PHY001 Final Exam Formula Sheet Speed of light in vacuum c = 3.0108 m/s Universal gas constant R = 8.314 J/mol. K Boltzmann’s constant kB = 1.3810−23 J/K Stefan-Boltzmann constant   = 5.67010−8Wm−2K4 Avogadro number NA = 6.0221023 particles/mole Density of water ρ = 103 kg/m3 Specific heat of water cw = 1.0 cal/g°C = 4186 J/kg°C Specific heat of steam c = 2010 J/kg°C Specific heat of ice c = 2090 J/kg°C Atmospheric pressure Po = 1.013×10 5 Pa Acceleration due to gravity g = 9.8 m/s2 Latent heat of fusion Lf = 3.33105 J/kg Latent heat of vaporisation Lv = 2.26106 J/kg Elementary charge e = 1.60  10-19 C Mass of electron me = 9.11  10-31 kg Mass of proton mp = 1.67  10-27 kg Permittivity constant o = 8.85  10-12 F m-1 Permeability constant µo = 4×10-7 H m-1 Coulomb’s constant ke = 8.987 ×109 N m2/C2 Mathematical formulae that may be useful: Quadratic equation ax2 + bx + c = 0, the solution: = − ±√2−4 2 Area of a circle = r2 Area of a sphere = 4r2 Volume of a sphere = 4/3r3 Mechanics Kinematic equations 2 2 2 0 0 0 1 2 = + 2 = tv v at v v as s v at= + + x = ½ (vi + vf) t Newton’s Second Law maF = Frictional Force F N= Momentum p mv= Elastic collision: v1i – v2i = – (v1f – v2f) Centripetal acceleration 2v a r = Work and energy W = F s cos  K = ½ mv2 U = mgh Oscillation F = − k x U = ½ k x2 = √ Rotational motion f = i + t f 2 = i2 + 2   = i + i t + ½ t2 s = r θ v = r  a = r  =  IL =  I= 2mrI = 221 IE = Moment of inertia Isolid cylinder = Idisk = ½ MR 2 I hollow sphere = 2 3 MR2 Icylindrical shell = Ihoop = MR 2 I solid sphere = 2 5 MR2 Irod = 1 12 ML2 Parallel axis theorem I = Icm + M d 2 Fluids Pressure /P F A= Fluid statics P = Po + gh B = fluid g Vdisp Fluid dynamics A1 v1 = A2 v2 p1 + ½ v12 + gy1 = p2 + ½ v22 + gy2 Thermodynamics Ideal gas law B pV nRT Nk T= = Adiabatic process 11 = 22 , 11 −1 = 22 −1 , = ⁄ Work dW PdV= − Isothermal process f ln i V W nRT V =       Monatomic Eint = 3 2 n R T Kave = 3 2 kB T Molar specific heats = 3 2 and = 5 2 for a monatomic gas. = 5 2 and = 7 2 for a diatomic gas. RMS speed = √ 3 Heat transferred Q = mcT and Q = mL Thermal conductivity dT dx kA=P Radiation P =   A T4 Length expansion ∆ = Δ Volume expansion ∆ = Δ Efficiency of an engine 1 C H H QW Q Q  = = − Coefficient of performance cooling heatingCOP COPor C H Q Q W W = = Entropy rev S dQ T  =  Carnot efficiency 1 C C H T T  = − Electricity & Magnetism Resistance R = V / I, R = L/A = L/(A) Capacitance C = Q / V, d A C 0  = or d A C 0  = Coulomb’s Law 2 0 21 2 21 4 r qq r qqk F ee  == Electric field 2 0 2 4 r q r qk E e  == Electric potential = Electric potential energy = 12 U = q V Capacitor energy CQVCVQU 22 2 1 )( 2 1 2 1 === Electrical power P = IV = I2R = (V)2/R Electric current AnqvI d= , dnqvJ = , EJ = , em nq    21 == Magnetic force Cyclotron frequency m qB r v == Magnetic flux Faraday’s Law dt d N B  −=





































































































































































































































































































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