Radiation Revision Notes

Thermal radiation is a type of electromagnetic radiation emitted by all objects due to their temperature. Unlike conduction and convection, which require particles or a medium, thermal radiation can travel through empty space (a vacuum). This is because it is a form of electromagnetic wave, specifically in the infrared region of the electromagnetic spectrum.

Infrared radiation has wavelengths longer than visible light, typically from about 700 nm to 1 mm. Thermal radiation emitted by objects at everyday temperatures is mostly infrared, which is why it is often called infrared radiation in this context.

• Thermal radiation is electromagnetic radiation emitted due to an object's temperature.
• It is primarily infrared radiation.
• It can travel through a vacuum without a medium.

All objects emit thermal radiation continuously, regardless of their temperature. Even objects at room temperature emit infrared radiation, although the intensity and wavelength distribution depend on the temperature.

The emission of thermal radiation is a fundamental property of matter and is related to the thermal motion of charged particles within the object. As these particles accelerate, they emit electromagnetic waves.

The intensity and spectrum of the emitted radiation change with temperature, described quantitatively by Planck's law (beyond the scope of this objective).

• Every object emits thermal radiation.
• Emission is due to thermal motion of charged particles.
• Emission intensity depends on temperature.

The amount of thermal radiation emitted by an object increases as its temperature increases. This is because higher temperatures correspond to more energetic particle motion, leading to greater electromagnetic emission.

The Stefan–Boltzmann law quantifies this relationship: the power radiated per unit area (P) of a perfect black body is proportional to the fourth power of its absolute temperature (T in kelvin):

\[ P = \sigma T^4 \] where \( \sigma = 5.67 \times 10^{-8} \, \mathrm{W m^{-2} K^{-4}} \) is the Stefan–Boltzmann constant. Although real objects are not perfect black bodies, this law provides a good approximation for thermal radiation emission trends.

• Thermal radiation intensity increases with temperature.
• Stefan–Boltzmann law: \( P = \sigma T^4 \).
• \( \sigma \) is the Stefan–Boltzmann constant.

Because all objects emit thermal radiation, this principle is used in technologies such as thermal imaging cameras, which detect infrared radiation to form images based on temperature differences.

The Sun emits thermal radiation across a broad spectrum, including visible light and infrared radiation, which warms the Earth.

Thermal radiation allows heat transfer through space, such as the warmth felt from sunlight, even though space is a vacuum.

• Thermal imaging detects emitted infrared radiation.
• Sun emits thermal radiation warming Earth.
• Thermal radiation enables heat transfer through vacuum.

To draw a diagram illustrating thermal radiation emission:

1. Sketch a solid object (e.g., a square or circle) labelled 'Object at temperature T'.

2. Draw wavy arrows emanating from the surface in all directions to represent emitted infrared radiation (thermal radiation). Use red or orange colour for clarity if possible, and label the arrows 'Thermal radiation (infrared)'.

• Object emits infrared radiation in all directions.
• Radiation represented by wavy arrows from surface.
• Label temperature and radiation type clearly.

Thermal radiation is the emission and transfer of thermal energy in the form of electromagnetic waves, primarily in the infrared region of the spectrum. Unlike conduction and convection, which require particles or fluids to transfer heat, thermal radiation can occur through empty space (a vacuum). This is because electromagnetic waves do not need a medium to propagate.

All objects emit thermal radiation if their temperature is above absolute zero. The amount and wavelength distribution of this radiation depend on the object's temperature and surface properties.

• Thermal radiation consists of electromagnetic waves.
• It is emitted by all objects with temperature above 0 K.
• It can travel through vacuum without a medium.
• The intensity and wavelength depend on temperature.

Heat can be transferred by three main methods: conduction, convection, and radiation. Conduction requires direct contact between particles in solids, while convection requires fluid movement. Thermal radiation differs because it does not require any particles or medium to transfer energy.

