Sustainable Energy 1st Edition By Richard Dunlap - Test Bank
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Sustainable Energy Test Bank
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Sustainable Energy Test Bank
Chapter 3
Fossil Fuel Resources and Use
3.1 A person's primary energy needs are supplied exclusively by burning oil (with an energy content of 3.85 × 107 J/L). If a person's average power consumption is 12 kW, how long would it take that person to use one barrel of oil (158.97 liters)?
So...
1.1 One liter of water is cubic meter of water is poured off a 50 m high tower every
second. If the change in gravitational potential energy is converted into electricity with an
efficiency of 86%, how many 60 W light bulbs can be illuminated?
Solution Potential energy is
.
One liter of water has a mass of 1 kg, so for a height difference of 50 m, the corresponding
energy is
E = (1 kg) × (9.8 m/s2) × (50 m) = 490 J.
If this energy is converted into electricity with an efficiency of 85% then the electrical
energy available will be (590 J) × (0.85) = 421 J. If this amount of energy is produced
every second then the corresponding power is
P = (421 J)/(1 s) = 421 W.
This will illuminate
(421 W)/(60 W) = 7 light bulbs.
1.2 A beam of light is comprised of photons with energy 2.1 eV. What is the wavelength of
the light?
Solution A photon's energy is related to frequency by
For an energy of 2.1 eV, the corresponding wavelength is
1.3 A boiler produces steam at 520°C and this steam is used to run a heat engine to
produce mechanical energy. It is desired to use a river as the cold heat reservoir and to
have a Carnot efficiency of 45%. Is this feasible?
Solution Converting to degrees K gives
520°C + 273 = 793 K.
The Carnot efficiency is given by
η = 100 × (1 – Tc/Th)
solving for Tc gives
Tc = Th(1 – η/100)
In order to have a Carnot efficiency of 45% when Th = 793 K requires
Tc = (793 k) × (1 – 0.45) = 436 K = 163°C.
Well within the possibilities of using a river as the cold reservoir.
1.4 Octane produces energy according to the reaction
2C8H18 + 25O2 → 16CO2 + 18H2O + 44.4 MJ/kg.
If an automobile burns octane and requires 3.0 MJ of thermal energy from combustion to
travel 1 km. How many moles of octane need to be burned for a trip of 100 km?
Solution At 3.0 MJ/km, a trip of 100 km will require 300 MJ of thermal energy from
combustion. As 1 kg of octane produces 44.4 MJ of energy, then to produce 300 MJ will
require
The molecular mass of octane C8H18 is (8 × 12) + (18 × 1) = 114 g/mol or 0.114 kg/mol.
Thus 6.76 kg will consist of
(6.76 kg)/(0.114 kg/mol) = 59.3 mol
1.5 Ethanol (heat of combustion 28.9 MJ/kg) is burned to produce heat and that heat is
used to raise the temperature of water. How many kg of ethanol will be needed to raise the
temperature of 1 m3 of water from 20°C to its boiling point (but not to convert the liquid to
vapor)?
Solution The energy required to heat an object is given by
E = mcΔT
where m is the mass, c is the specific heat and ΔT is the change in temperature. 1 m 3 of
water will have a mass of 1000 kg and the specific heat of water is 4180 J/(kg°C). So
substituting in the above expression gives the energy required as
E = (1000 kg) × (4180 J/(kg°C) × (100ºC – 20 ºC) = 334 MJ.
For ethanol with a heat of combustion of 28.9 MJ/kg the required heat corresponds to an
ethanol mass of
(334 MJ)/(28.9 MJ/kg) = 11.6 kg.
1.6 A heat pump is used to heat a house. The outside temperature is –5°C and the inside
temperature is +21°C. What is the coefficient of performance of the heat pump?
Solution The temperatures must be converted to Kelvin as
–5°C + 273 = 268 K
+21°C + 273 = 294 K
The coefficient of performance may then be calculated to be
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