# Thermodynamics equations and relations

1. Jun 4, 2015

### Frozen Light

1. The problem statement, all variables and given/known data
I don't have a specific problem I'm trying to solve, I'm trying relate all the concepts for basic thermodynamics. I'm not entirely sure where I am misunderstanding
1. What is work
2. What is internal energy?
3. What is heat?
4. What is enthalpy?
5. What is entropy?

2. Relevant equations
U (internal energy) = N(particles) * f (degrees of freedom) * 1/2 * k(boltz) * T(K)
ΔU = Q(heat) + W(work)
W = P(pressure)ΔV(change in V)
W = ∫[vi→vf] p(v)dv
W = PAΔx
Cv = (ΔU/ΔT)V = Nfk/2 T
CP = CV + R
PV = NkT
or PV = nRT
ΔS = dQ/T

Pv diagrams
isothermal work = P1V1 ln (V1/V2)
isobaricwork = W = P(V2 - 1)
(k = 1.4)
adiabatic work = P2V2 - P1V1 / 1 - k
isochoric work = 0

3. The attempt at a solution

1. What is work?
Force parallel to the distance something is accelerated w= F * D = N*M = J
It is analogous to heat in that heat yields microscopic kinetic energy and work yields macroscopic kinetic energy.
It can also be thought of as pressure (force)/(area) times the change in volume N/M^2 * M^3 = NM = J

2. What is internal energy?
Internal energy is the work plus the heat of a gas. (ΔU = Q(heat) + W(work))
I don't understand this fully - a gas can have heat but work is not a quantity something contains like mass. To me the only way work can be related is by the change in work to the change in internal energy. More heat can be added for a state of less or more internal heat if work is done to or by the gas, resulting in a higher or lower temperature for the gas at some pressure.

U thermal energy is defined as the Nk(boltz constant * number of molecules) * degrees of freedom / 2 * (Temperature in kelvin)

U = NkFT/2

F changes as the temperature of a gas increases, at STP it is usually 3 degrees of freedom.

3. What is heat?
average kinetic energy of molecules in a substance - defined by Uinternal(equation directly above) can take forms of translational or rotational modes of energy - law of dulong petit says that for a solid it's just 3 translational modes.

4. What is enthalpy?
defined as heat added at constant pressure.
H = U + pv

this confuses the crap out of me.
U = Work +\- Q
so. H = work + Q -\+ work
so H is just Q?

5. What is entropy?
equation is ΔS = dQ/T
defined as "disorder", heat per unit temperature.

Toss a hot iron bar at of some mass into an infinitely big ocean.
Entropy increases because dQ1 = dQ 2 = dQ, but delta T is different.

dQ / Thigher < dQ/ T lower so there is a net positive entropy.

2. Jun 5, 2015

### Andrew Mason

Heat flow and mechanical work are essentially the same phenomena but at different scales.

Energy is the ability to apply a force over a displacement (i.e. the ability to do work) [as measured in a particular frame of reference]. Whenever there is a transfer or flow of kinetic energy, whether at the microscopic or macroscopic level, work is being done by some mass on some other mass. When heat flow occurs, work is being done at the molecular level by molecules on other molecules - ie. faster ones do work on slower ones, thereby increasing the kinetic energy of the initially slower ones and decreasing the kinetic energy of the initially faster ones. When an adiabatic expansion of a gas against an external pressure occurs or a quantity of gas is heated and expands against an external pressure, the system does useful mechanical work ie. work that can be used to change the motion of macroscopic objects.

Q and W are not quantities contained in a system. A system has only internal energy, U. It consists of the total molecular kinetic energy and total molecular potential energy.

The first law of thermodynamics that you are quoting deals with processes - changes in a system's state that occur in a transition from one equilibrium state to another. U is a state function but Q and W depend on the process. The first law essentially says that the change in internal energy of a system from state A to state B is equal to the heat flow into the system minus the work done by the system (or + the work done on the system) during the process of going from state A to state B.

AM