University:
Eastern Kentucky University
Course:
PHY 202 | University Physics II
Academic year:

2021
Views:

357

Pages:

1
Author:

Prince Sampson

F or m u l ae 4 S h e e t f or Ph y si cs | pg. 7 Heat and Thermodynamics 4.4: Theromodynamic Processes First law of thermodynamics: ∆Q = ∆U + ∆W 4.1: Heat and Temperature Temp. scales: F = 32 + 59C, Work done by the gas: K = C + 273.16 Ideal gas equation: pV = nRT , n : number of moles   van der Waals equation: p + Va2 (V − b) = nRT Thermal expansion: L = L0 (1 + α∆T ), A = A0 (1 + β∆T ), V = V0 (1 + γ∆T ), γ = 2β = 3α F A Thermal stress of a material: =Y Wisothermal Z V2 pdV V 1  V2 = nRT ln V1 ∆W = p∆V, W = Wisobaric = p(V2 − V1 ) p 1 V1 − p 2 V2 Wadiabatic = γ−1 Wisochoric = 0 ∆l l 4.2: Kinetic Theory of Gases General: M = mNA , k = R/NA T1 Q1 Efficiency of the heat engine: n W Q2 T2 Maxwell distribution of speed: vp v̄ vrms RMS speed: vrms = q Average speed: v̄ = q 3kT m = 8kT πm = Most probable speed: vp = 2 Pressure: p = 31 ρvrms q 3RT M q q v work done by the engine Q1 − Q2 = heat supplied to it Q1 Q2 T2 ηcarnot = 1 − =1− Q1 T1 η= 8RT πM T1 Q1 Coeff. of performance of refrigerator: 2kT m W Q2 T2 COP = Equipartition of energy: K = 12 kT for each degree of freedom. Thus, K = f2 kT for molecule having f degrees of freedoms. Internal energy of n moles of an ideal gas is U = f nRT . 2 Q2 W Q2 Q1 −Q2 = Entropy: ∆S = ∆Q , T Sf − S i = Const. T : ∆S = Q , T Rf i ∆Q T Varying T : ∆S = ms ln Tf Ti Adiabatic process: ∆Q = 0, pV γ = constant 4.3: Specific Heat Specific heat: s = 4.5: Heat Transfer Q m∆T Conduction: Latent heat: L = Q/m ∆Q ∆t = −KA ∆T x x KA Thermal resistance: R = Specific heat at constant volume: Cv =  ∆Q  n∆T V  ∆Q  Specific heat at constant pressure: Cp = n∆T  Rseries = R1 + R2 = A1  x1 K1 + x2 K2  K1 K2 x1 x2 p Relation between Cp and Cv : Cp − Cv = R 1 Rparallel = 1 R1 + R12 = 1 x (K1 A1 + K2 A2 ) K2 A2 K1 A1 x Ratio of specific heats: γ = Cp /Cv Relation between U and Cv : ∆U = nCv ∆T Kirchhoff’s Law: emissive power absorptive power = Ebody abody Specific heat of gas mixture: Cv = n1 Cv1 + n2 Cv2 , n1 + n2 A = Eblackbody Eλ γ= n1 Cp1 + n2 Cp2 n1 Cv1 + n2 Cv2 Molar internal energy of an ideal gas: U = 2f RT , f = 3 for monatomic and f = 5 for diatomic gas. Wien’s displacement law: λm T = b λm Stefan-Boltzmann law: ∆Q ∆t Newton’s law of cooling: = σeAT 4 dT dt = −bA(T − T0 ) λ