Stefan's law & Wien's displacement law

All objects with a temperature above absolute zero emit a spectrum of electromagnetic radiation.

State what is meant by absolute zero.

The graph shows how the intensity of radiation emitted by the Earth varied with wavelength in 2020.

Explain the differences between this graph and a graph representing the emission of radiation by the Earth in 2050. Assume that the average global temperature increases over time.

At the end of the 19th century, Wien investigated the radiation emitted by hot objects and formulated a law.

The table shows data for some stars.

Deduce whether Wien’s law is confirmed by this data.

The Hertzsprung–Russell diagram below shows part of the main sequence of stars. The star Sirius A is marked on the diagram.

On a website it states that the radius of Sirius A is twice the radius of the Sun. Deduce whether this statement is correct. radius of the Sun = 6.96×10⁸m surface temperature of the Sun = 5800 K

Fuse wire is made of a metal that has a low melting point. The wire melts when the current exceeds a maximum value.

A student investigated how the cross‑sectional area affected the current at which a wire melted. She used wires of the same length and metal, but different diameters.

The student steadily increased the current through each wire and recorded the maximum current through the wire before it melted.

Describe how the student could determine an accurate value for the cross‑sectional area of a wire.

Explain why a current in a wire causes the resistance of the wire to change.

The length of a wire does not affect the value of current at which the wire melts.

Explain why. Assume the wire behaves as a black body.

Aldebaran is a red giant star.

For a black body radiator of Aldebaran’s surface temperature, the wavelength λ_max at which the intensity is maximum is 7.43 × 10^–7m.

Determine the luminosity of Aldebaran.

radius of Aldebaran = 3.14 × 10¹⁰m

Scientists can analyse light from stars that has passed through a diffraction grating.

*(a) Explain the pattern produced when a mixture of blue and red light, from the same source, passes through a diffraction grating.

Light interacts with atoms as it passes through the atmosphere of the star.

Explain how this leads to the formation of the dark lines within the spectrum.

The surface temperature of the star is 5800 K.

On the axes below, sketch a graph of the intensity of radiation against the wavelength of that radiation for this star.

This star is a main sequence star.

Explain why main sequence stars do not collapse due to gravitational forces.

Which of the following is a valid unit for luminosity?

One of the largest stars in our galaxy is VY Canis Majoris. This star’s radius is 1420 times the radius of the Sun. The luminosity of this star is 270 000 times the luminosity of the Sun.

A student states that the surface temperature of VY Canis Majoris must be much greater than the surface temperature of the Sun.

Determine whether the student’s statement is correct.

surface temperature of Sun = 5780 K

Calculate the wavelength with maximum intensity in the black body radiation spectrum of VY Canis Majoris.

Add the position of VY Canis Majoris to the Hertzsprung Russell diagram to determine which type of star it is.

The photograph shows a filament bulb.

The filament is an emitter with 35% of the power output of a black body radiator of the same temperature.

When a potential difference (p.d) of 2.0 V is applied across the bulb, there is a current of 0.37 A in the filament.

Calculate the temperature of the filament.

surface area of filament = 3.9 × 10⁻⁶m²

In an experiment to investigate the efficiency of a filament light bulb a p.d. was applied. The p.d. and current were measured and the light bulb was observed. The p.d. was then increased and new measurements taken.

When a small p.d. is applied to the bulb, no light is visible. If the p.d. is gradually increased, the filament starts to glow and eventually appears white.

Use your graph to explain why filament light bulbs are considered inefficient.

The photograph shows a filament bulb.

The filament is an emitter with 35% of the power output of a black body radiator of the same temperature.

When a potential difference (p.d) of 2.0 V is applied across the bulb, there is a current of 0.37 A in the filament.

Calculate the temperature of the filament.

surface area of filament = 3.9 × 10⁻⁶m²

In an experiment to investigate the efficiency of a filament light bulb a p.d. was applied. The p.d. and current were measured and the light bulb was observed. The p.d. was then increased and new measurements taken.

When a small p.d. is applied to the bulb, no light is visible. If the p.d. is gradually increased, the filament starts to glow and eventually appears white.

