  Quantum chromodynamics (QCD) with pure imaginary baryon number chemical
potential mu =i theta T, where T is temperature and theta is a real number, has
the Roberge-Weiss periodicity. We study the theta-dependence of the baryon
number density and the pressure in the hadron resonance gas model with excluded
volume effects of baryons. It is shown that the baryon number density and the
pressure are smooth periodic functions of theta at low or high temperature.
However, they have singular behavior at theta =(2k+1)pi where k is an integer,
when T sim 211MeV. This temperature is consistent with the Roberge-Weiss
transition temperature TRW obtained by lattice QCD simulations. This
singularity can be explained by the dual excluded volume effects in which the
roles of point-like and non point-like particles are exchanged each other in
the ordinary excluded volume effects. It is also indicated that the excluded
volume effect is visible just below TRW and is directly detectable by the
lattice QCD simulation at finite theta. We compare the results with the one
obtained by the Polyakov-loop extended Nambu-Jona-Lasinio model.
