Background

Energy is the capacity to do work. Potential, kinetic, molecular, bond, nuclear, magnetic, coloumbic.

Work is the integral of force times change in distance.

Surface Energy, it requires energy to make a surface.

Kinetic energy of a gas atom E = 3/2 kT. (T is in absolute units otherwise we would have negative kinetic energy.)

Ground state for energy.

We could consider T = 0 but this is inconvenient (impossible to achieve) and ignores atomic energy, E = mc², and chemical bond energy.

Often we define the ground state at STP.

In the end we are only interested in changes in energy for an event or process so the ground state is only important in so far as we use the same ground state for all components of a calculation.

For any spontaneous process the energy is reduced. In order for energy to increase we require work. So, E = PV for a gas, to increase the pressure at constant number of gas atoms requires force and a change in distance, compression, that leads to a reduciton in volume.

Internal Energy, U.

Thermal and repulsive/attractive enthalpy of molecular interaction. Ignores center of mass energy.

Enthalpy, H.

Energy related to specific bonding/reactions, PV work. So the sum of internal energy and PV.

Entropy, S.

If you mix two idea gasses at constant pressure there is no enthalpic interaction so the enthalpy of the system does not change. However, the system has changed since it requires a significant amount of work to separate the two ideal gasses and return to the pure states. This change is a change in entropy. The entropy change in this case is given by DS = nk_B(f_alnf_a +f_blnf_b) and the energy change DE = -TDS.

Philosophically How Thermodynamics Works.

We consider a subset of the universe called the system or the control volume. The system contains many molecular elements that are each subject to 3/2 k_BT kinetic energy. There are so many of these elementary units that they are almost uncountable. The most important step at the start of solving a problem in thermodynamics is to carefully define the system boundaries.

Closed System: Thermal transfer but no mass transfer, say an ice cube melts into a puddle and the ice cube is the system.

Open System: Mass and thermal transfer occurs, a system is a section of a river.

Isolated System: No heat or mass transfer. A perfectly insulated box in which a match is lit.

Equilibrium:

A system is at equilibrium when the energy is at a minimum. Two systems are at equilibrium with each other when every component of the two systems have the same chemical potential. The chemical potential is the change in energy when one element (molecule or mole) of that component is introduced to the system.

Heat Sink/Heat Reservoir:

A component with infinite capacity to absorb or generate heat (taransfer of thermal energy). The heat sink is at a constant tempearture. That is, it is isothermal.