Use your graph to explain why filament light bulbs are considered inefficient.

Solar panels consisting of combinations of photovoltaic cells use energy in the radiation received from the Sun to generate electricity.

An advertisement for solar panels claims that the intensity of radiation from the Sun incident at the top of the Earth’s atmosphere is more than 2 kW m⁻².

Assess the validity of this claim.

radius of Sun = 6.96 × 10⁸m

surface temperature of Sun = 5790 K

distance from Sun to Earth = 1.50 × 10¹¹m

The average intensity of radiation from the Sun incident at the Earth’s surface over a 24-hour period has been determined to be 164 W m⁻².

The average intensity of radiation from the Sun at the Earth’s surface is much less than the intensity incident at the top of the Earth’s atmosphere.

Explain why.

It is claimed that the area of solar panels needed to generate 100 GW of power is about 0.5% of the surface area of the Earth.

Assess the validity of this claim.

radius of Earth = 6.4 × 10⁶m

typical efficiency of solar panels = 25%

Scientists are developing a space station equipped with large solar panels. The space station would be located in a geostationary orbit. The space station would transfer energy to Earth as microwaves.

A space station in a geostationary orbit is above the equator and has a period of 24 hours.

Explain one advantage of locating the space station in a geostationary orbit.

Calculate the height h of the space station above the equator when it is in a geostationary orbit.

mass of Earth = 6.00 × 10²⁴kg

24 hours = 8.64 10⁴s

Solar panels consisting of combinations of photovoltaic cells use energy in the radiation received from the Sun to generate electricity.

An advertisement for solar panels claims that the intensity of radiation from the Sun incident at the top of the Earth’s atmosphere is more than 2 kW m⁻².

Assess the validity of this claim.

radius of Sun = 6.96 × 10⁸m

surface temperature of Sun = 5790 K

distance from Sun to Earth = 1.50 × 10¹¹m

The average intensity of radiation from the Sun incident at the Earth’s surface over a 24-hour period has been determined to be 164 W m⁻².

The average intensity of radiation from the Sun at the Earth’s surface is much less than the intensity incident at the top of the Earth’s atmosphere.

Explain why.

It is claimed that the area of solar panels needed to generate 100 GW of power is about 0.5% of the surface area of the Earth.

Assess the validity of this claim.

radius of Earth = 6.4 × 10⁶m

typical efficiency of solar panels = 25%

Scientists are developing a space station equipped with large solar panels. The space station would be located in a geostationary orbit. The space station would transfer energy to Earth as microwaves.

A space station in a geostationary orbit is above the equator and has a period of 24 hours.

Explain one advantage of locating the space station in a geostationary orbit.

Calculate the height h of the space station above the equator when it is in a geostationary orbit.

mass of Earth = 6.00 × 10²⁴kg

24 hours = 8.64 10⁴s

An oximeter is a device used in hospitals to monitor the oxygen level in a patient’s blood.

In an oximeter, two light-emitting diodes (LEDs) are mounted opposite light sensors in a clip and attached to the patient’s finger. One of the LEDs produces red light and the other produces infrared.

The intensity I of electromagnetic radiation received by the detector, after passing through a thickness x of blood, is given by

where I₀ is the intensity that would have been received if the blood were not present and is the attenuation coefficient of blood.

The red LED emits visible light of wavelength 650 nm and the infrared LED emits infrared of wavelength 950 nm.

The graph shows how varies with wavelength for oxygenated blood and deoxygenated blood.

I₀ for the infrared LED is 1.8 W m^–2.

Calculate I for the infrared after passing through 1.4 mm of oxygenated blood.

The oximeter determines I / I₀ the fraction of radiation transmitted at each wavelength.

Deduce whether I / I₀ will be smaller for the red or the infrared radiation if the blood is deoxygenated.

It is suggested that ambient light could affect the readings produced by the oximeter.

Halogen lamps have a filament temperature of 3200 K.

Deduce whether the light from such a lamp would have a significant effect on the oximeter readings.

A black body radiator of temperature T and surface area A has a luminosity L.

Which of the following is the luminosity of a black body radiator with surface area A/2 and temperature 2 T ?