Dimensional Analysis Quiz 5

See if you can determine the dimensions of "\(k\)" in each of the following (where \(x\) is a distance, \(R\) is a radius, \(h\) is Planck's constant with SI units of joules x second, \(f\) is frequency and \(T\) is absolute temperature):

  1. \(sin (kx)\)
  2. \(10^{kx}\)
  3. \(cot (kx^2/R)\)
  4. \(e^{hf/kT}-1\)
  1. dimensions of \(k = L^{-1}\)
  2. dimensions of \(k = L^{-1}\)
  3. dimensions of \(k = L^{-1}\)
  4. dimensions of \(k = M\cdot L^2\cdot T^{-2}\cdot \theta^{-1}\)
NOTE:  In 4, \(k\) is the Boltzmann constant, which has a value of \(1.3 \times 10^{-23} J/K\).