2. Forms of energy

Question 1

Potential energy equation?

Answer 1

E_pot = mgh

Question 2

Kinetic energy eq?

Answer 2

E_kin = (1/2)mv^2

Question 3

Rotational kinetical energy?

Answer 3

E_rot = (1/2)Iw^2

I: moment of inerta
w: rotational frequency (rpm)

Question 4

Give examples of two energy storage systems that uses mechanical potential energy?

Answer 4

Storage of water in basins and compressed air systems.

Question 5

Calculate the energy stored of 1 tonne of water brought up 100 meters. How much coal would be needed to achieve this?

Answer 5

E_pot = mgh.

Then convert from J to kWh to kgCE. (see notes)

Question 6

Derive the energy storage of compressed gases.

Answer 6

See notes

Question 7

What is the energy density of an infinite plane wave of electromagnetic radiation?

Answer 7

E/V = 1/2 eps eps_0 E(t)^2 + 1/2 µ µ_0 H(t)^2 = 1/2 ( ED + HB).
(see slides)

Question 8

What is the energy in a capacitor?

Answer 8

E = 1/2 CV^2, with C = eps eps_0 * A/d. (see slides)

Question 9

What can be done to increase the amount of energy stored in a capacitor?

Answer 9

We have to increase the capacitance. This can be done by increasing the area (through nanostructures, surface area), decreasing the electrode distance (through use of electrolytes which form a Helmholtz layer) or use an isolation medium with a large permittivity.

Question 10

How can one describe the energy stored in an inductor?

Answer 10

E = 1/2 L I^2 = 1/2 PHI I
Coil with n windings, length L and area A:

L = µµ_0 * n^2 A/l
PHI = n B A
E = 1/2 B^2 * lA/µµ_0 = 1/2 µ µ_0 H^2 V.

(see slides)

Question 11

How does the energy density in a supermagnetic storage medium compare to Li-ion batteries?

Answer 11

About one order of magnitude less. (for µ = 1 and B_max = 20T)

Question 12

How does the energy density of a commerical supercapacitor with C = 30 F compare to a Li-ion battery?

Answer 12

About two orders of magnitude less.

Question 13

Describe schematically how chemical energy is stored.

Answer 13

When molecules form, the interatomic potential energy is lowered, and thus the excess energy is released (exothermic reaction).

Question 14

Give examples of the volumetric energy densities for chemical energy.

Answer 14

For hydrogen stored at 700 bar this is about 5 * 10^9 J/m^3.

For gas this is an order of magnitude larger.

Question 15

Give examples of how chemical energy can be transformed to other forms of energy.

Answer 15

Heat in turbines.
Pressure in explosion engines.

Light in chemo-luminescence.
Electrical energy in batteries and fuel cells.

Question 16

What are primary, secondary and tertiary elements when talking about transformation of chemical energy into electrical energy?

Answer 16

Primary: non-rechargable.
Secondary: rechargable.

Tertiary: consume external masses.

Question 17

Explain the basics of a battery.

Answer 17

The basis for such systems is the voltage series of metals:

• Metal ions are dissolved in an electrolyte in contact with the surface of the metal
• Counter charge remains in the electrode
• A voltage, V, between the electrode and electrolyte is established and prevents further dissolution of ions from the electrode
• V is commonly given with respect to the standard hydrogen electrode (SHE), which is defined as a Pt wire surrounded by 1 atm H2

Question 18

What is the Nernst equation?

Answer 18

The Nernst equation relates the effective concentrations ( activities ) of the components of a cell reaction to the standard cell potential.

Question 19

Which atom has the highest binding energy per nucleon?

Answer 19

57_Fe

Question 20

Give an example of a fusion reaction and the associated energy released.

Answer 20

See note

Question 21

Give an example of a fission reaction and the associated energy released.

Answer 21

See note

Question 22

What is exergy?

Answer 22

Portion of energy that can be transformed to usable work

Question 23

What is anergy?

Answer 23

Portion of energy that cannot be transformed to usable work

Question 24

What happens to the anergy and exergy in a reversible process?

Answer 24

In an ideal reversible process, exergy and anergy are themselves conserved

Question 25

What happens to the anergy and exergy in an irreversible process?

Answer 25

During an irreversible process (e.g. friction, turbulence, gas mixing, heat conduction, diffusion) exergy is transformed into anergy

Question 26

How is anergy related to the increase in entropy?

Answer 26

Energy lost in irreversible processes is determined by the increase in entropy
See note

Question 27

How is the Carnot efficieny defined?

Answer 27

See note

Eff = T_H/(T_H-T_C)