Sustainable Energy 1st Edition By Richard Dunlap - Test Bank

Chapter 1

Energy Basics

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

Frequency is related to the wavelength by

so that

Solving for wavelength gives

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

= 100 × (1 – T_c/T_h)

solving for T_c gives

T_c = T_h(1 – /100)

In order to have a Carnot efficiency of 45% when T_h = 793 K requires

T_c = (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

(300 MJ)/(44.4 MJ/kg) = 6.76 kg of octane.

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 = mcT

where m is the mass, c is the specific heat and T is the change in temperature. 1 m³ 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

COP = 1/(1 – T_c/T_h)) = [1 – (268 K)/(294 K)]^–1 = 11.3

1.7 A steam engine uses steam at a temperature of 375°C and runs at a Carnot efficiency of 41%. What is the temperature of the cold reservoir?

Solution Converting the steam temperature to K gives

375°C + 273 = 648 K

The Carnot efficiency is defined as

= 100 × (1 – T_c/T_h)

Solving for T_c gives

T_c = T_h (1 – /100)

So substituting gives

T_c = (648 K) × (1 – 41/100) = 382 K or 382 K – 273 K = 109°C