This property allows thermal radiation to transfer heat through the vacuum of space, which is impossible by conduction or convection.

• Conduction: heat transfer via particle collisions in solids; requires medium.
• Convection: heat transfer via fluid movement; requires fluid medium.
• Radiation: heat transfer via electromagnetic waves; no medium needed.

A key example of thermal radiation is the heat from the Sun reaching the Earth. Space between the Sun and Earth is a vacuum, so conduction and convection cannot occur. Instead, energy travels as electromagnetic waves (thermal radiation).

This radiation is absorbed by the Earth's surface, warming it and sustaining life.

Other examples include feeling warmth from a fire without touching it and heat emitted from a hot object glowing red or infrared radiation.

• Sun’s heat reaches Earth by thermal radiation through space.
• Feeling warmth from a fire at a distance is due to radiation.
• Hot objects emit infrared radiation detectable by thermal cameras.

Thermal radiation is electromagnetic radiation emitted due to the thermal motion of charged particles in matter. As these particles vibrate, they emit waves across a range of wavelengths.

The Stefan-Boltzmann law quantifies the power radiated per unit area of a perfect black body: P = σT⁴, where P is power per unit area (W/m²), σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴), and T is absolute temperature in kelvin.

Because electromagnetic waves do not require a medium, thermal radiation can propagate through vacuum at the speed of light (approximately 3.0 × 10⁸ m/s).

• Thermal radiation arises from vibrating charged particles.
• Stefan-Boltzmann law: P = σT⁴ for black bodies.
• Radiation travels at speed of light through vacuum.
• No medium is needed for propagation.

To draw a diagram illustrating thermal radiation through vacuum:

1. Draw a hot object (e.g., the Sun) on the left side of the page.

2. Draw wavy arrows (representing electromagnetic waves) emanating from the hot object and travelling rightwards through empty space (labelled 'vacuum'). Use several arrows to indicate radiation spreading outwards in all directions, but focus on the direction towards the Earth or another object on the right side of the page (e.g., Earth).

• Wavy arrows represent thermal radiation.
• Label space between objects as vacuum.
• Show no particles or medium in the space.
• Indicate direction of radiation from hot object to cooler object.

Infrared radiation is a form of electromagnetic radiation emitted by all objects due to their temperature. The rate at which a surface emits or absorbs infrared radiation depends on its physical properties, especially colour and texture.

Surface colour refers to how a surface appears to visible light, commonly black or white in this context. Surface texture refers to how smooth or rough (shiny or dull) the surface is.

These properties influence the surface's emissivity, absorptivity, and reflectivity for infrared radiation, which are key factors in thermal radiation processes.

• Infrared radiation is emitted by all objects above absolute zero temperature.
• Surface colour and texture affect emissivity, absorptivity, and reflectivity.
• Emissivity is a measure of how effectively a surface emits infrared radiation.

Black surfaces absorb and emit infrared radiation more effectively than white surfaces. This is because black surfaces have a higher emissivity and absorptivity, meaning they absorb a greater fraction of incident infrared radiation and emit more radiation at a given temperature.

White surfaces reflect more infrared radiation and thus absorb and emit less. This lower absorptivity and emissivity means white surfaces tend to stay cooler under infrared radiation exposure.

The physical reason is that black surfaces absorb a wider range of wavelengths, including infrared, while white surfaces reflect more wavelengths, reducing absorption and emission.

• Black surfaces have high emissivity and absorptivity.
• White surfaces have low emissivity and absorptivity.
• Black surfaces absorb more infrared radiation and emit more infrared radiation at the same temperature.

Dull surfaces are better absorbers and emitters of infrared radiation than shiny surfaces. This is because dull surfaces scatter incident radiation, increasing absorption, and have higher emissivity.

Shiny surfaces reflect a larger proportion of infrared radiation, reducing absorption and emission. Their low emissivity means they emit less infrared radiation at the same temperature.

