Flashcards in Chapter 1 - Energy: Facts & Figures Deck (23):
Give a definition of energy.
Energy is the quantity of a state of a physical system which describes the capability of the system to perform work.
How is work defined mathematically?
W = ∫ F dr, from r_1 to r_2.
What is the SI unit of Joule?
J = Nm = kgm^2/s^2
What is the SI unit of Watt?
W = J/s = kgm^2/s^3
Name some usual units of energy.
kilowatt hour (kWh),
terawatt year (TWa),
kilogram coal equivalent (kgCE),
kilogram oil equivalent (kgOE),
British thermal unit (BTU)
What is the order of magnitude of a terawatt year in terms of kilowatt hours?
1 TWa ≈ 10^13 kWh.
What is the value of a kilowatt hour in terms of Joule?
1 kWh = 3.6 * 10^6 J.
What is the value of a kilowatt hour in terms of kgCE?
1 kWh = 0.123 kgCE
What is the value of an electronvolt in terms of Joule?
1 eV = 1.602 * 10^-19 J
How much coal must be burned to provide 1 TWa of energy?
Approximately 10^12 kg.
What is the total energy consumption (in 2012)?
2*10^13 kgCE / year.
What is the basic metabolic rate of a human being?
What is the definition of a conservative force?
That no work is performed along a closed curve (work performed between two points is path independent).
What can be defined for conservative forces, and how is it defined?
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
Derive the expression for the difference in kinetic energy.
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.
What can be said about the total energy in conservative systems?
It is non-dissipative, and the sum of potential and kinetic energy must be constant.
E_tot = E_pot + E_kin.
Give examples of dissipative processes.
What happens to classical mechanical energy in dissipative systems? Draw an example of such a process.
Part of it is transformed to undirected inner energy.
Example: a block is dropped to the floor. It starts of with potential energy E_pot = mgh. It gains kinetic energy E_kin = 1/2 mv^2, where E_kin equals the initial potential energy as it hits the ground. At this point each particle will have kinetic energy the same way, which is downward. As it hits the ground the block comes to a rest, but the particles retain the energy in form of random vibrations in the solid.
What does the Noether theorem say about energy conservation?
For any symmetry operation that exists, there exists a corresponding conserved quantity.
Which conserved quantity arises from translation symmetry?
Which conserved quantity arises from rotational symmetry?
Which conserved quantity arises from translation symmetry in a periodic lattice?
Crystal momentum, wavevector