Temperature, Ideal Gases and Related Topics

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Degree Physics Mind Map on Temperature, Ideal Gases and Related Topics, created by mickiebowen9359 on 08/04/2016.
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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
  1. Temperature
    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. 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
        1. An equation of state for a thermodynamic system is a mathematical relationship between state variables
          1. Isotherm - plot p vs V const T. Isobar - plot V ts T. const p. Isochors - plot p vs T. const V
          2. EQUATION OF STATE FOR AN IDEAL GAS
            1. p V = n R T
            2. VAN DER WAALS EQUATION OF STATE
              1. ( P + (a(n^2))/(v^2) )●(V-nb) = n R T
                1. nb = molecular volume . so the volume for molecules around it = V - nb.
                  1. Intermolecular attraction = (a(n^2))/(v^2)
                2. VIRIAL EQUATION OF STATE
                  1. (p V) / (n R T) = 1 + B_2(n/v) + B_3(n/v)^2 + B_4(n/v)^3 + ....
                    1. Valid for any isotropic substance if enough terms are used
                    2. EQUATION OF STATE FOR SIMPLE SOLIDS
                      1. V = V_0 [ 1 + β (T - T0) - K_t (P-P0) ]
                        1. β = ISOBARIC VOL EXPANSIVITY = ( + ΔV / V_0 ) / ΔT
                          1. K_t = ISOTHERMAL COMPRESSIBILITY = ( - ΔV / V_0 ) / ΔP
                      2. HEAT
                        1. Heat: a measure of the energy transferred between two systems as a result of a temperature difference
                          1. Heat Transfer Mechanisms = radiation, conduction, convection
                            1. STEFAN BOLTZMANN LAW FOR POWER RADIATED
                              1. P = Ɛ σ A (T^4)
                            2. HEAT TRANSFER RATE = Q dot = dQ/dT
                              1. Q dot = ( κ A / L ) ( T_1 - T_2 ) = - κ A (dT/dx)
                                1. THERMAL RESISTANCE = R_TH = L / κ A
                            3. SPECIFIC HEAT CAPACITY
                              1. Δ Q = c M Δ T
                                1. Specific Heat Cap = c Heat Capacity = C
                                  1. Specific Heat Capacity depends on Temperature so you use derivatives to define it.
                                    1. c_p (T) = (1/M) (δ Q / d T) _ p
                                      1. c_V (T) = (1/M) (δ Q / d T) _ V
                                  2. Kinetic Theory of Gases
                                    1. Assumptions
                                      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.
                                        1. Isotropic = same in all directions
                                          1. < (V_x) ^2 > = 1/3 < V^2>
                                        2. p V = 1/3 m N < V^2 > = 1/3 m N V^2 _rms
                                          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
                                            1. E_TR = MEAN TRANSLATIONAL KINETIC ENERGY / MOLECULE
                                              1. E_TR = 1/2 m <V ^2> = 3/2 k_b T
                                          2. INTERNAL ENERGY ASSUME: no intermolecular forces, no rotational or vibrational KE
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