  The constant temperature derivation, which is a model-free derivation of the
Boltzmann factor, is generalized in order to develop a new simple model-free
derivation of a power-law Tsallis factor based on an environment with constant
heat capacity. It is shown that the integral constant T_0 appeared in the new
derivation is identified with the generalized temperature T_q in Tsallis
thermostatistics. A constant heat capacity environment is proposed as a
one-real-parameter extension of the Boltzmann reservoir, which is a model
constant temperature environment developed by J.J. Prentis et al. [Am. J. Phys.
67 (1999) 508] in order to naturally obtain the Boltzmann factor. It is also
shown that the Boltzmann entropy of such a constant heat capacity environment
is consistent with Clausius' entropy.