Therefore, a dull surface tends to lose or gain heat more effectively through radiation compared to a shiny surface.

• Dull surfaces have higher emissivity and absorptivity than shiny surfaces.
• Shiny surfaces reflect more infrared radiation, reducing absorption and emission.
• Surface texture influences thermal radiation exchange significantly.

The combination of colour and texture determines the overall effectiveness of a surface in emitting and absorbing infrared radiation.

A dull black surface is the best emitter and absorber of infrared radiation because it has both high emissivity and absorptivity.

A shiny white surface is the poorest emitter and absorber, reflecting most infrared radiation and emitting little at a given temperature.

• Dull black surfaces: highest emissivity and absorptivity; best emitters and absorbers.
• Shiny white surfaces: lowest emissivity and absorptivity; poorest emitters and absorbers.
• Surface properties must be considered together to predict thermal behaviour.

Understanding how surface colour and texture affect infrared radiation is important in thermal management, such as in designing radiators, insulation, and thermal clothing.

For example, radiators are often painted black and have a dull finish to maximise infrared emission and heat loss.

In contrast, shiny metallic surfaces are used where heat loss by radiation needs to be minimised, such as in thermal insulation or reflective coatings.

• Black, dull surfaces are used to maximise heat emission (e.g., radiators).
• Shiny, white or metallic surfaces are used to minimise heat emission (e.g., thermal insulation).
• Surface properties influence energy balance and temperature regulation.

Temperature is a measure of the average kinetic energy of the particles in a substance. When energy is transferred to an object, its internal energy increases, often causing its temperature to rise. Conversely, when an object loses energy, its temperature tends to fall.

Thermal energy transfer occurs via conduction, convection, or radiation. The net energy transfer determines whether an object's temperature changes or remains constant.

• Temperature reflects average particle kinetic energy.
• Energy transfer changes internal energy and temperature.
• Three modes of thermal energy transfer: conduction, convection, radiation.

An object is in thermal equilibrium when its temperature remains constant over time. This occurs when the energy it gains per unit time equals the energy it loses per unit time.

Mathematically, if \( P_{in} \) is the power (rate of energy transfer) into the object and \( P_{out} \) is the power out, then for constant temperature:

\[ P_{in} = P_{out} \] This balance means no net change in internal energy, so temperature remains steady.

• Thermal equilibrium means constant temperature.
• Energy gained per second equals energy lost per second.
• No net change in internal energy at equilibrium.

Objects gain energy from their surroundings by absorbing radiation, conduction from warmer materials, or convection from warmer fluids.

They lose energy by emitting thermal radiation, conduction to cooler materials, or convection to cooler fluids.

The rate of energy loss or gain depends on factors such as surface temperature, surface area, emissivity, and temperature difference with surroundings.

• Energy gain: absorption, conduction, convection from warmer surroundings.
• Energy loss: emission, conduction, convection to cooler surroundings.
• Rates depend on temperature difference, surface properties, and area.

A cup of hot tea cools down because it loses energy faster than it gains energy from the room. When the tea reaches room temperature, energy gain and loss rates balance, and temperature stays constant.

In engineering, maintaining constant temperature in devices requires controlling energy input and output, such as insulation to reduce energy loss or heating elements to supply energy.

Living organisms maintain body temperature by balancing metabolic heat production with heat loss to the environment.

• Cooling tea reaches thermal equilibrium with surroundings.
• Insulation reduces energy loss to maintain temperature.
• Biological systems regulate energy balance for temperature control.

A simple diagram to illustrate energy balance shows an object with arrows indicating energy flow in and out.

Draw a box labelled 'Object' in the centre. Draw an arrow pointing towards the box labelled 'Energy in' and an arrow pointing away labelled 'Energy out'.

At constant temperature, the lengths of these arrows are equal, representing equal rates of energy transfer.

• Box labelled 'Object' represents the system.
• Equal-length arrows in and out represent balanced energy transfer.
• Unequal arrows indicate temperature change.

