# Advanced Notice Booklet Questions 1

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- Created by: OctaviaL
- Created on: 25-05-16 15:37

How many joules of energy correspond to 1Wh?

P = E/t = 1 Wh = 1 J/s x 3600 s = 3,600 J.

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A 1.5V battery has a capacity of 0.05Wh when fully charged. For how long could it deliver a current of 35 mA? What assumptions do you make?

t = E / P = E / VI = (0.05 x 3600) / (1.5 x 0.035) = 3430 s = 57.1 mins. Assumptions: no internal resistance; power output constant throughout discharge period; all energy can be used to exert power (step-function).

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The Sputnik satellite had a 1W radio transmitter powered by three silver-zinc batteries, with total mass 51kg. Assuming that the transmitter for the 22-day mission, calculate the energy per unit mass of the batteries in Wh/kg.

Energy / mass = 22 x 24 x 1 / 51 = 10.4 Wh/kg.

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How do photovoltaic cells transfer light into electrical energy?

Semiconductor is treated to form an electric field. When light strikes the cell, electrons knocked from atoms (photoelectric effect). If conductor attached to positive and negative sides, electric circuit formed so current flows.

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What is a module?

A numer of PV cells connected together to supply electricity at a certain voltage. Can be wired together to form an array.

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What is current directly dependent on in PV cells?

How much light strikes the module.

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Why are PV cells coated with an antireflection layer of thickness one-quarter of the wavelength passing through it?

Thickness chosed so that wave reflected from antireflective coating is out of phase with wave reflected from semiconductor surface. Extra path length: 1/4 + 1/4 = 1/2 so destructive superposition.

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The Sun's power output is about 4 x 10^26 W. Calculate the solar flux in W/m^2 at the Earth's distance from the Sun (150 million km).

Radiating in all direction so area of a sphere = 4(Pi)r^2. 4 x 10^26 / 4(Pi)(1.5 x 10^11)^2 = 1415 W/m^2

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On the Hubble telescope, assuming that the light to electrical conversion efficiency is 20%, what area of solar PV panels would be required to produce a power output of 5.6kW?

If output power is 5.6kW, input power = 5.6 kW x 5 = 28 kW. Solar flux = Watts / area so area = W / SF = 28, 000 / 1415 = 19.8 m^2.

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Assuming that solar PV panels are capable of generating 300W per kg of area, what is the mass of solar cells on the Hubble Space Telescope?

5600 / 300 = 18.7 kg.

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The mass of the Hubble Space Telescope is about 11,000kg. What faction of its mass is due to the solar PV panels? Is it significant?

18.7 / 11000 = 0.17%. Not significant.

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By equating gravitation force to centripetal force, show that a 97 minute orbital period for the Hubble Space Telescope corresponds to an orbital radius of 7000km. (Mass of Earth = 6 x 10^24 kg)

mrw^2 = (GMm / r^2). r^3 = GM / w^2. w = 2(Pi) / (97 x 60) = Pi / 2910 = (6.67 x 10^-11 x 6 x 10^24) / ( Pi / 2910)^2 = 3.4 x 10^20 so r = 7002521m.

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Confirm that the Hubble Space Telescope will be in the Earth's shadow for approximately 36 mins of each 97 min orbit. (Radius of Earth = 6360km)

cos a = 6360 / 7000. a = 0.431rads. (Pi / 2) - a = 1.14rads. 1.14 x 2 = 2.2797. 2Pi / 2.2797 = 97 / t. t = (97 x 2.2797) / 2Pi = 35mins

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Mars is 228 million km from the Sun. What is the solar flux at the surface of Mars in W/m^2 ?

SF = Sun's output / area (of sphere) = (4 x 10^26) / 4(Pi)(2.28 x 10^11)^2 = 612 W/m^2

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What area and mass of solar PV panels would be required for a colony on Mars with power demands of 500MW? Comment on the result.

