Greenhouse Effect (HL IB Physics)

One possible model of climate change is that the Earth will eventually have no atmosphere. 

Obtain an expression for the average intensity of light at the surface of the Earth in terms of albedo and the solar constant. 

A team of engineers are designing solar panels to power a Mars Rover on the surface of Mars.

Derive an expression for the intensity of radiation at a distance, r emitted from a point source. 

A planned Mars Rover will be powered using several solar panels each with dimensions of 2700 × 4900 mm. The equipment is tested on Earth at a point where the albedo of Earth’s atmosphere is 0.390. The following additional information is available: 

• The radiant power of the Sun is 3.90 × 10²⁶ W
• The average radius of Earth’s orbit around the Sun is 1.50 × 10¹¹ m
• Orbital radius between Mars and the Sun = 2.3 × 10¹¹ m
• Absorbed solar radiation on Mars = 493 W m^–2

Determine the ratio .

Where P_M is the power of solar radiation incident on the solar panel on Mars and P_E is the power of solar radiation incident on the solar panel on Earth.

Assume that the Sun is at its highest point and the light from the Sun is normally incident on the panel.

An industrial kiln is used for ‘firing’ ceramic and pottery items at very high temperatures.

The kiln emits electromagnetic radiation of peak wavelength, λ_max = 3.75 × 10⁻⁶ m and has a surface area of 150 m².

Calculate the energy radiated per second.

Justify each of the following safety features in the kiln by referring to thermal energy transfer.

The diagram shows a simple climate model for the Earth. The incoming solar power is P W and most of the subsequent absorbed and reflected solar powers are indicated on the diagram. Some of the information is missing. 

Determine the average albedo of the Earth predicted by this model. 

The power of the Sun's radiation at the position of the Earth is 4.16 × 10¹⁸ W. The radius of the Earth is 6.0 × 10⁶ m and the temperature of the Earth's surface is 15°. 

Determine the emissivity of the surface of the Earth. 

The Earth's atmosphere reaches 1.0 × 10⁷ m above the Earth's surface and its emissivity is 0.81.

Calculate the temperature of the Earth's atmosphere in degrees celsius.

The intensity of radiation from a source radiating energy at a rate of P follows an inverse square law with the distance, r, from the source.

A planned Mars Rover will be powered using several solar panels each with dimensions of 2800 × 5900 mm. The equipment is tested on Earth at a point where the albedo of Earth’s atmosphere is 0.310.

The radiant power of the Sun is 3.90 × 10²⁶ W and the average radius of Earth’s orbit around the Sun is 1.50 × 10¹¹ m.

Determine the power, in kW, incident on a single solar heating panel being tested on Earth.

Assume that the Sun is at its highest point and the light from the Sun is normally incident on the panel.

An astronomer uses the following data for a simple climatic model of Mars without an atmosphere:

Orbital radius between Mars and the Sun = 2.3 × 10¹¹ m
Absorbed solar radiation = 493 W m^–2

Determine the average albedo for Mars that is to be used in the modelling.

Determine the ratio $\frac{P_M}{P_E}$

Where P_M is the power of solar radiation incident on the solar panel on Mars and P_E is the power of solar radiation incident on the solar panel on Earth.

Scientists are studying the planet Venus.

Define the solar constant of Venus.

Venus is in orbit 108 × 10⁹ m from the Sun. The Sun has a power output of 4 × 10²⁶ W. 

Calculate the solar constant of Venus to two significant figures. 

Explain why the solar constant is different for all planets in the solar system. 

Explain why the incident radiative power on the upper atmosphere of Venus is 675 W m⁻².

The graph shows the range of albedos for different materials on Earth. 

Identify the materials or values of the following albedos:

Determine the ratio . 

A scientist is investigating the climate model of a planet where the incoming radiation intensity is 250 W m⁻² and the radiated radiation intensity is 180 W m⁻². The temperature of the planet remains constant.

Calculate the reflected radiation intensity of the planet. 

Calculate the albedo of the planet in part (c). 

Compare and contrast the roles of carbon dioxide and water vapour in the greenhouse effect. 

The intensity of solar radiation incident at the top of the Earth’s atmosphere is 1450 W m⁻². Assume that 55% of the incoming solar energy reaches the Earth’s surface and 45% of the incident energy is absorbed by a person sunbathing. The person is 1.5 m tall and an average of 30 cm wide.

Determine the amount of solar energy absorbed by the person sunbathing for 150 minutes.

The person sunbathing wishes to absorb less solar energy from the sun. 

Explain in terms of albedo why getting in the sea will make him cooler. 

The man's body is now lying horizontal but fully submerged in the seawater. The scattered solar radiation from his body under the water is 9.3 W. 

Calculate the albedo of the seawater.