text: Thermal desorption is described by the Polanyi–Wigner equation derived from the Arrhenius equation.
  where 
  : the desorption rate [mol/(cm s)] as a function of ,
  : order of desorption,
  : surface coverage,
  : pre-exponential factor [Hz] as a function of ,
  : activation energy of desorption [kJ/mol] as a function of ,
  : gas constant [J/(K mol)],
  : temperature [K].
  This equation is difficult in practice while several variables are a function of the coverage and influence each other. The “complete analysis method” calculates the pre-exponential factor and the activation energy at several coverages. This calculation can be simplified. First we assume the pre-exponential factor and the activation energy to be independent of the coverage.
  We also assume a linear heating rate:
  <br />
  (equation 1)
  where:
  : the heating rate in [K/s],
  : the start temperature in [K],
  : the time in [s].
  We assume that the pump rate of the system is indefinitely large, thus no gasses will absorb during the desorption. The change in pressure during desorption is described as:
  <br />
  (equation 2) 
  where:
  : the pressure in the system,
  : the time in [s].
  : the sample surface [m],
  : a constant,
  : volume of the system [m],
  : the desorption rate [mol/(cm s)],
  : the pump rate,
  : volume of the system [m],
  We assume that  is indefinitely large so molecules do not re-adsorp during desorption process and we assume that 
  where: 
  : the desorption rate[mol/(cm s)],
  : order of desorption,
  : surface coverage,
  : pre-exponential factor [Hz],
  : activation energy of desorption [kJ/mol],
  : gas constant,
  : temperature [K].
  Using the before mentioned Redhead method (a method less precise as the "complete analysis" or the "leading edge" method) and the temperature maximum  one can determine the activation energy:
  <br />
  (equation 5)
  <br />	
  for n=1 
  <br />
  (equation  6)
  <br />	
  for n=2
  M. Ehasi and K. Christmann described a simple method to determine the activation energy of the second order.
  Equation 6 can be changed into:
  <br />
  (equation  6a)
  where:
   is the surface area of a TDS or TPD peak.
  A graph of  versus  results in a straight line with a slope equal to .
  Thus in a first-order reaction the  is independent of the surface coverage. Changing the surface coverage one can determine . Usually a fixed value of the pre-exponential factor is used and is  known, with these values one can derive the  iteratively from .