500 x 5 = incident light = 2500MW. area = (2500 x 10^6) / 612 = 4.1 x 10^6 m^2. Mass = (500 x 10^6) / 300 = 1.67 x 10^6 kg. Very large mass to be transported from Earth. More sensible to use alternatives e.g RTGs or fission reactor.

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Why does the rate of heat production of an RTG decrease during its lifetime?

The amount of plutonium decreases so activity decreases as A= yN. (y = decay constant)

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Calculate the efficiency of the production of energy in one of Cassini's RTGs at launch.

Efficiency = output / input = 296 / 4394 = 6.7%

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Use the half life of Pu-238 to estimate the decrease in power output of an RTG during the 11-year lifetime of the Cassini project.

P = Poe^-yt. T1/2 = ln(2) / y so y = ln(2) / 87.7 = 7.9 x 10^-3. P = 296e^(-7.9 x 10^-3 x 11) = 271 W.

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The plutonium oxide fuel in an RTG is in ceramic form. What are the properties of ceramics?

Hard, stiff, strong, brittle, high melting points, chemically unreactive.

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Why do the properties of ceramics mean there is less chance of human casulaties if there is an accident during the launch of a spacecraft?

Fuel will remain in larger lumps that are too big to inhale. It will not corrode when it comes into contact with other materials e.g. water.

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Estimate the mass of plutonium-238 in each 10.9kg block of fuel. (1 eV = 1.6 x 10^-19 J, Avogadro constant Na = 6.02 x 10^23 / mol)

Energy released per decay at launch = 5.5 x 10^6 x 1.6 x 10^-19. Thermal output / decay = activity. y = ln(2) / T1/2 (secs). N = A/y. Moles = N / Avogadro. Mass = moles x 0.238 = 7.87kg.

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How do thermocouple junctions work?

Temperature difference between tail end and junction end means a voltage difference can be measured between the two thermoelements at reference end so thermcouple is a temperature-voltage inducer.

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What other than temperature affects emf induced in a thermocouple?

Seebeck coefficient of each thermoelement.

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Why can larger volatages be generated by RTGs in space than in terrestrial applications?

Temperature of the junction end is much lower in space than on earth. So a much larger temperature difference = much larger EMFs.

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Calculate the orbital speed of a satellite with an electrodynamic tether at the same orbital radius as the Hubble Space Telescope.

mv^2/r = GMm/r^2 so v = (GM/r)^0.5

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Calculate the area swept out each second by the tether attached to the satellite assuming that the tether is 20km long.

20 x 10^3 x speed

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Assuming that the Earth's magnetic field strength at this orbit is approximately 20 x 10^-6 Tesla, use Faraday's law to show that the voltage generated in the tether is approximately 3 kV.

Induced EMF = flux change / time taken = Blx / t = Blv

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Give reasons why the voltage will vary during one orbit of the satellite.

Earth's magnetic field not uniform over path of orbit; angle of earth's magnetic field's flux lines will vary with respect to plane swept out over course of an orbit; earth's magnetic field may vary with time due to interaction with solar wind etc.

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## Other cards in this set

### Card 2

#### Front

A 1.5V battery has a capacity of 0.05Wh when fully charged. For how long could it deliver a current of 35 mA? What assumptions do you make?

#### Back

t = E / P = E / VI = (0.05 x 3600) / (1.5 x 0.035) = 3430 s = 57.1 mins. Assumptions: no internal resistance; power output constant throughout discharge period; all energy can be used to exert power (step-function).

### Card 3

#### Front

The Sputnik satellite had a 1W radio transmitter powered by three silver-zinc batteries, with total mass 51kg. Assuming that the transmitter for the 22-day mission, calculate the energy per unit mass of the batteries in Wh/kg.

#### Back

### Card 4

#### Front

How do photovoltaic cells transfer light into electrical energy?

#### Back

### Card 5

#### Front

What is a module?

#### Back

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