid, liquid, or gas) into another.

Melting is when a substance changes from a solid to a liquid as it absorbs thermal energy.

Freezing is when a substance changes from a liquid to a solid as it releases thermal energy.

Vaporisation is when a substance changes from a liquid to a gas as it absorbs thermal energy.

Condensation is when a substance changes from a gas to a liquid as it releases thermal energy.

Thermal energy affects the potential energy, so the spacing between the molecules changes during a phase change.

At the boiling point of a substance, vaporisation and condensation occur.

The boiling point of water is 100 °C and the freezing point is 0 °C.

When thermal energy is released from water vapour at 100 °C, it condenses back into liquid water.

Specific heat capacity is the amount of energy required to change the temperature of 1 kg of a substance by 1 K (or 1°C).

The equation for thermal energy transferred, , to a substance is .

Where:

• = mass of substance, measured in kilograms (kg)

• = specific heat capacity of substance, measured in joules per kilogram per kelvin (J kg^-1 K^-1)

• = change in temperature, measured in kelvin (K) or degrees Celsius ()

False.

The higher the specific heat capacity of a substance, the longer it takes to warm up or cool down.

represents the specific heat capacity of a substance measured in J kg^–1 K^–1.

The greater the mass of an object, the more thermal energy needed to change its temperature.

The phase changes that require thermal energy to be absorbed by a substance are melting and vaporisation.

is the change in temperature in kelvin or degrees Celsius (K or °C).

The specific heat capacity indicates how much energy is required to change the temperature of a substance.

The temperature of the water as it is melted is 0 C.

Specific latent heat is defined as the amount of energy required to change the state of 1 kg of a substance without changing its temperature.

The equation for thermal energy transferred in terms of specific latent heat is

Where:

• = thermal energy transferred, measured in joules (J)

• = mass of substance, measured in kilograms (kg)

• = specific latent heat, measured in joules per kilogram (J kg^–1)

represents the specific latent heat of a substance in J kg^–1.

The specific latent heat of fusion is defined as the energy required to change 1 kg of a substance from solid to liquid (or vice versa) at constant temperature.

The specific latent heat of vaporisation describes the energy required to change 1 kg of a substance from liquid to gas (or vice versa) at constant temperature.

The specific latent heat of vaporisation is always higher than the specific latent heat of fusion for a given substance.

The intermolecular forces of a substance during vaporisation need to be completely overcome.

The specific latent heat of fusion, , is the energy absorbed when 1 kg of solid melts to become liquid at a constant temperature or the energy released when 1 kg of liquid freezes to become solid at a constant temperature.

The temperature gradient equation in terms of heat flow is

Where:

• = flow of thermal energy per second, measured in watts (W)

• = thermal conductivity of the material, measured in watts per metre per kelvin (W m^–1 K^–1)

• = temperature difference, measured in kelvin (K) or degrees Celsius (C)

• = thickness of material, measured in metres (m)

True.

Metals are the best thermal conductors because they have a high number of free electrons.

Thermal energy is transferred in conduction through atomic vibrations.

The main mechanism of thermal energy transfer in solids is conduction.

Copper has the highest thermal conductivity among air, rubber, and copper.

Free electron collision is a mechanism in conduction where free electrons in metals collide with atoms, transferring energy.

Delocalised electrons increase the rate of energy transfer in thermal conduction in metals, making metals good thermal conductors.

The air moves vertically upward above the fire as the hot gas expands and becomes less dense.

The cooler, denser air moves vertically downward away from the heat of the fire.

Convection is the main way that heat travels through liquids and gases.

Thermal convection is the transfer of thermal energy through the movement of a fluid due to variations in density.

A convection current is the motion that results when hot fluid rises and cooler fluid sinks, creating a circular flow.

False.

Convection cannot occur in solids because the particles are unable to travel relative to one another.

The density of a fluid decreases when it is heated because the fluid expands.

Thermal energy is transferred during convection by the movement of groups of atoms or molecules in a fluid as a result of variations in density.

Convection occurs in liquids and gases.

Examples of convection in nature are:

• atmospheric convection (which leads to winds and sea breezes)

• thunderheads (clouds that appear before a storm)

• convection currents in the Earth's mantle (leading to continental drift)

• ocean currents

• solar convections (leading to sunspots and solar flares)

In a beaker of water with potassium permanganate, the heated water rises, carrying the dissolved purple crystal, while cooler water sinks, forming a convection current.

