Dimensions of Constants

Transcript

Dimensions of Constants A constant can be dimensionless or can have dimensions. REFRACTIVE INDEX μ = c / v Both c and v are speeds. [μ] = [LT⁻¹] / [LT⁻¹] [μ] = [M⁰L⁰T⁰] Refractive index is dimensionless and has no unit. UNIVERSAL GRAVITATIONAL CONSTANT F = Gm₁m₂ / r² G = Fr² / (m₁m₂) [G] = [MLT⁻² × L² / M²] [G] = [M⁻¹L³T⁻²] G is dimensional. PLANCK’S CONSTANT E = hf h = E / f [h] = [ML²T⁻² / T⁻¹] [h] = [ML²T⁻¹] BOLTZMANN CONSTANT Using PV = kT for one particle: k = PV / T Pressure = Force / Area [Pressure] = [ML⁻¹T⁻²] [k] = [ML⁻¹T⁻² × L³ / Θ] [k] = [ML²T⁻²Θ⁻¹] COEFFICIENT OF VISCOSITY F = ηA(Δv / Δz) η = FΔz / (AΔv) [η] = [MLT⁻² × L / (L² × LT⁻¹)] [η] = [ML⁻¹T⁻¹] MOLAR HEAT CAPACITY Q = nCΔT C = Q / (nΔT) [C] = [ML²T⁻²N⁻¹Θ⁻¹] SI unit: J mol⁻¹ K⁻¹ DIMENSIONLESS QUANTITIES Plane angle and solid angle are dimensionless but have named SI units: radian and steradian. Some quantities, such as refractive index and relative density, have neither dimensions nor units.