Energy and Climate Change Problems
3. When a car is driving at 80 km/hr it is doing work against air
resistance at a rate of 40 kW
a.How far will the car travel in 1 hour?
b.How much work does the car do against air resistance in 1 hour?
c.If the engine of a modern diesel car is 75% efficient, how much
energy must the car get from the fuel?
d.If the energy density of diesel is 45.8 MJ/kg, how many kg of
diesel will the car use?
e.If the energy of diesel is 0.9kg/L, how many litres will the car
use?
f.Calculate the litres of fuel used per kilometer.
80 km, 1.44E8 J, 1.92E8 J, 4.2 kg, 4.7 litres, 0.06 ltr/km
4. A coal-fired power station gives out 1000 MW of power.
a.How many joules will be produced in one day?
b.If the efficiency is 40%, how much energy goes in?
c.The energy density of coal is 32.5 MJ/kg. How many kg are
used?
d.How many rail trucks containing 100 tonnes each delivered per
day?
86.4E13J, 2.16E14J, 6.65E10kg, 67 Truck loads
5. Write the nuclear equation for:
a.U-238  U-239
b.U-239  Np-239
c.Np-239  Pu-239
92-U-2381-N 92-U-239, 92-Np-23993-Np-239+B- +V, 93-U-239+94-Pu-239+
B- + V
6. Barium-142(56-BA-142) is a possible product of the fission of
U-236. It decays by B-decay to lanthanum (La) with a half-life of
11 months.
a.Write the equation for the decay of barium.
b.Estimate how long will it take for the activity of the barium in a
simple of radioactive waste to fall to 1/1000 of it’s original value.
56-Ba-142 57-La + B- + V, 9 years
7.Plutonium-239 splits into zirconium-96 and xenon-136. Use the
table to answer the following questions
Isotope
Mass(U)
Pu-239
239.052158
Zr-96
95.908275
Xe-136
135.907213
Neutron
1.008664
a. How many Neutrons will be emitted?
b. Write the nuclear equation for the reaction.
c. How much energy is released when the fission takes place?
d. What is the mass of 1 mole of plutonium
e. How many atoms are there in 1kg of plutonium
f. How much energy in eV is released if 1kg of plutonium undergoes fission?
g. Convert the answer of part F into joules.
7, 94-Pu-239 54-Xe-136 + 40-Zr-96 + 7n^0, 164 MeV, 239g, 2.5E24 atoms,4.13E26
MeV, 6.6E13 J
8. A sample of nuclear fuel contains 3% U-235. If the energy
density of U-235 is 9E13 J/kg, how much energy will 1kg of fuel
release?
2.7E12 J
9. An individual uses around 10,000kWh of energy in a year.
a. How many joules is this?
b. From your answer to Q8, calculate how much nuclear fuel this
amounts to.
3.6E10, 13g
10. A 4m^2 solar heating panel is positioned in a place where the
intensity of the sun is 1000W/m^2.
a. What is the power incident on the panel?
b. If it is 50% efficient, how much energy is absorbed per second?
c. If 1 litre (1kg) of water flows through the system in 1 minute,
by how much will its temperature increase? (Specific heat
capacity of water = 4200J/kg/C)
4000W, 2000J, 28.6C
11.A photovoltaic cell of 1cm^2 is placed in a position where the
intensity of the Sun is 1000W/m^2
a. If it is 15% efficient, what is the power absorbed?
b. If the potential difference across the cell is 0.5 V, how much
current is produced? (Power= IV)
c. If 10 of these cells were placed in series, what would the total
potential difference be?
d. If 10 of these cells were placed in parallel, what would the
current be?
e. How many of these cells would you need to produce 100W?
0.0015W, 0.03A, 5V, 0.3A, 6667
12. Draw a Sankey diagram for the photovoltaic cell.
13. The Hoover Dam is 221 m high with an area of 694 km2.
a.Estimate the mass of water in the dam.
b.How much PE is stored in this water?
c.The Hoover Dam can produce 1.5x109w of electricity. If the
power station is 80% efficient.
d.What mass of water must flow though the turbines each second to
produce this power?
1.5E14 kg, 1.6E17 J, 1.9E9 J, 1.7E6 Kg
14. A mountain hut has 4x 50w light bulbs, a 1kw electric heater
and a 2 kW cooker.
A.Calculate the total power consumed if all appliances are in use.
B. Outside the hut is a 5m high waterfall. the owner is interested in
building a small hydro generator. How many kg of water must flow
per second to generate enough power? (Assume 100% efficiency)
3.2 kW, 64kg
15. A turbine with a turbine blade length of 54m is operated in a
wind speed ms-1. The density of air is 1.2kgm -3.
a. How much power is in the wind passing through the turbine?
b. How much electrical power can be generated if the turbine is
20% efficient?
c. If the wind speed increased to ms-1, how much power would be
produced?
5.5MW, 1.1MW, 3.7MW
16.Waves of amplitude of 1m roll onto a beach at a rate of one
every 12s. If the wave length is 120m, calculate
A. The velocity of the waves
B. How much power there is per meter along the shore
C. The power along a 2 km length of beach.
10ms-1, 2E6w, 4E9w
17. Calculate the intensity of the Sun’s radiation on the surface of
A.Mercury
B.Jupiter
9552wm-2, 51.3wm-3
18. Calculate the amount of energy in one photon of light of wave
length 600nm. The sun is a hot dense gas so can be treated like a
black body.
3.3E10-19(2eV)
19. The temperature of surface of the Sun is 6000k. Use Wien’s
displacement law to calculate the most intense wavelength in the
spectrum of emitted radiation.
4.8E-7m
20. Use the Stefan-Boltzmann law to calculate the power per m2
emitted from the sun
7.35E7Wm-2
21. The Sun’s Radius is 7x108m. Use your answer to question 20 to
calculate the total energy radiated by the Sun per second.
4.52E26W
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