Temperature: The
temperature of a substance
is a measure of the mean
translational kinetic energy
associated with the
disordered microscopic
motion of its constituent
atoms or molecules.
A thermodynamic temperature
scale is one that does not
depend on properties of
substances that are used to
measure temperature. e.g.
kelvin
Equations of State
An equation of state for a
thermodynamic system is a
mathematical relationship
between state variables
Isotherm - plot p vs V const T.
Isobar - plot V ts T. const p.
Isochors - plot p vs T. const V
EQUATION OF STATE FOR AN IDEAL GAS
p V = n R T
VAN DER WAALS EQUATION OF STATE
( P + (a(n^2))/(v^2) )●(V-nb) = n R T
nb = molecular
volume . so the
volume for
molecules
around it = V -
nb.
Heat: a measure of the energy
transferred between two
systems as a result of a
temperature difference
Heat Transfer Mechanisms =
radiation, conduction,
convection
STEFAN BOLTZMANN LAW FOR
POWER RADIATED
P = Ɛ σ A (T^4)
HEAT TRANSFER RATE = Q dot = dQ/dT
Q dot = ( κ A / L ) ( T_1 - T_2 )
= - κ A (dT/dx)
THERMAL RESISTANCE = R_TH = L / κ A
SPECIFIC HEAT CAPACITY
Δ Q = c M Δ T
Specific Heat Cap = c
Heat Capacity = C
Specific Heat Capacity
depends on Temperature
so you use derivatives to
define it.
c_p (T) = (1/M) (δ Q / d T) _ p
c_V (T) = (1/M) (δ Q / d T) _ V
Kinetic Theory of Gases
Assumptions
Molecular radius small compared with avg distance between
molecules. Constant rapid motion. Obey Newtons Laws. No force
acting between - all collisions perfectly elastic. Container walls are
perfectly rigid and infinitely massive. Gas in equilibrium.
Isotropic = same in all directions
< (V_x) ^2 > = 1/3 < V^2>
p V = 1/3 m N < V^2 > = 1/3 m N V^2 _rms
Comapring this to pressure eqn ( p V = N k_b T ) gives k_b T = 1/3 m < V ^2 > = 2/3 E_TR
E_TR = MEAN TRANSLATIONAL KINETIC ENERGY / MOLECULE
E_TR = 1/2 m <V ^2> = 3/2 k_b T
INTERNAL ENERGY ASSUME: no
intermolecular forces, no rotational
or vibrational KE