Energy intake is the rate at which an object absorbs energy from its surroundings. This energy can be transferred by heating (conduction, convection, radiation), work done on the object, or chemical reactions within it.

Energy loss is the rate at which an object transfers energy to its surroundings, often by radiation, conduction, convection, or work done by the object on the environment.

Both energy intake and loss are measured in watts (W), where 1 W = 1 joule per second (J/s). The balance between these rates determines the object's energy state.

• Energy intake sources: heat transfer, mechanical work, chemical energy.
• Energy loss mechanisms: thermal radiation, conduction, convection, mechanical work done by the object.

If the rate of energy intake is greater than the rate of energy loss, the object gains net energy. This increases the internal energy, often raising the object's temperature.

If the rate of energy loss exceeds the rate of energy intake, the object loses net energy, causing a decrease in internal energy and a drop in temperature.

When the rates are equal, the object is in thermal equilibrium and its temperature remains constant.

• Net energy gain → temperature rises.
• Net energy loss → temperature falls.
• Equal rates → constant temperature (thermal equilibrium).

When an object absorbs enough energy to reach a substance’s melting or boiling point, the extra energy goes into changing the state rather than increasing temperature.

During melting, boiling, freezing, or condensation, energy transfer occurs without temperature change because energy is used to break or form intermolecular bonds.

If energy intake exceeds loss during a phase change, the object changes state (e.g., solid to liquid). If loss exceeds intake, the reverse change occurs (e.g., liquid to solid).

• Energy used in phase changes is called latent heat.
• Temperature remains constant during phase changes despite energy transfer.
• Energy imbalance drives phase transitions.

Consider a metal block heated by a flame. The block absorbs energy from the flame (energy intake) and loses energy to the surroundings by radiation and conduction (energy loss).

If the flame supplies energy faster than the block loses it, the block’s temperature rises.

If the flame is removed, energy loss continues and the block cools down until thermal equilibrium with the environment is reached.

• Energy intake rate depends on flame intensity and contact area.
• Energy loss rate depends on surface temperature, surface properties, and surroundings.
• Temperature change rate depends on net energy gain or loss.

The rate of change of an object’s internal energy (ΔE/Δt) equals the difference between energy intake rate (P_in) and energy loss rate (P_out):

\[ \frac{\Delta E}{\Delta t} = P_{in} - P_{out} \]

If the object’s temperature changes, the energy change relates to mass (m), specific heat capacity (c), and temperature change (ΔT): \[ \Delta E = mc\Delta T \] Combining these: \[ mc \frac{\Delta T}{\Delta t} = P_{in} - P_{out} \] Rearranged to find temperature change rate: \[ \frac{\Delta T}{\Delta t} = \frac{P_{in} - P_{out}}{mc} \] This formula allows calculation of how quickly the temperature changes given energy rates and object properties.

• P_in and P_out in watts (J/s).
• m in kilograms (kg).
• c in joules per kilogram per degree Celsius (J/kg°C).
• ΔT/Δt in °C/s.

The Earth's temperature depends on the balance between the energy it receives from the Sun and the energy it radiates back into space. The Sun emits short-wavelength radiation (mostly visible light and ultraviolet), which reaches Earth as incoming solar radiation. The Earth absorbs some of this energy, warming its surface, and then emits long-wavelength infrared radiation back into space.

For Earth's temperature to remain stable, the power absorbed from the Sun must equal the power radiated away. If more energy is absorbed than emitted, the Earth warms; if less, it cools.

• Incoming solar radiation is mostly shortwave (visible and UV).
• Outgoing radiation from Earth is longwave infrared.
• Energy balance determines Earth's average temperature.

Certain gases in Earth's atmosphere, called greenhouse gases (e.g., carbon dioxide, methane, water vapour), absorb some of the outgoing infrared radiation emitted by Earth's surface. These gases then re-radiate infrared radiation in all directions, including back towards the surface, effectively trapping heat in the atmosphere.

