Efficiency

Solar cells are being used in increasing numbers around the world.

The current I from a solar cell can be varied by connecting it to a variable resistor. The graph shows how I and the terminal potential difference V across a solar cell vary.

Complete the circuit diagram below to show how the data for the graph could be obtained.

Show that the maximum power output from the solar cell is about 2 W. You should use values from the graph.

The area of the solar cell is 104 cm².

Determine the efficiency of the solar cell when operating at maximum power.

intensity of sunlight = 1000 W m^–2

Calculate the internal resistance of the solar cell when operating at maximum power.

Electrical power is transmitted from Norway to Britain using a cable laid under the North Sea.

The following information is published on a website.

Deduce, by calculation, whether the claim for efficiency is correct.

In a boiler, energy is transferred to water at a rate of 40 kW. The corresponding power loss from the boiler to the surroundings is 4.0 kW.

Which of the following is the efficiency of this boiler?

It was suggested on an online forum that it would be possible to cook a chicken by repeatedly slapping the chicken with one hand.

It was claimed that the energy transferred to a chicken in 8000 slaps would be sufficient to raise the temperature of the chicken from 23 °C to 165 °C.

In an investigation to test the claim, the effective mass of the hand was taken as 1.75 kg and the speed of the hand just before impact with the chicken as 6.25 m s⁻¹.

Deduce whether the data confirms that 8000 slaps would be sufficient. Assume that no energy is transferred from the chicken to the surroundings.

mass of chicken = 0.875 kg specific heat capacity of chicken = 1770 J kg⁻¹K⁻¹ efficiency of energy transfer from the hand = 65%

Explain whether the assumption made in (a) is realistic.

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

Beam engines contributed to powering the Industrial Revolution in Britain in the 18th century. A beam engine consisted of a beam which could rock to and fro around a well-oiled pivot. Attached to the beam there are two rods, one connected to a piston in a steam cylinder and the other connected to a pump.

The diagram below shows a simplified arrangement of a beam engine.

The beam has a constant thickness and a mass of 3.05 10⁴ kg. The length of the beam is 11.0 m. The pivot P is positioned 6.0 m from the steam cylinder end of the beam.

In its resting position the steam cylinder rod is supported by the base of the steam cylinder with the beam at an angle of 20 to the horizontal.

The steam cylinder rod exerts a force T on the beam. The force exerted on the beam by the pump rod can be neglected.

Calculate the force T.

The engine, which ran continuously, could lift a mass of 2500 kg of water through 12 m each minute. The engine used 1250 kg of coal a day. 1 kg of coal can release 22.3 MJ of energy. The beam engine was said to have an efficiency of 10 %.

Deduce whether this claim for efficiency was correct.