# Temperature, Ideal Gases and Related Topics

Mind Map by mickiebowen9359, updated more than 1 year ago
 Created by mickiebowen9359 almost 4 years ago
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### Description

Degree Physics Mind Map on Temperature, Ideal Gases and Related Topics, created by mickiebowen9359 on 04/08/2016.

## Resource summary

Temperature, Ideal Gases and Related Topics
1 Temperature
1.1 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.
1.2 A thermodynamic temperature scale is one that does not depend on properties of substances that are used to measure temperature. e.g. kelvin
2 Equations of State
2.1 An equation of state for a thermodynamic system is a mathematical relationship between state variables
2.1.1 Isotherm - plot p vs V const T. Isobar - plot V ts T. const p. Isochors - plot p vs T. const V
2.2 EQUATION OF STATE FOR AN IDEAL GAS
2.2.1 p V = n R T
2.3 VAN DER WAALS EQUATION OF STATE
2.3.1 ( P + (a(n^2))/(v^2) )●(V-nb) = n R T
2.3.1.1 nb = molecular volume . so the volume for molecules around it = V - nb.
2.3.1.2 Intermolecular attraction = (a(n^2))/(v^2)
2.4 VIRIAL EQUATION OF STATE
2.4.1 (p V) / (n R T) = 1 + B_2(n/v) + B_3(n/v)^2 + B_4(n/v)^3 + ....
2.4.2 Valid for any isotropic substance if enough terms are used
2.5 EQUATION OF STATE FOR SIMPLE SOLIDS
2.5.1 V = V_0 [ 1 + β (T - T0) - K_t (P-P0) ]
2.5.1.1 β = ISOBARIC VOL EXPANSIVITY = ( + ΔV / V_0 ) / ΔT
2.5.1.2 K_t = ISOTHERMAL COMPRESSIBILITY = ( - ΔV / V_0 ) / ΔP
3 HEAT
3.1 Heat: a measure of the energy transferred between two systems as a result of a temperature difference
3.1.1 Heat Transfer Mechanisms = radiation, conduction, convection
3.1.1.1 STEFAN BOLTZMANN LAW FOR POWER RADIATED
3.1.1.1.1 P = Ɛ σ A (T^4)
3.1.2 HEAT TRANSFER RATE = Q dot = dQ/dT
3.1.2.1 Q dot = ( κ A / L ) ( T_1 - T_2 ) = - κ A (dT/dx)
3.1.2.1.1 THERMAL RESISTANCE = R_TH = L / κ A
3.2 SPECIFIC HEAT CAPACITY
3.2.1 Δ Q = c M Δ T
3.2.2 Specific Heat Cap = c Heat Capacity = C
3.2.3 Specific Heat Capacity depends on Temperature so you use derivatives to define it.
3.2.3.1 c_p (T) = (1/M) (δ Q / d T) _ p
3.2.3.2 c_V (T) = (1/M) (δ Q / d T) _ V
4 Kinetic Theory of Gases
4.1 Assumptions
4.1.1 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.
4.1.2 Isotropic = same in all directions
4.1.2.1 < (V_x) ^2 > = 1/3 < V^2>
4.2 p V = 1/3 m N < V^2 > = 1/3 m N V^2 _rms
4.2.1 Comapring this to pressure eqn ( p V = N k_b T ) gives k_b T = 1/3 m < V ^2 > = 2/3 E_TR
4.2.1.1 E_TR = MEAN TRANSLATIONAL KINETIC ENERGY / MOLECULE
4.2.1.1.1 E_TR = 1/2 m <V ^2> = 3/2 k_b T
4.3 INTERNAL ENERGY ASSUME: no intermolecular forces, no rotational or vibrational KE

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