This process, known as the greenhouse effect, raises Earth's surface temperature above what it would be without an atmosphere. Without greenhouse gases, Earth's average temperature would be about -18°C instead of the current +15°C.

An increase in greenhouse gas concentration enhances this effect, reducing the amount of infrared radiation escaping to space and causing global warming.

• Greenhouse gases absorb and re-emit infrared radiation.
• They trap heat, warming Earth's surface.
• Increased greenhouse gases intensify the greenhouse effect.

The Sun's energy output is not constant; it varies slightly over time due to solar cycles and other factors. Changes in solar output alter the amount of incoming solar radiation reaching Earth.

An increase in solar output raises the incoming radiation, potentially warming Earth, while a decrease can cool it. These variations contribute to natural climate fluctuations but are generally small compared to human-induced changes.

• Solar output varies over time.
• Higher solar output increases incoming radiation.
• Solar variations influence Earth's climate naturally.

Albedo is the fraction of incoming solar radiation reflected by a surface. Earth's surface albedo varies depending on surface type: ice and snow have high albedo (reflecting most sunlight), while forests and oceans have low albedo (absorbing more sunlight).

Changes in surface albedo affect how much solar energy is absorbed. For example, melting ice reduces albedo, causing more absorption and further warming (a positive feedback).

Thus, surface properties influence the radiation balance and Earth's temperature.

• Albedo is the reflectivity of Earth's surface.
• High albedo surfaces reflect more solar radiation.
• Changes in albedo affect Earth's energy absorption.

Human activities, especially burning fossil fuels, increase atmospheric greenhouse gas concentrations, enhancing the greenhouse effect and reducing outgoing infrared radiation.

Deforestation and land-use changes can alter surface albedo, affecting how much solar radiation is absorbed.

These changes disrupt the natural radiation balance, leading to global warming and climate change, with significant environmental impacts.

• Fossil fuel burning increases greenhouse gases.
• Land-use changes affect surface albedo.
• Human actions disrupt Earth's radiation balance.

All objects emit infrared radiation as a form of thermal radiation, which depends on their temperature and surface properties. The efficiency with which a surface emits infrared radiation is called its emissivity, a dimensionless quantity ranging from 0 (no emission) to 1 (perfect emitter).

Surfaces that are dark and matte generally have high emissivity and are effective emitters of infrared radiation. Conversely, light-coloured or shiny surfaces tend to have low emissivity and are ineffective emitters.

Understanding emissivity is important because it affects how objects lose thermal energy by radiation, influencing temperature regulation and heat transfer in practical applications.

• Emissivity measures how effectively a surface emits infrared radiation.
• Dark, matte surfaces have high emissivity (effective emitters).
• Light, shiny surfaces have low emissivity (ineffective emitters).

To differentiate between effective and ineffective emitters, the experiment requires:

A steady heat source, such as a radiant lamp or a heated filament bulb, to provide infrared radiation.

Samples of different materials or surfaces, for example, black-painted paper, white paper, and shiny aluminium foil, cut to the same size and shape to ensure consistent surface area exposure to the heat source. Each sample should be mounted on a non-conductive holder to avoid heat conduction effects.

• Heat source (e.g., lamp) providing constant infrared radiation.
• Samples with different surface properties but identical size and shape.
• Thermal detectors such as thermocouples or infrared sensors to measure temperature changes.
• Non-conductive holders to isolate samples thermally.

1. Place the heat source at a fixed distance from the samples to ensure equal radiation intensity.

2. Position each sample individually at the same distance from the heat source.

3. Use a thermocouple or infrared thermometer to measure the temperature of each sample before exposure to the heat source (initial temperature). Record this value.

• Measure initial temperature of each sample.
• Expose sample to heat source for a fixed time interval (e.g., 5 minutes).
• Measure final temperature immediately after exposure.
• Repeat measurements to improve reliability and calculate average temperature change.
• Control variables: distance from heat source, exposure time, sample size, and ambient conditions.

