1. Energy: Facts and Figures

Question 1

Give a definition of energy.

Answer 1

Energy is the quantity of a state of a physical system which describes the capability of the system to perform work.

Question 2

How is work defined mathematically?

Answer 2

W = ∫ F dr, from r_1 to r_2.

F: force

Question 3

What is the SI unit of Joule?

Answer 3

J = Nm = kgm^2/s^2

Question 4

What is the SI unit of Watt?

Answer 4

W = J/s = kgm^2/s^3

Question 5

Name some usual units of energy.

Answer 5

Joule (J),
electronvolt (eV),

kilowatt hour (kWh),
calories (cal),
terawatt year (TWa),
kilogram coal equivalent (kgCE),
kilogram oil equivalent (kgOE),
British thermal unit (BTU)

Question 6

What is the order of magnitude of a terawatt year in terms of kilowatt hours?

Answer 6

1 TWa ≈ 10^13 kWh.

Question 7

What is the value of a kilowatt hour in terms of Joule?

Answer 7

1 kWh = 3.6 * 10^6 J.

Question 8

What is the value of a kilowatt hour in terms of kgCE? CE: coal equivalent

Answer 8

1 kWh = 0.123 kgCE

Question 9

What is the value of an electronvolt in terms of Joule?

Answer 9

1 eV = 1.602 * 10^-19 J

Question 10

How much coal must be burned to provide 1 TWa of energy?

Answer 10

Approximately 10^12 kg.

Question 11

What is the total energy consumption (in 2012)?

Answer 11

2*10^13 kgCE / year.

Question 12

What is the basic metabolic rate of a human being?

Answer 12

80W.

Question 13

What is the definition of a conservative force?

Answer 13

That no work is performed along a closed curve, trajectory (work performed between two points is path independent).

Question 14

What can be defined for conservative forces, and how is it defined?

Answer 14

A potential energy. It is defined as the negative gradient of the force (- grad F), and the difference in potential energy it two points equals the work being done.

∆E_pot = E_pot(r_2) - E_pot(r_1) = W_12
E_pot = - grad F

Question 15

Derive the expression for the difference in kinetic energy.

Answer 15

The kinetic energy is the work performed to accelerate a mass m.

∆E_kin = ∫ F dr from r_1 to r_2.
= ∫ ma dr = ∫ m * dv/dt * dr = ∫ m * dv * dr/dt = ∫ m * dv * v
= [1/2 mv^2] evaluated from r_1 to r_2
= 1/2 mv_2^2 - 1/2 mv_1^2.

Question 16

What can be said about the total energy in conservative systems?

Answer 16

E = E_kin + E_pot = const

Question 17

Give examples of dissipative processes.

Answer 17

• friction
• turbulance
• diffusion

Question 18

What is the atmospheric CO2 concentration in 2019 in ppm? (with three significant digits)

Answer 18

420 ppm

Question 19

Choose the correct CO2 emission (in gCO2/KWh) for the following energy sources. And, what can we learn from these values?

Answer 19

Coal -  300
Petrol - 240
Natural gas - 190
Solar PV - Utility scale - 48
Hydropower - 24
Wind - 11