Convection currents in the Earth's mantle are caused by the movement of heated and cooled material, leading to continental drift.

Thermal radiation is heat transfer by means of electromagnetic radiation, usually in the infrared region.

False.

Thermal radiation does not require matter to propagate and can travel through a vacuum.

Black-body radiation is the thermal radiation emitted by all bodies, which can be in the form of infrared light, visible light, or other wavelengths depending on the temperature.

A perfect black body is an object that absorbs all of the radiation incident on it and does not reflect or transmit any.

The surface colour of an object affects thermal radiation because:

• dark, dull objects are better at emitting and absorbing radiation

• light, shiny objects are worse at emitting and absorbing radiation

The thermal radiation of an object increases as its temperature increases.

The electromagnetic waves that are most commonly emitted as thermal radiation are infrared.

The relationship between temperature and the peak wavelength of emitted radiation is they are inversely proportional.

A meteorite dissipates thermal energy on the Moon via conduction (to the Moon's surface) and radiation (infrared photons travelling through the vacuum of space).

The factors affecting the amount of thermal radiation emitted by an object are:

• surface colour

• texture

• surface area

Apparent brightness is the intensity of radiation received on Earth from a star.

Luminosity is the total power output of radiation emitted by a star.

Apparent brightness is measured in watts per metre squared (W m⁻²).

Luminosity is measured in units of watts (W).

False.

The luminosity is the total power output of the star, whereas the apparent brightness is what is measured by an observer on Earth.

The inverse square law of radiation is

Where:

• = apparent brightness of light observed on Earth, measured in watts per metre squared (W m^-2)

• = luminosity of light source, measured in watts (W)

• = distance between star and Earth, measured in metres (m)

The apparent brightness of a star decreases with the square of the distance to the observer.

The factors that determine the apparent brightness of a star are:

• the luminosity of the star

• the distance to the observer

The intensity of light is reduced to one-fourth when the distance to the observer is doubled.

The Stefan-Boltzmann Law states that the total energy emitted by a black body per unit area per second is proportional to the fourth power of the absolute temperature of the body.

The Stefan-Boltzmann Law calculates the total power radiated by a perfect black body based on its temperature and surface area.

The equation for the Stefan-Boltzmann law is

Where:

• = total power emitted across all wavelengths, measured in watts (W)

• = Stefan-Boltzmann constant

• = surface area of body, measured in metres squared (m²)

• = absolute temperature of a body, measured in kelvin (K)

The Stefan-Boltzmann constant, , is a physical constant equal to 5.67×10⁻⁸ Wm⁻²K⁻⁴.

The formula for the Stefan-Boltzmann law is

Where:

• = luminosity of the star, measured in watts (W)

• = radius of star, measured in metres (m)

• = Stefan-Boltzmann constant

• = absolute temperature of a body, measured in kelvin (K)

The relationship between the temperature and power emitted by a black body is that power is directly proportional to temperature to the power of four.

The surface area formula of a spherical object is

Where:

• = radius of the sphere, measured in metres (m)

True.

The Stefan-Boltzmann Law is often used to calculate the luminosity of celestial objects, such as stars.

The factors that determine the total power radiated by a black body are absolute temperature and surface area.

The equation is used to find the radius of a star if its luminosity and temperature are known is

Where:

• = radius of star, measured in metres (m)

• = luminosity of the star, measured in watts (W)

• = Stefan-Boltzmann constant

• = absolute temperature of a body, measured in kelvin (K)

Wien’s displacement law states that the black body radiation curve for different temperatures peaks at a wavelength that is inversely proportional to the temperature.

The quantity in Wien's displacement law is the wavelength at which radiation is emitted at the greatest intensity.

The equation for Wien’s displacement law is

Where:

• = surface temperature of an object, measured in kelvin (K)

True.

The peak wavelength of a black body decreases as temperature increases.

Wien’s displacement law indicates that the higher the temperature of an object, the shorter the wavelength at the peak intensity.

The radiation intensity increases for every wavelength as an object heats up.

The quantity in the equation for Wien’s displacement law is the surface temperature of an object in kelvin (K).

The relationship between wavelength and temperature in Wien’s displacement law is inverse proportionality.