Calculate the temperature change for each sample by subtracting the initial temperature from the final temperature. A greater temperature increase indicates that the sample absorbs more infrared radiation and, by reciprocity, is also a better emitter.

Effective emitters will show a larger temperature rise because they absorb and emit infrared radiation efficiently. Ineffective emitters will show a smaller temperature rise due to their lower emissivity.

This experiment demonstrates the principle that good absorbers of infrared radiation are also good emitters, consistent with Kirchhoff's law of thermal radiation.

• Temperature change (ΔT) = Final temperature − Initial temperature.
• Higher ΔT indicates higher emissivity and better emission.
• Compare ΔT values for black, white, and shiny surfaces to rank emission effectiveness.

To improve accuracy: repeat measurements multiple times and calculate averages to reduce random errors.

Ensure the heat source intensity remains constant during the experiment.

Use identical sample sizes and shapes to avoid differences in surface area affecting results.

• Repeat trials and average results to reduce uncertainty.
• Maintain constant distance and exposure time.
• Avoid direct contact with hot surfaces to prevent burns.
• Use heat-resistant holders and keep electrical equipment away from water.

Infrared radiation is a form of electromagnetic radiation with wavelengths longer than visible light, typically emitted by warm objects. When infrared radiation strikes a surface, it can be absorbed, reflected, or transmitted. The amount of infrared radiation absorbed depends on the material's surface properties such as colour and texture.

Effective absorbers of infrared radiation absorb a large proportion of the incident radiation, causing their temperature to rise significantly. Ineffective absorbers absorb less radiation and show smaller temperature increases under the same conditions. Understanding which materials are effective absorbers is important in thermal physics and practical applications like insulation and heating.

• Infrared radiation is emitted by all objects above absolute zero.
• Absorption of infrared radiation increases an object's internal energy and temperature.
• Surface colour and texture influence absorption effectiveness.

To distinguish between effective and ineffective absorbers, an experiment can be designed using the following apparatus:

Infrared radiation source (e.g., an infrared lamp or a heat lamp)

Thermometers or thermocouples to measure temperature changes accurately (digital thermometers preferred)  - Samples of different materials or surfaces (e.g., black-painted card, white-painted card, shiny aluminium foil, dull aluminium foil)  - Insulating stands to hold samples at a fixed distance from the radiation source  - Stopwatch or timer to measure exposure time  - Ruler or measuring tape to ensure consistent distance  - Data recording sheet or computer for logging temperatures

• Use a consistent and stable infrared source to ensure uniform radiation intensity.
• Place all samples at the same distance from the source to control intensity.
• Use identical sample sizes and shapes to minimise surface area differences.
• Measure initial temperature of each sample before exposure.

1. Arrange the samples so that each is exposed to the infrared radiation source at the same distance, ensuring equal intensity of radiation.

2. Record the initial temperature of each sample using a thermometer or thermocouple.

3. Switch on the infrared source and expose the samples for a fixed time interval (e.g., 5 minutes).  4. Record the final temperature of each sample immediately after exposure.  5. Calculate the temperature change (ΔT) for each sample by subtracting the initial temperature from the final temperature.  6. Repeat the experiment multiple times to improve reliability and calculate an average temperature change for each sample.

• Independent variable: type of material/surface (absorber).
• Dependent variable: temperature change of the sample.
• Control variables: distance from source, exposure time, sample size, initial temperature.

The temperature change (ΔT) indicates how much infrared radiation the sample absorbed. A larger ΔT means the sample absorbed more infrared radiation and is therefore a more effective absorber.

Plotting a bar chart with sample types on the x-axis and average temperature change (°C) on the y-axis can visually compare absorption effectiveness.

