Chapter 2 - Forms of Energy

Question 1

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

Answer 1

Storage of water in basins and compressed air systems.

Question 2

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

Answer 2

E_pot = mgh.

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

Question 3

Derive the energy storage of compressed gases.

Answer 3

See notes.

Question 4

What is the expression for rotational energy?

Answer 4

E_rot = 1/2 I w^2 (inertial momentum of sphere is 2/5 mr^2).

Question 5

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

Answer 5

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 6

What is the energy in a capacitor?

Answer 6

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

Question 7

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

Answer 7

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

Question 8

How can one describe the energy stored in a coil?

Answer 8

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 9

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

Answer 9

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

Question 10

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

Answer 10

About two orders of magnitude less.

Question 11

What is latent heat? Give an example of a technical realization of latent heat as energy storage.

Answer 11

The inner potential energy of condensed matter related to a phase change.

One example is phase change salt. Energy density of around 10^9 J / m^3 (comparable to Li-ion batteries). Used for buffering of solar thermal power plants.

Question 12

Describe schematically how chemical energy is stored.

Answer 12

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

Question 13

Give examples of the volumetric energy densities for chemical energy.

Answer 13

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 14

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

Answer 14

Heat in turbines.
Pressure in explosion engines.
Light in chemo-luminescence.
Electrical energy in batteries and fuel cells.

Question 15

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

Answer 15

Primary: non-rechargable.
Secondary: rechargable.
Tertiary: consume external masses.

Question 16

Explain the basics of a battery.

Answer 16

Defined by the voltage row, that is the “willingness” of an element to undergo reduction. In an electrolyte, the metal is dissolved into metal ions. The countercharge remains in electrode (electrons), which makes a voltage between electrode and electrolyte build up to prevent further dissolution. When connected to another electrode of a different reduction potential, there is a flow of electrons.

Question 17

What is the Nernst equation?

Answer 17

It gives the relationship between differences of ion concentration and the resulting voltage.

c = c_0 exp (-zeU/kT)
U = -kT/Ze ln c/c_0

Question 18

Which atom has the highest binding energy per nucleon?

Answer 18

Iron.

Question 19

What is the energy of 1 kg U in terms of kilogram coal equivalent?

Answer 19

Approx. 19 000 kgCE.

Question 20

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

Answer 20

2H + 3H -> 4He + n + 17.6 MeV

Question 21

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

Answer 21

n + 235U -> T_1 + T_2 + 2.43 n + 200MeV.

Question 22

What is exergy?

Answer 22

The part of energy which can be transformed into work.

Question 23

What is anergy?

Answer 23

The part of energy which can not be transformed into work.

Question 24

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

Answer 24

Both quantities are conserved.

Question 25

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

Answer 25

Exergy is tranformed into anergy.

Question 26

How is anergy related to the increase in entropy?

Answer 26

E_an = T_c ∆S = T_c * Q_c/T_c = Q_c

where T_c is the temperature of a the cold reservoir in a heat engine and Q_c is the heat transfered to the cold reservoir.

Question 27

How is the Carnot efficieny defined?

Answer 27

n_C = |W| / |Q_w| = |Q_w| - |Q_c| / |Q_w|