Kinetic Theory Large numbers of particles moving in continuous random motion. Evidence: Brownian motion, diffusion. Assumptions - large numbers - elastic collisions - no intermolecular forces - negligible collision time - negligible volume. Note: ideal gases have no Ep component to their internal energy but... so... p = 1/3Ï âŸ¨c2⟩ Root mean square speed, rms speed The speed term in the equation above is the average of the square speed which has a different value from the square of the average speed - do you see the difference? The root mean square speed is the square root of the mean square speed. The Gas Laws The three gas laws this ideal gas obeys perfectly are: pV = constant (at constant temperature) constant (at constant volume) constant (at constant pressure) Note: T stands for absolute temperature (in kelvin), not temperature in °C. Boltzmann constant and Ek The Boltzmann constant, k, is the universal molar gas constant for 1 atom or molecule. Use it to derive: 1/2m ⟨c2⟩ = 3/2 NkT This shows that the temperature of a gas sample depends only on the kinetic energy of the particles (atoms or molecules) that make it up. Equations c = Q/mΔT pV = nrt l = Q/m p V = N k T ΔU = ΔQ - ΔW W = pΔV p = 1/3 Ï âŸ¨c 2 ⟩ Symbols c = specific heat capacity, Jkg-1K-1 U = internal energy, J lv = specific latent heat of vaporisation (liquid to gas and back), Jkg-1 Q = thermal energy, J lf = specific latent heat of fusion (solid to liquid and back), Jkg-1 W = work done, J Q = thermal energy, J ΔV = change in volume, m3 m = mass, kg p = pressure, Pa ΔT = change in temperature, K or °C T = temperature, K t = temperature, °C R = universal molar gas constant T = thermodynamic temperature, K n = number of moles Xt = value of thermometric property at temperature 't' N = number of molecules Xo = value of thermometric property at the ice point, 0°C k = Boltzmann constant X100 = value of thermometric property at the steam point, 100°C Ï = density, kgm-3 ⟨c 2⟩ = mean square speed, ms-1