Effective absorbers, such as black and dull surfaces, typically show higher temperature increases because they absorb more infrared radiation. Ineffective absorbers, such as white or shiny surfaces, reflect more radiation and show smaller temperature increases.

• Calculate average ΔT from repeated trials to reduce random errors.
• Use consistent units (°C or K) for temperature change.
• Interpret results in terms of surface properties affecting absorption.

Infrared lamps and heat sources can become very hot and may cause burns if touched. Handle the lamp carefully and avoid direct skin contact.

Ensure the electrical equipment is set up safely, with no exposed wires or risk of electric shock.

Keep flammable materials away from the heat source to prevent fire hazards.

• Do not touch the infrared lamp during or immediately after use.
• Use heat-resistant gloves if adjusting the lamp.
• Switch off the lamp when not in use.
• Ensure the experiment is conducted in a well-ventilated area.

All objects emit thermal radiation due to the thermal motion of charged particles within them. The rate at which an object emits radiation depends strongly on its surface temperature, measured in kelvin (K).

The Stefan-Boltzmann law states that the power radiated per unit area (P/A) of a perfect black body is proportional to the fourth power of its absolute temperature (T):

P/A = σT⁴, where σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ (Stefan-Boltzmann constant). This means that if the temperature doubles, the power radiated per unit area increases by 2⁴ = 16 times.

• Power radiated per unit area increases rapidly with temperature.
• Temperature must be in kelvin for the Stefan-Boltzmann law.
• The Stefan-Boltzmann constant σ is a fundamental physical constant.

The total power radiated by an object depends on both the power radiated per unit area and the total surface area (A) of the object. The total power emitted is given by:

P = σAT⁴, where A is in square metres (m²). Larger surface areas allow more radiation to be emitted because there is more surface available to radiate energy.

For example, a hot object with a large surface area emits more radiation than a smaller object at the same temperature.

• Total radiation power is proportional to surface area.
• Doubling surface area doubles total radiation emitted.
• Surface area is measured in square metres (m²).

Thermal radiation arises from the vibrations and accelerations of charged particles inside matter. Higher temperatures mean particles vibrate more vigorously, increasing the energy and frequency of emitted radiation.

Since radiation is emitted from the surface, a larger surface area means more particles are exposed to emit radiation, increasing total emission.

Thus, both the microscopic particle motion (temperature) and macroscopic size (area) determine radiation emission rate.

• Higher temperature increases particle vibration and radiation energy.
• Larger surface area exposes more particles to emit radiation.
• Emission depends on microscopic and macroscopic properties.

Calculate the power radiated by a hot metal plate of surface area 0.5 m² at a temperature of 600 K, assuming it behaves as a perfect black body.

Use Stefan-Boltzmann law: P = σAT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.

Substitute values: P = 5.67 × 10⁻⁸ × 0.5 × (600)⁴ W. Calculate (600)⁴ = 600 × 600 × 600 × 600 = 1.296 × 10¹¹. Then: P = 5.67 × 10⁻⁸ × 0.5 × 1.296 × 10¹¹ = 5.67 × 0.5 × 1.296 × 10³ W = 3.674 × 10³ W = 3674 W (rounded). The plate emits approximately 3674 watts of radiation power.

• Use absolute temperature in kelvin.
• Calculate T⁴ carefully.
• Multiply by surface area and Stefan-Boltzmann constant.
• Check units: W m⁻² K⁻⁴ × m² × K⁴ = W.

Draw a graph with temperature (T) on the x-axis (in kelvin) and power radiated per unit area (P/A) on the y-axis (in W m⁻²).

The graph is a curve starting near zero at low temperatures and rising steeply as temperature increases, reflecting the T⁴ dependence.

The gradient is not constant; it increases with temperature, showing the non-linear relationship between temperature and radiation power.

• X-axis: Temperature (K).
• Y-axis: Power per unit area (W m⁻²).
• Curve shape: steep upward curve due to T⁴ dependence.
• No straight line; gradient increases with T.