5073769
Description
Mind Map by mickiebowen9359, updated more than 1 year ago
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Created by mickiebowen9359
over 8 years ago
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Temperature, Ideal
Gases and Related
Topics
- Temperature
- 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
- 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.
- 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
- 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
- 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.
- Intermolecular
attraction =
(a(n^2))/(v^2)
- nb = molecular
volume . so the
volume for
molecules
around it = V -
nb.
- ( P + (a(n^2))/(v^2) )●(V-nb) = n R T
- VIRIAL EQUATION OF STATE
- (p V) / (n R T) = 1 + B_2(n/v) + B_3(n/v)^2 + B_4(n/v)^3 + ....
- Valid for any isotropic
substance if enough
terms are used
- (p V) / (n R T) = 1 + B_2(n/v) + B_3(n/v)^2 + B_4(n/v)^3 + ....
- EQUATION OF STATE FOR SIMPLE SOLIDS
- V = V_0 [ 1 + β (T - T0) - K_t (P-P0) ]
- β = ISOBARIC VOL EXPANSIVITY
= ( + ΔV / V_0 ) / ΔT
- K_t = ISOTHERMAL
COMPRESSIBILITY =
( - ΔV / V_0 ) / ΔP
- β = ISOBARIC VOL EXPANSIVITY
= ( + ΔV / V_0 ) / ΔT
- V = V_0 [ 1 + β (T - T0) - K_t (P-P0) ]
- An equation of state for a
thermodynamic system is a
mathematical relationship
between state variables
- HEAT
- 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)
- P = Ɛ σ A (T^4)
- STEFAN BOLTZMANN LAW FOR
POWER RADIATED
- 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
- THERMAL RESISTANCE = R_TH = L / κ A
- Q dot = ( κ A / L ) ( T_1 - T_2 )
= - κ A (dT/dx)
- Heat Transfer Mechanisms =
radiation, conduction,
convection
- 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
- c_p (T) = (1/M) (δ Q / d T) _ p
- Δ Q = c M Δ T
- Heat: a measure of the energy
transferred between two
systems as a result of a
temperature difference
- 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>
- < (V_x) ^2 > = 1/3 < V^2>
- 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.
- 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
- E_TR = 1/2 m <V ^2> = 3/2 k_b T
- E_TR = MEAN TRANSLATIONAL KINETIC ENERGY / MOLECULE
- Comapring this to pressure eqn ( p V = N k_b T ) gives k_b T = 1/3 m < V ^2 > = 2/3 E_TR
- INTERNAL ENERGY ASSUME: no
intermolecular forces, no rotational
or vibrational KE
- Assumptions
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